🧮Calculators

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Carbon/Nitrogen Ratio (C/N)

Compute the C/N ratio of an organic material by dividing the carbon content by the nitrogen content. It governs composting and decomposition: the ideal range to compost is ~25–30/1. A high ratio (straw, sawdust) breaks down slowly and immobilizes nitrogen; a low one (manure, legumes) breaks down fast and releases ammonia. Balancing 'brown' and 'green' materials starts here. Enter the carbon and nitrogen contents.

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Hull Speed

Compute the hull speed of a displacement vessel, V ≈ 2.43·√(LWL), in knots, from the waterline length (LWL, in meters). It is the theoretical limit of a hull's economical speed: as the boat approaches it, it gets trapped in its own bow wave and the required power soars. That is why sailboats and displacement craft rarely exceed it. Enter the waterline length.

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Block Coefficient (Cb)

Compute a ship's block coefficient (Cb), Cb = ∇/(L·B·T), the ratio of the displaced (carene) volume to the enclosing box (length × beam × draft). It measures how 'full' the hull is: slow cargo ships have a high Cb (~0.8); fast, fine vessels a low Cb (~0.5). It is one of the central parameters of naval architecture. Enter the displaced volume, the length, the beam and the draft.

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Prismatic Coefficient (Cp)

Compute a hull's prismatic coefficient (Cp), Cp = ∇/(Am·L), the ratio of the displaced volume to that of a prism with the midship section area (Am) along the whole length. It indicates how volume is distributed lengthwise: a low Cp concentrates volume amidships (good for low speeds), a high Cp pushes it to the ends (better at high speeds). It is decisive in resistance design. Enter the displaced volume, the midship section area and the length.

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Tons per Centimeter Immersion (TPC)

Compute the tons per centimeter of immersion (TPC), TPC = Awp·ρ/100, from the waterplane area (Awp, in m²) and the water density (ρ ≈ 1.025 t/m³ at sea). It indicates how many tons of cargo must be loaded (or removed) for the ship to sink (or rise) by 1 cm. It is essential in the loading plan and draft control. Enter the waterplane area and the water density.

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Power by Admiralty Coefficient

Estimate a ship's propulsive power by the Admiralty formula, P = (∆^(2/3)·V³)/C, from the displacement (∆, t), the speed (V, knots) and the Admiralty coefficient (C), characteristic of similar hulls. It is a classic, fast method to predict the required power in the preliminary design stage, based on similarity with existing ships. The V³ dependence shows the high cost of speed. Enter the displacement, the speed and the coefficient C.

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Hull Wetted Surface

Estimate the hull's wetted surface area by Denny's formula, S = 1.7·L·T + ∇/T, from the length (L), the draft (T) and the displaced volume (∇). The wetted surface drives frictional resistance — the largest share of drag at low speeds — and underlies power calculation and the area to be coated with antifouling paint. Enter the length, the draft and the displaced volume.

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Anchor Rode Length (Scope)

Compute the length of anchor rode (chain or line) to pay out, L = scope·(depth + bow roller height), from the scope ratio (typically 5:1 to 7:1), the water depth and the height of the attachment point above the water. A proper ratio makes the rode pull the anchor horizontally, ensuring it sets and the anchored boat stays safe. Enter the depth, the bow roller height and the scope ratio.

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True Heading from Magnetic

Convert a magnetic heading (read off the compass) into a true heading, TH = (MH + variation) mod 360°, by adding the local magnetic variation (positive East, negative West). The compass points to magnetic north, which differs from true north depending on your position on Earth — correcting this difference is essential for navigating on the nautical chart. Enter the magnetic heading and the magnetic variation.

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Nautical Travel Time (ETA)

Compute a vessel's travel time (and estimated time of arrival, ETA), t = distance/speed, by dividing the route distance (in nautical miles) by the speed (in knots). Since 1 knot is exactly 1 nautical mile per hour, the result comes directly in hours. It is the basic calculation of passage planning and fuel estimation. Enter the distance in nautical miles and the speed in knots.

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Reserve Buoyancy

Compute a vessel's reserve buoyancy, R = (total_volume − submerged_volume)/submerged_volume·100%, the percentage of watertight volume above the waterline relative to the submerged volume. It is the safety margin against sinking: the larger it is, the more cargo or flooding the hull tolerates before submerging. It defines the freeboard and the damage survivability. Enter the total watertight volume and the submerged volume.

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Stripping Ratio (SR)

Compute the stripping ratio (SR) of an open-pit mine by dividing the amount of waste (worthless rock that must be removed) by the ore extracted. It is the central economic indicator of open-pit mining: the higher the SR, the more useless material is moved per tonne of ore, and the higher the cost. It defines the pit limit and the viability of the operation. Enter the waste and ore quantities.

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Metallurgical Recovery

Compute the metallurgical recovery of a processing plant, R = (metal in concentrate / metal in feed)·100%, the fraction of the metal contained in the ore that is actually recovered into the concentrate. It is the key measure of plant efficiency: the unrecovered metal is lost in the tailings. Small recovery gains represent large value in large-scale operations. Enter the mass of metal in the concentrate and in the feed.

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Ore Dilution

Compute ore dilution in mining, D = waste/(ore + waste)·100%, the proportion of waste that ends up mixed with the ore during extraction, lowering the grade reaching the plant. Every operation has some dilution (irregular contacts, imprecise blasting); controlling it is essential, since diluted ore consumes energy and reagents to process worthless material. Enter the masses of diluting waste and ore.

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Mineral Reserve Tonnage

Compute a mineral reserve's tonnage, T = Volume · Density, multiplying the ore body volume (m³) by the rock bulk density (t/m³). It is the step that turns the estimated geometry of a deposit (from drilling and modeling) into ore mass — the basis of any economic evaluation of a deposit. Enter the volume and the ore density.

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Soil Swell Factor

Compute the swell factor, E = (loose_volume/in-situ_volume − 1)·100%, the volume increase soil or rock undergoes when excavated and loosened, relative to the original compact (bank) volume. It is essential in sizing haulage and spoil: 1 m³ of rock in the bank can become 1.5 m³ loose in the truck. Each material has its factor (sand ~10–15%, rock ~50–60%). Enter the loose volume and the in-situ (bank) volume.

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Powder Factor

Compute the powder factor of a rock blast by dividing the explosive mass (kg) by the volume of rock broken (m³), in kg/m³. It is the central parameter of the blast design: too low produces boulders and poor fragmentation; too high wastes explosive and increases vibration and flyrock. Optimizing it reduces downstream crushing costs. Enter the explosive mass and the rock volume.

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RQD (Rock Quality Designation)

Compute the RQD (Rock Quality Designation), R = (sum of core pieces ≥ 10 cm / total drilled length)·100%, an index of rock-mass quality obtained from drill-core logging. It measures the degree of fracturing: an RQD above 90% indicates excellent, intact rock; below 25%, heavily fractured, poor-quality rock. It underlies geomechanical classification (RMR, Q) in tunnels and slopes. Enter the sum of pieces ≥ 10 cm and the total length.

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Metal Equivalent Grade

Compute the metal equivalent grade of a polymetallic ore by adding to the main metal's grade the contribution of secondary metals weighted by the price ratio: Eq = main_grade + secondary_grade · (price_sec/price_main). It converts a deposit with several metals (e.g. copper with gold and silver) into a single comparable grade, used to set the cutoff grade and evaluate the deposit. Enter the main grade, the secondary grade and the price factor (price_sec/price_main).

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Mining Recovery

Compute the mining recovery, R = (mined ore / in-situ ore)·100%, the fraction of the ore originally present in the deposit that is actually extracted. Not all ore is recoverable: support pillars, blasting losses and contacts leave part behind. Together with dilution, it defines the extraction efficiency and the mineable reserves. Enter the mined ore and the in-situ ore.

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Concentration Ratio

Compute the concentration ratio of a processing operation, CR = feed mass / concentrate mass, how many tonnes of raw ore are needed to produce one tonne of concentrate. It measures the degree of upgrade: high ratios indicate lean ores that require heavy processing. It is useful in the mass balance and plant sizing. Enter the feed mass and the concentrate mass.

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Propeller (Propulsive) Efficiency

Compute a propeller's propulsive efficiency, η = (T·V/P)·100%, the ratio of useful propulsion power (thrust × speed) to the power delivered to the shaft. It measures how much of the engine power the propeller converts into forward thrust — well-designed propellers reach 80–88% in cruise. It drops sharply at low speed (takeoff) and near the speed of sound at the blade tips. Enter the thrust, the speed and the shaft power.

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Aircraft Center of Gravity

Compute the center-of-gravity (CG) position of an aircraft with two weight stations, CG = (W₁·a₁ + W₂·a₂)/(W₁ + W₂), the total moment divided by the total weight, measured from a reference datum. The CG must stay within a safe envelope: too far forward the aircraft is nose-heavy and hard to rotate; too far aft, unstable. It is an essential part of the weight-and-balance check before each flight. Enter the weights and arms of the two stations.

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Aircraft Climb Time

Compute an aircraft's climb time, t = Δaltitude/rate of climb (ROC), dividing the altitude gain by the rate of climb (in ft/min or m/min). It estimates how long the aircraft takes to reach cruise altitude — used in flight planning, climb fuel burn and traffic separation. The rate of climb decreases with altitude, so the result is an average estimate. Enter the altitude gain and the rate of climb.

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Glide Distance

Compute the horizontal distance an aircraft (or glider) travels in an unpowered glide, d = altitude · glide ratio, multiplying the available height by the glide ratio (how many meters it advances per meter descended, equal to L/D). A glider with a 40:1 ratio at 1000 m reaches 40 km. It is the engine-out range and landing-circuit calculation. Enter the altitude and the glide ratio.

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Rotation Speed (Takeoff)

Estimate the rotation speed (Vr) at takeoff, Vr = factor · Vstall, multiplying the stall speed by the safety margin (typically ~1.1). Vr is the speed at which the pilot pulls back to raise the nose and start the takeoff; it ensures enough margin above the stall at the critical moment. Enter the stall speed and the safety factor.

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Expanded Uncertainty

Compute the expanded uncertainty of a measurement, U = k · uc, multiplying the combined uncertainty (uc) by the coverage factor k. While the combined uncertainty corresponds to ~68% confidence (1σ), the expanded one defines a higher-confidence interval — with k = 2, about 95%, the standard in most calibration certificates. It is the final value reported as '± U' in the result. Enter the coverage factor k and the combined uncertainty.

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ADC Resolution

Compute the resolution of an analog-to-digital converter (ADC), R = FSR/2ⁿ, dividing the full-scale range (FSR, in volts) by the number of levels (2 to the power of the number of bits). It is the smallest voltage step the converter distinguishes — the more bits, the finer the resolution: a 12-bit ADC divides the range into 4096 levels. Fundamental in data-acquisition and digital-instrumentation design. Enter the full-scale range and the number of bits.

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Sensor Sensitivity

Compute a sensor's sensitivity, S = Δoutput/Δinput, the ratio of the output-signal change to the measured-quantity change that caused it. It is the slope of the calibration curve: a more sensitive sensor produces a larger signal change for the same input change, making reading easier. Expressed, for example, in mV/°C or mA/bar. Enter the output change and the input change.

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4-20 mA Current Scaling

Convert a 4-to-20 mA current signal into the corresponding process variable, PV = LRV + (I − 4)/16 · (URV − LRV), the universal standard of industrial instrumentation. The 4 mA represents 0% of the range and 20 mA, 100%; the 'live zero' at 4 mA distinguishes a null reading from a broken cable (0 mA). Enter the measured current and the lower and upper range values.

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Valve Rangeability

Compute the rangeability (turndown) of a control valve, R = Qmax/Qmin, the ratio of the largest to the smallest flow it controls accurately. A high rangeability (e.g. 50:1) means the valve works well at both high and low flows, offering fine control over a wide range. It is a key criterion in valve selection. Enter the maximum and minimum controllable flows.

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Linearity Error

Compute the linearity error (non-linearity) of an instrument, LE = (maximum deviation/span)·100%, the largest departure of the actual curve from the ideal straight line, expressed as a percentage of span. It measures how much the instrument's response deviates from a straight line — the smaller, the more 'linear' and predictable the reading. It is one of the components of specified accuracy. Enter the maximum deviation and the instrument span.

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Encoder Resolution

Compute the angular resolution of an incremental rotary encoder, R = 360°/PPR, dividing 360° by the pulses per revolution (PPR). It is the smallest angle increment the encoder can distinguish — the more pulses per turn, the finer the position measurement. A 3600-PPR encoder resolves 0.1° per pulse. The basis of position control in servomechanisms and CNC. Enter the pulses per revolution.

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Instrument Hysteresis

Compute an instrument's hysteresis, H = (maximum up-down difference/span)·100%, the largest difference between the readings obtained for the same input value when it is reached increasingly and then decreasingly. It reveals 'memory' or mechanical slack in the sensor: ideally zero, but present in springs, gears and magnetic materials. Expressed as a percentage of span. Enter the hysteresis difference and the span.

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Accuracy as % of Full Scale

Convert an accuracy specification given as a percentage of full scale (% FS) into the absolute error in engineering units, Error = (accuracy% · span)/100. Since the %FS error is constant across the range, it represents a larger relative error at low readings — so it is important to translate it into real units. Enter the accuracy percentage and the instrument span.

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Stepper Motor Resolution

Compute the angular resolution of a stepper motor, R = 360°/(steps per revolution · microsteps), the smallest angle the shaft can position. A common 200-step motor (1.8°/step) with 16 microstepping reaches 0.1125° per microstep — 3200 positions per revolution. Microstepping smooths motion and raises resolution, though it lowers the holding torque per microstep. Enter the steps per revolution and the microstepping factor.

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Forward Kinematics (2 DOF)

Compute the (x, y) position of the end of a planar 2-degree-of-freedom robotic arm from the joint angles: x = L1·cos(θ1) + L2·cos(θ1+θ2) and y = L1·sin(θ1) + L2·sin(θ1+θ2). This is forward kinematics — given the joint angles, find where the tool is. Fundamental in manipulator control and robot simulation. Enter the link lengths (L1, L2) and the joint angles (θ1, θ2) in degrees.

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Degrees of Freedom (Grübler)

Compute the degrees of freedom (mobility) of a planar mechanism by the Grübler-Kutzbach equation, DOF = 3·(n − 1) − 2·j1 − j2, where n is the number of links (including the fixed one), j1 the 1-DOF joints (pin, slider) and j2 the 2-DOF joints. A four-bar linkage (n=4, j1=4) has DOF=1: a single input motion controls the whole mechanism. The basis of mechanism and robot synthesis. Enter the number of links, 1-DOF joints and 2-DOF joints.

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Lead Screw Lead

Compute the lead of a ball screw or power screw, Lead = pitch · number of starts, the linear distance the nut travels per full turn of the screw. On a single-start screw the lead equals the pitch; with multiple starts the lead increases proportionally, allowing more linear speed at the same rotation. The basis of rotation-to-displacement conversion in CNC and linear actuators. Enter the pitch and the number of starts.

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Trapezoidal Profile Time

Compute the total time of a motion with a trapezoidal velocity profile, t = d/Vmax + Vmax/a, adding the cruise-velocity time to the acceleration and deceleration phases. It is the most common motion profile in motors and robots: accelerate to maximum speed, hold constant and decelerate. Enter the distance, the maximum velocity and the acceleration (assuming equal acceleration and deceleration).

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Harmonic Drive Reduction

Compute the reduction ratio of a harmonic drive (strain wave gear), R = Nf/(Nc − Nf), where Nf is the flexspline tooth count and Nc the circular spline's (usually Nc = Nf + 2). This ingenious mechanism reaches huge reductions (50:1 to 300:1) in a single compact stage with zero backlash — which is why it is the heart of industrial and collaborative robot joints. Enter the flexspline and circular spline tooth counts.

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Steps per Millimeter (3D Printer)

Compute the steps per millimeter (steps/mm) of a 3D-printer or CNC axis, steps/mm = (steps per revolution · microsteps)/travel per revolution, the calibration value entered in the firmware. For a GT2-belt axis (40 mm/rev travel), a 200-step motor and 16 microsteps, it gives 80 steps/mm. Correct calibration ensures accurate part dimensions. Enter the steps per revolution, the microsteps and the travel per revolution.

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Jerk (Rate of Acceleration Change)

Compute the jerk, J = Δacceleration/Δtime, the rate of change of acceleration over time — the third derivative of position. High jerk causes jolts, vibration and wear; controlling it (jerk-limited or S-curve profiles) makes motion smooth, protecting mechanisms and improving the finish on CNC machines and elevators. Enter the acceleration change and the time interval.

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Motor Power (Torque × RPM)

Compute a motor's mechanical power from torque and rotation, P = τ·ω = τ·2π·n/60, where τ is the torque (N·m), n the rotation (rpm) and P the power (W). It is the fundamental relation linking the three quantities of a rotating motor: the same motor delivers high torque at low speed or high speed at low torque, but the power is the product of the two. The basis of drive sizing. Enter the torque and the rotation.

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Servo Angle from PWM

Convert a servo motor's PWM pulse width into the corresponding angle, angle = (pulse − 1000)/1000 · 180°, in the hobby standard where 1000 µs ≈ 0°, 1500 µs ≈ 90° (center) and 2000 µs ≈ 180°. Hobby and robotics servos are commanded by this pulse width, typically at 50 Hz. Knowing the relation helps to calibrate and program movements. Enter the pulse width in microseconds.

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Yarn Count (Tex)

Compute a yarn's count in the Tex system, Tex = (mass in grams / length in meters) · 1000, i.e. the mass in grams of 1000 meters of the yarn. It is a 'direct' system (the higher the number, the thicker the yarn), standardized internationally. Tex links mass to length — the fundamental quantity defining yarn fineness and influencing strength, hand and fabric weight. Enter the mass and length of the yarn sample.

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Tex ↔ Ne Conversion

Convert a yarn count from the Tex (direct) system to Ne (English count, indirect), Ne = 590.5/Tex. In the Ne system, unlike Tex, the higher the number the <em>finer</em> the yarn — so they are inversely proportional. Ne is traditional in cotton spinning. The conversion is essential to compare yarns specified in different systems. Enter the count in Tex.

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Fabric Weight (GSM)

Compute a fabric's weight in grams per square meter (GSM) by dividing a sample's mass by its area. It is the main measure of fabric 'weight': light T-shirt knits are 140–180 g/m², sweatshirts 280–340, canvas and denim much more. GSM defines hand, drape, durability and price, and is specified in almost every textile spec sheet. Enter the sample's mass and area.

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Marker Efficiency (Cutting)

Compute the efficiency of a pattern marker in cutting, E = (pieces area / marker area) · 100%, the fraction of the lay actually used by the patterns. The rest is the 'waste' between pieces, an unrecoverable fabric loss — the largest variable cost in garment making. Each percentage point of utilization saves a lot of fabric in scale production. Enter the pieces area and the total marker area.

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Yarn Twist (TPM)

Compute a yarn's twist in turns per meter (TPM) by dividing the number of turns by the length. Twist is what holds the fibers together and gives the yarn strength: too little produces a weak, fuzzy yarn; too much, a hard yarn prone to kinking. The direction (S or Z) and twist level define the yarn's character — knitting yarns are low-twist, crepe yarns high. Enter the number of turns and the length.

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Fabric Thread Count

Compute a woven fabric's thread density by adding the warp threads (lengthwise) and weft threads (widthwise) per centimeter. It is an indicator of construction and quality: higher density usually means a firmer, more durable and fuller fabric. It appears on spec sheets as 'threads/cm' or 'thread count'. Enter the warp and weft threads per cm.

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Fabric Shrinkage

Compute a fabric's shrinkage after washing, S = (initial measure − final measure)/initial measure · 100%, the percentage reduction in length or width. Almost every fabric shrinks in the first wash (cotton can exceed 5%), so the pattern must compensate for that percentage and the fabric is usually pre-shrunk (sanforized). Ignoring it makes the garment come out smaller than the nominal size. Enter the measures before and after washing.

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Fabric Cover Factor

Compute a fabric's cover factor, CF = thread density (threads/cm) · √(Tex), an index of how 'closed' the weave is — how much the threads cover the area, leaving more or fewer open spaces. High factors indicate dense, opaque fabrics (canvas, twill); low ones, sheer, breathable fabrics (voile, mesh). It influences air permeability, opacity and strength. Enter the thread density and the count in Tex.

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Sewing Thread Consumption

Estimate the thread consumption of a seam by multiplying the seam length by the stitch consumption factor (the ratio of thread used to seam length — ~2.5 for lockstitch, more for overlock and coverstitch). Knowing the thread consumption per piece is essential to budget, buy cones and avoid stopping production for lack of thread. Enter the seam length and the consumption factor.

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Welding Heat Input

Compute the heat input of a weld, H = (V·I·60)/(v·1000), in kJ/mm, from the arc voltage (V), the current (I) and the travel speed (v, in mm/min). It is one of the most important welding parameters: it controls the cooling rate, the microstructure, the heat-affected-zone hardness and the cracking risk. High input softens and distorts; low input hardens and embrittles. Enter the voltage, the current and the travel speed.

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Carbon Equivalent (CEq)

Compute a steel's carbon equivalent by the (simplified) IIW formula, CEq = C + Mn/6 + Cr/5 + Ni/15, weighting the alloying elements' effect relative to carbon on the hardening and cracking tendency. It is the key weldability index: a CEq below 0.40 indicates easily weldable steel; above 0.45–0.50 it requires preheating and care to avoid cold cracking. Enter the carbon, manganese, chromium and nickel contents (%).

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Weld Deposition Rate

Compute a weld's deposition rate by dividing the mass of deposited metal by the arc-on time, giving kg/h. It is a central indicator of process productivity: processes like submerged arc and MIG/MAG have far higher rates than stick electrode. Combined with the operating factor (actual arc time), it estimates a joint's output. Enter the deposited mass and the arc time.

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Weld Dilution

Compute a weld's dilution, D = (melted base-metal area / total bead area)·100%, the proportion of the bead that came from the base metal rather than the filler. It is crucial in cladding and dissimilar-metal joints: high dilution mixes in more base metal, altering the bead's composition and properties (anti-corrosion cladding aims for low dilution). Enter the melted base-metal area and the total bead area.

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Electrode Consumption

Estimate the number of electrodes needed for a weld by dividing the total mass of metal to deposit by the mass deposited per electrode (rounding up). It is a practical planning and budgeting calculation in stick-electrode welding, avoiding over-buying or stopping the job for lack of consumables. Enter the total weld mass and the mass deposited per electrode.

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Welding Preheat Temperature

Estimate the preheat temperature for welding, Tp = 350·√(CE − 0.25), as a function of the steel's carbon equivalent (CE). Preheating reduces the cooling rate, giving hydrogen time to escape and preventing the formation of brittle martensite and cold cracks in the heat-affected zone. Steels with a high CE require more preheating. Enter the steel's carbon equivalent.