🧮Calculators

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Electrode Potential (Nernst)

Calculate the electrode potential by the Nernst equation at 25 °C, E = E° − (0.0592 ÷ n) × log₁₀(Q), from the standard potential E° (V), the number of electrons exchanged n and the reaction quotient Q (ratio of product to reactant activities). The result, in volts, is the actual electrode potential under non-standard conditions — essential to predict the spontaneity of redox reactions, a metal's tendency to corrode in a given medium and the operation of cells, batteries and electrochemical sensors. Enter the standard potential, the number of electrons and the reaction quotient.

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Cathodic Protection Current

Calculate the current needed for cathodic protection, I = current density × area ÷ 1000, multiplying the required protection current density (mA/m²) by the metal surface area to protect (m²). The result, in amperes, sizes cathodic protection systems — impressed current or sacrificial anodes — that protect pipelines, buried tanks, ship hulls and offshore structures by polarizing the metal to a corrosion-immune potential. The required density depends on the medium and the coating. Enter the protection current density and the area to protect.

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Sacrificial Anode Life

Calculate the life of a sacrificial anode, life = (mass × capacity) ÷ (current × 8760), from the anode mass (kg), the material's current capacity (A·h/kg), the protection current drained (A) and the 8760 hours in a year. The result, in years, shows how long the anode (zinc, aluminium or magnesium) will provide protection before being consumed and needing replacement — essential in designing galvanic cathodic protection of tanks, pipelines and marine structures. Enter the mass, the material capacity and the current.

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Corrosion Inhibitor Efficiency

Calculate the efficiency of a corrosion inhibitor, η = (CR₀ − CR_inh) ÷ CR₀ × 100%, comparing the corrosion rate without inhibitor (CR₀) with the rate in its presence (CR_inh). The result, in %, measures how much the inhibitor slowed corrosion — the standard indicator to evaluate and compare inhibitors in laboratory tests (mass loss, polarization or impedance). Effective inhibitors form protective films on the surface and reach efficiencies above 90%. It is widely used in boiler water treatment, cooling systems and well acidizing. Enter the corrosion rates without and with inhibitor.

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Free Space Path Loss (FSPL)

Calculate the free space path loss (FSPL), L = 20·log₁₀(d) + 20·log₁₀(f) + 32.44, from the distance d (km) and the frequency f (MHz). The result, in dB, is the attenuation a radio signal suffers simply by spreading through space, with no obstacles — proportional to the square of distance and frequency. It is the central term of any link budget: the greater the distance or frequency, the higher the loss and thus the more power or antenna gain needed. The 32.44 constant applies for km and MHz. Enter the distance and the frequency.

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Fresnel Zone Radius

Calculate the first Fresnel zone radius, r = 17.31·√(d₁·d₂ ÷ (f·(d₁+d₂))), from the distances of each end to the point d₁ and d₂ (km) and the frequency f (GHz). The result, in metres, defines the ellipsoid around the line of sight that must stay clear of obstacles for a radio link to work without diffraction loss. Rule of thumb: at least 60% of the first Fresnel zone should be unobstructed. It is essential in designing point-to-point, microwave and long-range Wi-Fi links. Enter the distances and the frequency.

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VSWR (Standing Wave Ratio)

Calculate the voltage standing wave ratio (VSWR), VSWR = (1 + |Γ|) ÷ (1 − |Γ|), from the magnitude of the reflection coefficient |Γ|. The result (dimensionless, expressed as X:1) measures how well an antenna or load is matched to the transmission line: VSWR = 1:1 is a perfect match (all power delivered); higher values mean part of the wave is reflected back, forming standing waves that reduce efficiency and may damage the transmitter. Typically VSWR up to 1.5:1 or 2:1 is acceptable. Enter the magnitude of the reflection coefficient.

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EIRP (Effective Radiated Power)

Calculate the equivalent isotropically radiated power (EIRP), EIRP = P_tx + G − L, adding the transmitter power P_tx (dBm) to the antenna gain G (dBi) and subtracting cable and connector losses L (dB). The result, in dBm, is the power a theoretical isotropic antenna would need to radiate to produce the same power density in the direction of the real antenna's maximum gain. It is the quantity regulated by telecom authorities (legal EIRP limits) and the transmit-side starting point of a link budget. Enter the transmitter power, the antenna gain and the losses.

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Channel Capacity (Shannon)

Calculate the maximum channel capacity by the Shannon-Hartley law, C = B·log₂(1 + SNR), from the bandwidth B (Hz) and the signal-to-noise ratio SNR (linear value, not in dB). The result, in bits per second, is the absolute theoretical limit of error-free data rate a noisy channel can support — no modulation or coding can beat it. It shows the two paths to more speed: widen the bandwidth or improve the signal-to-noise ratio. It is a pillar of information theory and digital communication system design. Enter the bandwidth and the linear SNR.

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Reflection Coefficient

Calculate the reflection coefficient, Γ = (Z_L − Z₀) ÷ (Z_L + Z₀), from the load impedance Z_L and the line's characteristic impedance Z₀ (ohms). The result (dimensionless, between −1 and 1) gives the fraction of the incident wave reflected by the impedance discontinuity: Γ = 0 means a perfect match (no reflection); Γ = ±1 is total reflection (open or short circuit). It is the basis of impedance matching in transmission lines and relates directly to VSWR and return loss. Enter the load impedance and the characteristic impedance.

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Parabolic Antenna Gain

Calculate the gain of a parabolic antenna, G = 10·log₁₀(η·(π·D ÷ λ)²), from the aperture efficiency η (typically 0.5–0.7), the reflector diameter D (m) and the wavelength λ (from λ = 0.3/f, with f in GHz). The result, in dBi, shows the gain grows with the square of diameter and frequency: larger dishes and higher frequencies concentrate energy into narrower, more directive beams. It is the fundamental calculation in designing microwave, radar and satellite communication antennas. Enter the efficiency, the diameter and the frequency.

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Half-Wave Dipole Length

Calculate the physical length of a half-wave dipole, L = (150 ÷ f)·VF, from the frequency f (MHz) and the velocity factor VF (typically ~0.95 for wires, correcting the end effect). The result, in metres, is the total length of the dipole antenna resonant at the desired frequency — each arm is half this value. The half-wave dipole is the most used reference antenna, with 2.15 dBi gain. The velocity factor makes the antenna slightly shorter than a half wavelength in vacuum. Enter the frequency and the velocity factor.

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Fade Margin

Calculate the fade margin, M = P_rx − S, subtracting the receiver sensitivity S (dBm) from the received power P_rx (dBm). The result, in dB, is the slack between the arriving signal and the minimum the receiver can demodulate — the reserve available to absorb temporary fades caused by rain, multipath, vegetation and atmospheric variations. Reliable links typically require margins of 10 to 30 dB, depending on the desired availability and environment. It is the final check of a radio link budget. Enter the received power and the receiver sensitivity.

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Antenna Beamwidth

Estimate the half-power (−3 dB) beamwidth of a parabolic antenna, θ = 70·λ ÷ D, from the wavelength λ (from λ = 0.3/f, with f in GHz) and the reflector diameter D (m). The result, in degrees, is the angle within which the antenna concentrates most of its energy: larger dishes and higher frequencies produce narrower beams and thus more directive, higher-gain antennas, but with more critical pointing. The ~70 factor applies to typical parabolic reflectors. Enter the reflector diameter and the frequency.

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Specific Fire Load

Calculate the specific fire load of a space, q = (mass × LHV) ÷ area, dividing the total energy of the combustible materials (mass × lower heating value) by the floor area. The result, in MJ/m², is the heat that would be released per unit area if all the material burned — the parameter that classifies a building's fire risk and sets protection requirements (fire resistance, exits, sprinklers) in fire codes. The higher the fire load, the more severe the potential fire. Enter the fuel mass, the heating value and the area.

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Sprinkler Flow (K-Factor)

Calculate the flow of an automatic sprinkler, Q = K × √P, from the head's K-factor and the pressure at the sprinkler P. The result, in L/min, is the water discharged by the sprinkler at a given pressure — the basis of the hydraulic design of sprinkler systems, which must ensure enough flow and application density over the most unfavourable operating area. The K-factor characterizes the orifice (the larger it is, the more flow at the same pressure). Mind the units of K and P, which must be consistent. Enter the K-factor and the pressure.

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Fire Water Reserve (RTI)

Calculate the fire water reserve volume, V = flow × time ÷ 1000, multiplying the system's required flow (L/min) by the required autonomy time (min) and converting to cubic metres. The result, in m³, is the water volume the tank must keep reserved exclusively for firefighting — sized to feed hydrants and/or sprinklers for the minimum time set by codes (typically 30 to 60 min, depending on risk). It is a central calculation in building firefighting installation design. Enter the flow and the autonomy time.

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Heat Release Rate (HRR)

Calculate the heat release rate of a fire (HRR), Q̇ = ṁ × ΔH_c, multiplying the fuel burning rate (kg/s) by the effective heat of combustion (MJ/kg). The result, in MW, is the fire's power — the single most important quantity in fire science, governing gas temperatures, flame height, smoke production and spread rate. It is the fundamental input to fire safety engineering models and to the design of smoke control and detection systems. Enter the burning rate and the heat of combustion.

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Evacuation Time

Estimate the evacuation time of a space, t = N ÷ (F × width), dividing the number of occupants N by the product of the specific people flow F (people per minute per metre) and the total exit width (m). The result, in minutes, is the movement time for everyone to pass through the exits — part of the total egress time used in escape route design and fire safety verification. Adequate exit widths and flows ensure evacuation occurs before conditions become untenable. Enter the number of occupants, the specific flow and the exit width.

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Emergency Exit Width

Calculate the required width of an emergency exit, W = (population ÷ unit capacity) × 0.55, dividing the population to be discharged by the capacity of people per exit unit and multiplying by one unit's width (0.55 m). The result, in metres, sizes doors, corridors, stairs and ramps of escape routes by the exit-unit criterion of fire safety codes. The capacity per unit varies with the type of exit (door, stair, ramp) and the occupancy. Enter the population and the capacity per exit unit.

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Required Fire Flow

Calculate the water flow required for a firefighting system, Q = area × application rate, multiplying the operating area (m²) by the required application density (L/min per m²). The result, in L/min, is the minimum flow the sprinkler or spray system must deliver over the most unfavourable area to control the fire. The application rate depends on the occupancy's hazard class — the higher the fire load and combustibility, the higher the density required by codes (NBR/NFPA). It is the basis of hydraulic design and water reserve. Enter the area and the application rate.

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Flame Height (Heskestad)

Estimate the mean height of a diffusion flame by the Heskestad correlation, L = 0.235·Q̇^(2/5) − 1.02·D, from the heat release rate Q̇ (kW) and the fire base diameter D (m). The result, in metres, is the visible flame height above the base — essential to assess the risk of fire spread by radiation, the thermal reach over structures and the activation of detectors and sprinklers. Height grows with the fire power to the 2/5 power and decreases with the base diameter. It is one of the classic fire dynamics correlations. Enter the heat release rate and the base diameter.

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Number of Sprinklers

Calculate the number of automatic sprinklers needed, N = area ÷ coverage area per head, dividing the total area to protect (m²) by the maximum coverage area of each sprinkler (m²). The result is the minimum number of heads to cover the space, spaced within code limits (coverage per head depends on hazard class and sprinkler type). In practice, always round up and adjust to the piping and beam layout. It is an initial quantity calculation in sprinkler system design. Enter the area to protect and the coverage area per head.

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Smoke Plume Mass Flow

Calculate the mass flow of a fire's smoke plume by the Heskestad correlation, ṁ = 0.071·Q̇_c^(1/3)·z^(5/3), from the convective part of the heat release rate Q̇_c (kW) and the height above the fire base z (m). The result, in kg/s, is the amount of hot gases and smoke rising and accumulating, governing the design of smoke control and exhaust systems (mechanical or natural) that keep a smoke-free layer for safe evacuation. The flow grows strongly with height. Enter the convective heat fraction and the height.

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Noise Dose

Calculate the occupational noise dose, D = (C ÷ T) × 100%, dividing the effective exposure time C by the maximum allowed time T for the measured noise level and multiplying by 100. The result, in %, shows how much of the maximum daily exposure the worker accumulated: 100% is the tolerance limit (85 dB(A) for 8 hours, with a 5 dB exchange rate in Brazil). Doses above 100% require controls and indicate risk of noise-induced hearing loss. For several levels, the C/T terms are summed. Enter the exposure time and the maximum allowed time.

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Normalized Exposure Level (NEN)

Calculate the 8-hour normalized exposure level (NEN), NEN = NE + 10·log₁₀(t ÷ 480), from the measured exposure level NE (dB(A)) and the actual exposure time t (minutes). The result, in dB(A), converts an exposure of any duration into the equivalent level that would produce the same dose over a standard 8-hour (480 min) shift, allowing direct comparison with the tolerance limit and action level. It is the quantity used by occupational hygiene standards to assess continuous or intermittent noise. Enter the measured level and the exposure time.

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WBGT (Occupational Heat Index)

Calculate the WBGT (wet bulb globe temperature) for indoor environments without solar load, WBGT = 0.7·t_nw + 0.3·t_g, from the natural wet-bulb temperature t_nw and the globe temperature t_g (°C). The result, in °C, is the heat stress index used to assess heat exposure: compared with tolerance limits according to the activity's metabolic rate, it sets the allowed work-rest regime. For environments with solar load, the dry-bulb temperature is also included. Enter the natural wet-bulb and globe temperatures.

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Hearing Protector Attenuation

Calculate the effective noise level at the ear with a hearing protector by the NIOSH method, L_eff = SPL − (NRR − 7) ÷ 2, from the ambient sound pressure level SPL (dB(A)) and the protector's NRR (Noise Reduction Rating). The result, in dB(A), estimates real protection by applying the 7 dB derating (dBC→dBA correction) and a 50% safety factor on the nominal attenuation, which is usually far lower in real use than in the lab. It lets you check whether the chosen protector brings exposure below the tolerance limit. Enter the ambient noise level and the protector's NRR.

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Dilution Ventilation Flow

Calculate the airflow needed to dilute a contaminant, Q = (G × K) ÷ C, from the contaminant generation rate G, a safety/mixing factor K and the allowable limit concentration C. The result, in the consistent flow unit, is the volume of clean air that must be supplied/exhausted to keep the contaminant concentration below the tolerance limit in the breathing zone. General dilution ventilation suits low-toxicity, diffusely generated contaminants; the K factor corrects for imperfect air mixing. Enter the generation rate, the safety factor and the limit concentration.

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Maximum Noise Exposure Time

Calculate the maximum daily allowed noise exposure time, T = 8 ÷ 2^((SPL − 85) ÷ 5), from the sound pressure level SPL (dB(A)). The result, in hours, is the maximum exposure duration before reaching a 100% dose under the Brazilian NR-15 (85 dB(A) limit for 8 h, with a 5 dB dose-doubling rate). Every 5 dB above 85 halves the allowed time: 90 dB(A) allows 4 h, 95 dB(A) only 2 h. It is the basis for dose calculation and the planning of rotation and breaks. Enter the sound pressure level.

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Mixture Exposure Index

Calculate the combined exposure index to a mixture of chemical agents by the additivity rule, I = (C₁ ÷ TLV₁) + (C₂ ÷ TLV₂), summing the ratio of measured concentration to tolerance limit (TLV) for each substance. The dimensionless result assesses the joint effect of contaminants acting on the same target organ: if the sum exceeds 1, the combined exposure surpasses the limit, even if no single substance is above its own. It is the ACGIH and NR-15 criterion for mixtures with additive effects. Enter the concentrations and tolerance limits of two substances.

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Hand-Arm Vibration A(8)

Calculate the normalized hand-arm vibration exposure A(8), A(8) = a_w·√(t ÷ 8), from the resultant acceleration a_w (m/s²) and the exposure time t (hours). The result, in m/s², normalizes the exposure to an 8-hour shift, allowing comparison with the action and tolerance levels. Prolonged exposure to tool vibration (grinders, breakers, chainsaws) causes hand-arm vibration syndrome, with vascular and neurological damage. Enter the resultant acceleration and the exposure time.

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Vibration Dose Value (VDV)

Calculate the vibration dose value (VDV) for whole-body vibration exposure, VDV = a_w·t^(1/4), from the acceleration a_w and the exposure time t. The result, in m/s^1.75, is a cumulative metric that, by using the fourth power, is more sensitive to peaks and shocks than the RMS average (important in jolting vehicles and machines). It is used by ISO 2631 to assess the spinal risk of forklift, tractor and bus operators. The higher the VDV, the greater the injury risk. Enter the acceleration and the exposure time.

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Capture Flow (Local Exhaust)

Calculate the capture flow of an unflanged local exhaust hood, Q = V·(10·X² + A), from the capture velocity V (m/s), the source-to-hood distance X (m) and the hood face area A (m²). The result, in m³/s, is the flow needed for contaminated air to be drawn into the hood with enough velocity to overcome air currents and the contaminant's inertia. The Della Valle/ACGIH equation shows the flow grows with the square of distance — hoods should be as close to the source as possible. It is the basis of local exhaust ventilation design. Enter the capture velocity, the distance and the hood area.

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Sommerfeld Number

Calculate the Sommerfeld number of a journal bearing, S = (r ÷ c)²·(μ·N ÷ P), from the radius-to-clearance ratio (r/c), the lubricant dynamic viscosity μ, the rotational speed N (rev/s) and the specific pressure P (load over projected area). The dimensionless result is the characteristic parameter defining a hydrodynamic bearing's behaviour: it sets the minimum oil film thickness, shaft position, friction and lubricant flow. Low values mean a heavily loaded bearing (contact risk); high values, excessive clearance. It is the basis of bearing design via Raimondi-Boyd charts. Enter the r/c ratio, the viscosity, the speed and the pressure.

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Archard Wear

Calculate the volume of material removed by wear using Archard's law, V = k·F·s ÷ H, from the dimensionless wear coefficient k, the normal force F, the sliding distance s and the hardness of the softer material H. The result is the worn volume, proportional to load and distance and inversely proportional to hardness. It is the fundamental model of adhesive and abrasive wear, used to predict the life of sliding-contact surfaces — gears, guides, bushings, tools. Harder materials and lower loads reduce wear. Enter the wear coefficient, the force, the distance and the hardness.

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Hersey Number

Calculate the Hersey number of a bearing, H = μ·N ÷ P, from the dynamic viscosity μ, the rotational speed N and the specific pressure P. The dimensionless result is the horizontal-axis variable of the Stribeck curve, which maps the lubrication regimes: very low values indicate boundary lubrication (metal-to-metal contact, high friction and wear); intermediate values, mixed lubrication; and high values, full hydrodynamic lubrication (complete film, minimum friction). Tracking the Hersey number helps keep the bearing in the hydrodynamic regime, away from contact. Enter the viscosity, the speed and the pressure.

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Viscosity Index (VI)

Calculate the viscosity index (VI) of a lubricating oil, VI = (L − U) ÷ (L − H) × 100, from the reference kinematic viscosities L and H (of VI-0 and VI-100 standard oils with the same viscosity at 100 °C) and the oil's viscosity U at 40 °C. The dimensionless result measures how much the oil's viscosity changes with temperature: a high VI means little change (good lubrication both cold and hot), desirable in multigrade automotive and hydraulic oils. A low VI means an oil that thins greatly when heated. Enter the viscosities L, U and H.

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Film Thickness Ratio (λ)

Calculate the specific film thickness ratio (lambda), λ = h_min ÷ √(Ra₁² + Ra₂²), from the minimum lubricant film thickness h_min and the surface roughnesses Ra of the two contacting surfaces. The dimensionless result indicates the elastohydrodynamic lubrication regime: λ < 1 means direct asperity contact (boundary lubrication, high wear); 1 < λ < 3, mixed lubrication; and λ > 3, full separation of the surfaces by the oil film (full regime, long life). It is a key criterion in gear and rolling-bearing design. Enter the minimum film thickness and the surface roughnesses.

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Bearing Radial Clearance

Calculate the radial clearance of a journal bearing, c = (D_bore − D_shaft) ÷ 2, subtracting the shaft diameter from the bearing bore diameter and dividing by two. The result is the radial space between shaft and bearing, where the lubricant oil film forms. Clearance is a critical design parameter: too small hampers film formation and heat dissipation (seizure risk); too large reduces load capacity and increases vibration and noise. A rule of thumb uses a radial clearance of about one thousandth of the diameter. Enter the bore and shaft diameters.

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Eccentricity Ratio

Calculate the eccentricity ratio of a hydrodynamic bearing, ε = e ÷ c, dividing the eccentricity e (shaft centre offset from bearing centre) by the radial clearance c. The result (between 0 and 1) describes the shaft position within the bearing under load: ε = 0 means a centred shaft (no load); ε near 1 means the shaft nearly touches the bearing (heavily loaded, minimum film at the limit). Eccentricity grows with load and decreases with viscosity and speed. The minimum film thickness is h_min = c·(1 − ε). Enter the eccentricity and the radial clearance.

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Friction Torque

Calculate the friction torque in a shaft or bearing, T = μ·F·r, multiplying the friction coefficient μ by the normal force (load) F and the radius r where friction acts. The result, in N·m, is the moment friction opposes to rotation — the torque the motor must overcome just to turn the assembly, without doing useful work. Reducing friction torque (with lubrication, rolling bearings and good finishes) saves energy and lowers heating. Multiplied by the angular velocity, it gives the power dissipated by friction. Enter the friction coefficient, the force and the radius.

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Bearing PV Factor

Calculate the PV factor of a bearing or self-lubricating bushing, PV = P × V, multiplying the specific pressure P (load over projected area) by the sliding velocity V at the surface. The result, in MPa·m/s, is the limiting criterion for selecting materials for non-force-lubricated bearings (sintered bronze bushings, polymers like PTFE and nylon): each material has a maximum allowable PV value, above which the friction heat cannot be dissipated and the bearing fails by melting or accelerated wear. PV is kept below the material limit with a safety margin. Enter the specific pressure and the velocity.

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Bearing Power Loss

Calculate the power dissipated by friction in a bearing, P = T × ω, multiplying the friction torque T by the angular velocity ω (rad/s). The result, in watts, is the mechanical energy converted to heat per unit time by friction — a loss that reduces efficiency and heats the lubricant and components. This heat must be dissipated (by convection or oil circulation) to keep a safe operating temperature, since overheating degrades the lubricant and can cause seizure. Estimating the dissipated power is essential to size the cooling and the oil flow. Enter the friction torque and the angular velocity.

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Peak Flow Rate (PHF)

Calculate the peak flow rate of a roadway, q = V ÷ PHF, dividing the hourly volume V (vehicles/h) by the peak hour factor PHF (between 0 and 1, the ratio of the hour's volume to four times the busiest 15-minute volume). The result, in vehicles/h, is the equivalent flow rate of the busiest 15-minute period — always greater than or equal to the hourly volume, since traffic does not arrive uniformly. It is the design flow used in capacity and level-of-service analysis by the HCM, since sizing by the hourly average would underestimate the peaks. Enter the hourly volume and the peak hour factor.

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Average Headway

Calculate the average headway (time interval between successive vehicles), h = 3600 ÷ q, dividing 3600 seconds by the flow rate q (vehicles/h). The result, in seconds, is the average time between two consecutive vehicles passing a point. Headway is the inverse of flow: the higher the traffic volume, the shorter the intervals. It is a central concept of traffic flow theory, used in signal design, capacity analysis and car-following models. The smallest safe headway defines the maximum capacity of a lane. Enter the flow rate.

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Average Vehicle Spacing

Calculate the average vehicle spacing, s = 1000 ÷ k, dividing 1000 metres by the traffic density k (vehicles/km). The result, in metres, is the average distance between the fronts of two consecutive vehicles in a traffic stream. Spacing is the inverse of density: congested roads have high density and small spacing; free-flowing roads have low density and large spacing. It is the spatial analogue of headway (which is temporal) and relates to speed by s = v·h. The smallest spacing, at jam density, equals the vehicle length plus the minimum gap. Enter the traffic density.

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Space Mean Speed

Calculate the space mean speed of two vehicles by the harmonic mean, v_s = 2 ÷ (1/v₁ + 1/v₂), from the individual speeds v₁ and v₂. The result, in the same unit as the speeds, is the harmonic mean — not the arithmetic — which is the correct way to compute the mean speed of a traffic stream when observing a road section (average over space). Space mean speed is always less than or equal to the time mean speed (the arithmetic mean observed at a point), because it gives more weight to slow vehicles, which spend more time in the section. It is the speed used in the fundamental equation q = k·v. Enter the two speeds.

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Greenshields Speed

Calculate the speed of a traffic stream by the linear Greenshields model, v = v_f·(1 − k ÷ k_j), from the free-flow speed v_f, the current density k and the jam density k_j (vehicles/km). The result, in the unit of v_f, shows speed falls linearly with density: on an empty road (k = 0), vehicles travel at free-flow speed; as density rises, speed decreases, reaching zero at total jam (k = k_j). It is the most classic macroscopic traffic flow model, the basis of the parabolic flow-density relationship. Enter the free-flow speed, the current density and the jam density.

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Signal Cycle Time (Webster)

Calculate the optimum signal cycle time by Webster's formula, C = (1.5·L + 5) ÷ (1 − Y), from the total lost time per cycle L (seconds) and the sum of critical flow ratios Y (flow/saturation flow of each phase). The result, in seconds, is the cycle that minimizes total vehicle delay at the intersection. Lost time includes the intergreen intervals and start-up; Y must be less than 1 (otherwise the intersection is saturated and the cycle tends to infinity). It is the fundamental formula for designing isolated signals. Enter the total lost time and the sum of flow ratios.

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Saturation Flow

Calculate the saturation flow of a signalized approach, S = S₀ × N, multiplying the base saturation flow per lane S₀ (vehicles/h per lane, typically ~1800–1900) by the number of lanes N. The result, in vehicles/h, is the maximum rate of vehicles that can cross the stop line if the signal stayed green continuously and a queue existed — the queue discharge rate during green. It is a central parameter in signal design and intersection capacity, adjusted by lane width, grade, turning and parking factors. Enter the base saturation flow per lane and the number of lanes.

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Volume/Capacity Ratio (V/C)

Calculate the volume/capacity ratio (degree of saturation), X = V ÷ C, dividing the traffic volume V by the capacity C of the road or intersection. The dimensionless result measures the road's utilization: X near 0 indicates a free road; X = 1 means the road operating exactly at capacity; X > 1 indicates demand above capacity, with growing queues and congestion. The V/C ratio is the main indicator to classify the level of service (LOS A to F) and identify bottlenecks. Values above 0.85–0.90 already indicate near-saturation operation. Enter the volume and the capacity.

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Number of Lanes Required

Calculate the number of lanes required on a road, N = V ÷ C_lane, dividing the design traffic volume V by the capacity of one lane C_lane (vehicles/h per lane). The result is the minimum number of lanes to serve the demand within capacity; in practice, always round up to the next integer. It is a basic sizing calculation in the geometric design of highways and urban roads, defining the cross-section from the predicted volume and the per-lane capacity (which depends on speed, road type and traffic conditions). Enter the traffic volume and the per-lane capacity.

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Equivalent Flow (PCE)

Calculate the equivalent flow in passenger car equivalents (PCE), q = Q_cars + Q_heavy × E, adding the car flow to the heavy-vehicle flow multiplied by the equivalence factor E (how many passenger cars each truck or bus equals in road occupancy — typically 1.5 to 3.0). The result, in PCE/h, converts a mixed traffic stream into an equivalent homogeneous one, allowing volumes to be compared and the capacity of roads with different traffic compositions to be computed. Heavy vehicles occupy more space and accelerate more slowly, especially on grades. Enter the car flow, the heavy-vehicle flow and the equivalence factor.

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Damped Natural Frequency

Calculate the damped natural frequency of a vibrating system, ω_d = ω_n·√(1 − ζ²), from the undamped natural frequency ω_n and the damping ratio ζ. The result, in the unit of ω_n (rad/s or Hz), is the actual frequency at which an underdamped system oscillates freely after a disturbance — always lower than the undamped natural frequency, since damping slows the oscillation. For small ζ (lightly damped systems), ω_d ≈ ω_n; as ζ → 1 (critical damping), ω_d → 0 and the system stops oscillating. Enter the natural frequency and the damping ratio.

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Amplification Factor (Q)

Calculate the resonance amplification factor (quality factor Q), Q = 1 ÷ (2·ζ), from the damping ratio ζ. The dimensionless result shows how many times the vibration amplitude at resonance exceeds the equivalent static deflection: lightly damped systems (small ζ) have high Q and sharp, dangerous resonance peaks; well-damped systems have low Q and smooth response. It is central to designing structures, machines and instruments to avoid destructive amplification and to characterizing the selectivity of filters and resonators. Enter the damping ratio.

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Equivalent Stiffness (Springs in Series)

Calculate the equivalent stiffness of two springs in series, 1 ÷ k_eq = 1/k₁ + 1/k₂, from the individual stiffnesses k₁ and k₂. The result, in the same unit (N/m), is always smaller than the smallest stiffness — springs in series are more flexible, since each deforms under the same force and the displacements add. It is the fundamental calculation to reduce suspension systems, isolators and structures with elastic elements in sequence to a single-degree-of-freedom model, the basis for finding the natural frequency. Enter the two stiffnesses.

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Equivalent Stiffness (Springs in Parallel)

Calculate the equivalent stiffness of two springs in parallel, k_eq = k₁ + k₂, by adding the individual stiffnesses. The result, in the same unit (N/m), is always larger than the largest stiffness — springs in parallel are stiffer, since they share the load under the same displacement and the forces add. This is the case of mounts, isolators and supports placed side by side carrying the same component. Reducing spring assemblies to an equivalent stiffness is the first step to compute a vibrating system's natural frequency. Enter the two stiffnesses.

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Vibration Transmissibility

Calculate the transmissibility of an undamped vibration isolator, TR = 1 ÷ |r² − 1|, from the frequency ratio r = f ÷ f_n (excitation frequency over natural frequency). The dimensionless result is the fraction of force (or motion) transmitted through the isolator: TR < 1 means isolation (the transmitted vibration is less than the applied one), which only occurs for r > √2. Near r = 1 (resonance), TR spikes; the higher r, the lower the transmissibility and the better the isolation. It is the key criterion in designing antivibration mounts. Enter the frequency ratio.

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Vibration Isolation Efficiency

Calculate the vibration isolation efficiency, I = (1 − TR) × 100%, from the transmissibility TR. The result, in %, shows how much of the source vibration is blocked by the isolator before reaching the supporting structure (or vice versa): TR = 0.1 corresponds to 90% isolation. High efficiencies require soft isolators (low natural frequency), so that the frequency ratio r is well above √2. It is the practical indicator to specify mounts and antivibration bases for machines, engines and sensitive equipment. Enter the transmissibility.