🧮Calculators

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Compressor Volumetric Displacement

Compute the volumetric displacement of a reciprocating compressor, Vd = (π/4)·D²·L·n, the volume swept by the pistons, from the cylinder bore (D), the stroke (L) and the number of cylinders (n). It is the compressor's 'displacement' — the theoretical volume aspirated per revolution, which, multiplied by the speed and the volumetric efficiency, gives the actual flow. It defines the compressor capacity. Enter the bore, the stroke and the number of cylinders.

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Refrigerant Mass Flow

Compute the refrigerant mass flow needed in a cycle, ṁ = refrigerating capacity / refrigerating effect, dividing the desired cooling load (kW) by the specific refrigerating effect (kJ/kg, the enthalpy absorbed per kilo at the evaporator). It is how much refrigerant must circulate per second to meet the demand — the basis for sizing the compressor, the piping and the system gas charge. Enter the refrigerating capacity and the refrigerating effect.

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Real COP / Carnot Efficiency

Compute a refrigerator's second-law efficiency, η = (real COP/Carnot COP)·100%, comparing the measured real COP with the theoretical Carnot maximum for the same temperatures. It shows how close to thermodynamic perfection the system operates: real systems are typically at 40–60% of Carnot, due to compression irreversibilities, pressure losses and finite temperature differences in the heat exchangers. Enter the real COP and the Carnot COP.

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Cold Room Heat Load

Compute the product cooling heat load in a cold room, Q = m·cp·ΔT, from the product mass, its specific heat and the desired temperature change. It is the sensible-heat portion to remove to lower the product temperature — one of the components of the room's total load (which also includes wall transmission, infiltration, lighting, motors and people). It defines the refrigerating capacity needed. Enter the mass, the specific heat and the ΔT.

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Pulping Yield

Compute the yield of a pulping (wood cooking) process, Y = (dry pulp mass / dry wood mass)·100%, the fraction of wood converted into usable cellulose. Chemical (kraft) pulping has a low yield (~45–55%), since it dissolves lignin and part of the hemicelluloses; mechanical pulping reaches ~95%, but with lower-quality fibers. It is a central indicator of the process economics and type. Enter the dry pulp mass and the dry wood mass.

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Kappa Number → Lignin

Estimate the residual lignin content of a cellulose pulp from the Kappa number, Lignin% ≈ Kappa · 0.15. The Kappa number measures the pulp's permanganate consumption, proportional to the lignin remaining after cooking — the higher the Kappa, the more lignin (dark color, stiffer fibers) remained. It is the main control of delignification, defining the bleaching load needed. Enter the Kappa number.

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Fiber Suspension Consistency

Compute the consistency of a fiber suspension, C = (dry fiber mass / total suspension mass)·100%, the fiber concentration in the water, a control parameter throughout the paper mill. The suspension is very dilute at the start (low consistency, ~0.5%, to form the sheet uniformly) and concentrates along the machine. Controlling consistency is essential for sheet formation and water and energy use. Enter the dry fiber mass and the total suspension mass.

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Paper Tensile Index

Compute the paper tensile index, index = tensile strength (N/m) / grammage (g/m²), in N·m/g, normalizing the strength by the grammage to allow comparing papers of different weights. It is one of the most important mechanical properties, linked to fiber strength, inter-fiber bonding and refining. Packaging and sack papers require a high tensile index. Enter the tensile strength and the grammage.

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Paper Bulk (Specific Volume)

Compute the bulk (apparent specific volume) of paper, bulk = thickness (µm) / grammage (g/m²), in cm³/g, the inverse of density. A high bulk means a 'fluffier', more voluminous paper for the same weight (book papers, boards, tissue), giving stiffness and softness; a low bulk gives dense, thin paper (high-quality printing papers, glassine). It is a key paper-design parameter. Enter the thickness and the grammage.

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Paper Breaking Length

Compute the breaking length (self-rupture) of paper, L = tensile index / 9.80665, in km — the length of a paper strip that, hung from one end, would break under its own weight. It is an intuitive, classic way to express tensile strength, independent of grammage. Common papers break around 3–8 km; high-strength papers, more. Enter the tensile index (N·m/g).

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Cobb (Paper Water Absorption)

Compute the Cobb value of a paper, Cobb = mass gain (g) / area (m²), in g/m², the amount of water absorbed by one face of the paper in a standardized time (usually 60 s). It measures resistance to water penetration, crucial in packaging papers, printing (glue/ink control) and products that contact liquids. A low Cobb indicates good sizing. Enter the mass gain and the tested area.

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Paper Tear Index

Compute the paper tear index, index = tear force (mN) / grammage (g/m²), in mN·m²/g, normalizing the tear resistance by the grammage. Tearing depends greatly on fiber length (long fibers resist more) — which is why packaging papers use long softwood fibers. It is a property that often competes with tensile (more refining raises tensile but lowers tear). Enter the tear force and the grammage.

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Ash Content (Mineral Filler)

Compute the ash content of a paper, ash = (ash mass after ignition / paper mass)·100%, corresponding to the mineral filler (fillers and mineral pigments such as calcium carbonate, kaolin and titanium dioxide) added to the sheet. Fillers improve opacity, brightness, smoothness and cost (replacing expensive fiber), but in excess reduce strength. Printing papers have 10–25% ash. Enter the ash mass and the paper mass.

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Paper Burst Index

Compute the burst index of paper, index = burst strength (kPa) / grammage (g/m²), in kPa·m²/g, normalizing the bursting pressure by the grammage. The Mullen test applies increasing pressure with a rubber diaphragm until the sheet ruptures. It is the most used strength property in packaging papers, sacks and corrugated board, reflecting combined tensile and stretch. Enter the burst strength and the grammage.

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Firing Shrinkage (Ceramic)

Compute the linear firing shrinkage of a ceramic piece, FS = (L_dry − L_fired)/L_dry·100%, the size reduction during sintering in the kiln, when pores close and particles draw together. It is a critical dimensional-control parameter: porcelain tiles shrink a lot (~7%), while porous ceramics shrink little. Variations in shrinkage cause product miscalibration. Enter the dry and fired lengths.

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Water Absorption (Ceramic)

Compute the water absorption of a ceramic piece, WA = (wet mass − dry mass)/dry mass·100%, the amount of water the open pores absorb by immersion. It is the property that classifies ceramic tiles: porcelain (WA ≤ 0.5%, very dense and strong), stoneware, semi-stoneware, semi-porous and porous (wall tile, WA > 10%). The lower the absorption, the more sintered and resistant the piece. Enter the wet mass and the dry mass.

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Apparent Porosity (Ceramic)

Compute a ceramic's apparent porosity, AP = (wet mass − dry mass)/(wet mass − immersed mass)·100%, the volume fraction occupied by open pores (accessible to water), measured by Archimedes' method. Unlike water absorption (relative to mass), apparent porosity is relative to volume. Open pores reduce mechanical strength and increase permeability. Enter the wet, dry and immersed masses (hydrostatic weighing).

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Bulk Density (Ceramic)

Compute the bulk (apparent) density of a ceramic, BD = dry mass/(wet mass − immersed mass), by Archimedes' method, considering the total piece volume (including pores). It is an indicator of the densification achieved in firing: higher bulk density means fewer pores and generally higher strength. Water density (1 g/cm³) is used in the hydrostatic weighing. Enter the dry, wet and immersed masses.

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Loss on Ignition (Ceramic)

Compute the loss on ignition (LOI) of a ceramic raw material, LOI = (mass before − mass after ignition)/mass before·100%, the mass lost during heating at high temperature. It corresponds to the release of combined water (clay minerals), the burning of organic matter and the decomposition of carbonates (releasing CO₂). A high LOI indicates much clay/volatile matter and requires care to avoid defects (bubbles, cracks). Enter the mass before and after ignition.

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Flexural Modulus of Rupture (Ceramic)

Compute the three-point flexural modulus of rupture (MOR) of a ceramic, MOR = 3·F·L/(2·b·d²), from the breaking load (F), the support span (L), the width (b) and the thickness (d) of the test bar. It is the main mechanical-strength measure of ceramics and tiles (ISO 10545): porcelain tiles exceed 35 MPa. The d² dependence shows why thicker pieces resist far more. Enter the load, the support span, the width and the thickness.

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Drying Shrinkage (Ceramic)

Compute the linear drying shrinkage of a ceramic piece, DS = (L_wet − L_dry)/L_wet·100%, the size reduction as it loses the forming water before firing. The water that separated the clay particles evaporates and they draw together. Excessive or non-uniform drying shrinkage causes cracks and warping — which is why drying is slow and controlled. Enter the wet and dry lengths.

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Sintering Relative Density

Compute the relative density of a sintered body, RD = (bulk density/theoretical density)·100%, the fraction of the maximum density (of the fully dense, pore-free material) the piece reached. It is the central measure of the degree of sintering: advanced ceramics aim for RD above 99% (almost pore-free) for maximum strength and properties. The residual porosity is 100% − RD. Enter the bulk (sintered) density and the theoretical density.

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Total Shrinkage (Ceramic)

Compute the total linear shrinkage of a ceramic piece, TS = (L_wet − L_fired)/L_wet·100%, combining the drying and firing effects from the formed piece to the final product. It is the shrinkage the mold designer must compensate for: the cavity must be larger than the final piece by the total shrinkage, so the fired piece comes out at the exact size. Enter the wet (formed) and fired (final) lengths.

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Vitrification Degree (Ceramic)

Estimate the vitrification degree of a ceramic, VD = (1 − WA/WA_green)·100%, comparing the current water absorption with that of the green (non-vitrified) material, as a measure of how much the glassy phase filled the pores during firing. Vitrification — the formation of molten glass that seals the pores — densifies the piece, lowers absorption and raises strength and impermeability. It is what turns porous clay into vitreous porcelain. Enter the current and green water absorptions.

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Volumetric Organic Loading Rate

Calculate the volumetric organic loading rate (OLR) of a biological reactor, OLR = BOD load ÷ volume, dividing the influent organic load (kg BOD/day) by the reactor's working volume (m³). The result, in kg BOD/(m³·day), shows how much organic matter is applied per unit volume and is central to sizing lagoons, trickling filters, UASB and activated sludge: high loads demand more biomass and oxygen, while low loads indicate an oversized reactor. Enter the daily BOD load and the reactor volume.

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Hydraulic Retention Time (HRT)

Calculate the hydraulic retention time (HRT) of a reactor or tank, HRT = volume ÷ flow, dividing the working volume (m³) by the influent flow (m³/h). The result, in hours, is the average time the liquid stays in the unit and is decisive in designing clarifiers, anaerobic reactors, lagoons and aeration tanks: short times prevent reactions or settling from completing, while long times raise cost and footprint. Enter the working volume and the inlet flow.

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Sludge Volume Index (SVI)

Calculate the sludge volume index (SVI), SVI = (V₃₀ × 1000) ÷ MLSS, from the 30-minute settled sludge volume (mL/L) and the mixed-liquor suspended solids concentration (mg/L). The result, in mL/g, measures activated-sludge settleability: values of 50–150 mL/g indicate well-settling sludge, while values above 150 signal filamentous bulking that impairs clarification. Enter the settled volume and the MLSS concentration.

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Solids Loading Rate (Clarifier)

Calculate the solids loading rate (SLR) of a secondary clarifier, SLR = Q × X ÷ A, multiplying the flow (m³/day) by the mixed-liquor solids concentration (mg/L, converted to kg/m³) and dividing by the surface area (m²). The result, in kg/(m²·day), is a design criterion independent of the surface overflow (hydraulic) rate: an activated-sludge secondary clarifier must satisfy both the hydraulic limit and the solids loading limit, since it receives a concentrated mixed liquor that must thicken at the bottom. Excessive solids loading causes sludge to wash out with the effluent. Enter the flow, the solids concentration and the clarifier area.

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Sludge Recycle Ratio

Calculate the sludge recycle ratio (R) of an activated-sludge system by mass balance, R = X ÷ (X_r − X), from the mixed-liquor suspended solids (MLSS) and the return sludge concentration. The result (dimensionless, or ×100%) gives the fraction of influent flow that must be recycled from the secondary clarifier to keep the desired biomass in the reactor. Typical ratios range from 0.25 to 1.0. Enter the reactor MLSS and the return sludge concentration.

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Oxygen Requirement (Aeration)

Calculate the oxygen requirement of an aerobic treatment system, O₂ = Q × ΔS ÷ 1000 × f, multiplying the flow (m³/day) by the BOD removed (mg/L) and an oxygen-demand factor (typically 1.0–1.5 kg O₂/kg BOD). The result, in kg O₂/day, sizes blowers and aerators in activated sludge and aerated lagoons, ensuring enough oxygen for the biological oxidation of organic matter. Enter the flow, the BOD removed and the oxygenation factor.

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Velocity Gradient (Mixing)

Calculate the mean velocity gradient (G) in rapid-mix and flocculation chambers, G = √(P ÷ (μ × V)), from the dissipated power (W), the water dynamic viscosity (Pa·s) and the chamber volume (m³). The result, in s⁻¹, measures mixing intensity: rapid mixing needs high G (700–1000 s⁻¹) to disperse the coagulant, while flocculation uses low G (20–70 s⁻¹) to promote floc collision and growth without breaking them. Enter power, viscosity and volume.

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Chlorine Demand

Calculate the chlorine demand of a water, demand = applied dose − chlorine residual, subtracting the measured chlorine residual (mg/L) from the applied chlorine dose (mg/L). The result, in mg/L, is the chlorine consumed by organic matter, ammonia, iron, manganese and other reducers before free chlorine remains for disinfection. Knowing the demand is essential to dose chlorine correctly and keep an adequate residual in the network without waste or underdosing. Enter the applied dose and the measured residual.

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Sludge Production

Calculate the biological sludge production of a plant, P_x = Y × ΔS ÷ 1000 × Q, multiplying the cell yield coefficient (Y, kg VSS/kg BOD), the BOD removed (mg/L) and the flow (m³/day). The result, in kg/day, estimates the excess sludge mass generated by biomass growth, key to sizing wasting, thickening, dewatering and final disposal — a step that often drives much of a treatment plant's operating cost. Enter the yield Y, the BOD removed and the flow.

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Coagulant Dosing

Calculate the coagulant consumption of a water treatment plant, consumption = flow × dose ÷ 1000, multiplying the treated flow (m³/day) by the coagulant dose (mg/L) set by jar test. The result, in kg/day, sizes the storage, dilution and dosing pumps for products such as aluminium sulphate, ferric chloride or PAC, ensuring efficient coagulation of colloidal particles. Enter the treated flow and the coagulant dose.

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Boiler Efficiency

Calculate the thermal efficiency of a boiler by the direct method, η = (m_steam × Δh) ÷ (m_fuel × LHV) × 100%, comparing the useful heat absorbed by the water/steam (steam flow × enthalpy gain) with the energy released by burning the fuel (fuel flow × lower heating value). The result, in %, shows how much fuel energy actually reached the steam; the rest is lost in flue gases, blowdown, radiation and unburnt fuel. Well-run industrial boilers reach 80–90%. Enter the steam flow, enthalpy gain, fuel flow and LHV.

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Rankine Cycle Efficiency

Calculate the thermal efficiency of a Rankine cycle, η = (w_turbine − w_pump) ÷ q_boiler × 100%, dividing the net work (turbine work minus pump work) by the heat added in the boiler, all in kJ/kg. The Rankine cycle is the basis of steam power plants: water is pumped, heated and vaporized in the boiler, expands through the turbine producing work, then condenses. The result, in %, measures how much boiler heat becomes useful work; real cycles run 30–45%. Enter the turbine work, the pump work and the boiler heat.

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Steam Turbine Power

Calculate the mechanical power generated by a steam turbine, P = ṁ × (h₁ − h₂), multiplying the steam mass flow (kg/s) by the enthalpy drop between turbine inlet and outlet (kJ/kg). The result, in kW, is the shaft power delivered to the generator, accounting for the expansion of high-pressure, high-temperature steam down to condenser pressure. It is the core calculation in sizing thermal power and cogeneration plants: the larger the enthalpy drop, the more power per kg of steam. Enter the steam flow and the inlet and outlet enthalpies.

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Pump Work (Rankine)

Calculate the specific work consumed by the pump of a Rankine cycle, w_pump = v × (P₂ − P₁), multiplying the liquid specific volume (m³/kg, ~0.001 for water) by the pump pressure rise (kPa). The result, in kJ/kg, is the energy spent pressurizing the condensate before the boiler. Because the liquid is nearly incompressible, this work is tiny compared with the turbine's — which is why the Rankine cycle pumps a liquid (not a gas, as a gas Carnot cycle would), sharply reducing the back work. Enter the specific volume and the pump outlet and inlet pressures.

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Back Work Ratio (BWR)

Calculate the back work ratio (BWR) of a power cycle, BWR = w_compressor ÷ w_turbine, dividing the work consumed by the compressor (or pump) by the gross work produced by the turbine. The dimensionless result shows what fraction of turbine work is reinvested to compress the fluid. In gas turbines (Brayton cycle) the BWR is high (0.4–0.6), since compressing gas is costly; in steam Rankine cycles it is tiny (~0.01), since pumping liquid is cheap. A high BWR makes the cycle sensitive to component efficiencies. Enter the compressor work and the turbine work.

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Specific Steam Consumption

Calculate the specific steam consumption (steam rate) of a turbine, SSC = 3600 ÷ Δh, dividing 3600 (s/h) by the available enthalpy drop in the turbine (kJ/kg). The result, in kg/kWh, gives how many kilograms of steam are needed to generate one kilowatt-hour. The lower the specific consumption, the more efficient the conversion: larger enthalpy drops (hotter steam and greater expansion) cut the steam needed per kWh. It is a practical indicator to compare turbines and estimate the steam flow required for a given power. Enter the available enthalpy drop.

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Heat Rate

Calculate the heat rate of a power plant, HR = 360000 ÷ η, dividing 360000 by the thermal efficiency in percent. The result, in kJ/kWh, is the fuel energy consumed to generate one kilowatt-hour of electricity — the inverse of efficiency expressed on an energy basis. It is the power-generation industry's standard metric: the lower the heat rate, the more efficient and economical the plant. A 40% efficiency equals 9000 kJ/kWh; modern combined-cycle plants reach ~6000 kJ/kWh. It lets you compare plants and estimate fuel use. Enter the thermal efficiency in percent.

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Combined Cycle Efficiency

Calculate the efficiency of a gas-steam combined cycle, η_cc = η_gas + η_steam − (η_gas × η_steam ÷ 100), combining the gas turbine efficiency (Brayton, topping) with the steam cycle (Rankine, bottoming) that recovers heat from the exhaust gases. The result, in %, exceeds either cycle alone because the heat rejected by the gas turbine, instead of being wasted, raises steam for a second turbine. This is why modern combined-cycle plants top 60% efficiency, the highest in thermal generation. Enter the gas-cycle and steam-cycle efficiencies (in %).

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Steam Quality

Calculate the quality (title) of a wet steam, x = (h − h_f) ÷ (h_g − h_f), from the mixture enthalpy and the enthalpies of saturated liquid (h_f) and saturated vapour (h_g) at the same pressure. The result (between 0 and 1, or ×100%) is the vapour mass fraction in the liquid-vapour mixture: x = 0 is saturated liquid, x = 1 is dry saturated vapour, and intermediate values are wet steam. Quality is essential in steam cycles to know the state at the turbine outlet (very low quality erodes the blades) and at the condenser inlet. Enter the mixture enthalpy, h_f and h_g.

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Regenerator Effectiveness

Calculate the effectiveness of a regenerator (heat recuperator), ε = (T_out − T_in) ÷ (T_hot − T_in), comparing the actual heating of the cold fluid with the maximum possible (if it reached the hot exhaust gas temperature). The result (between 0 and 1, or ×100%) measures heat-exchange effectiveness: a regenerator uses a gas turbine's exhaust heat to preheat the air before the combustor, cutting fuel use and raising the regenerative Brayton cycle efficiency. Typical effectiveness is 0.7–0.9. Enter the inlet, outlet and hot-gas temperatures.

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Vickers Hardness (HV)

Calculate the Vickers hardness, HV = 1.8544 × F ÷ d², from the applied load F (kgf) and the mean diagonal d (mm) of the indentation left by a square-based diamond pyramid indenter (136° angle). The result, in kgf/mm² (HV), measures the material's resistance to penetration. The Vickers test is versatile: one scale spans soft to extremely hard materials, and with small loads (microhardness) it can measure individual phases, thin layers and weld-adjacent regions. Enter the load and the mean indentation diagonal.

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Knoop Hardness (HK)

Calculate the Knoop hardness, HK = 14.229 × F ÷ d², from the load F (kgf) and the long diagonal d (mm) of the elongated rhombic indentation left by a Knoop diamond indenter. The result, in kgf/mm² (HK), is used mainly for microhardness of brittle materials, coatings, glass and ceramics, and thin samples: the Knoop's elongated, shallow indentation measures narrow layers and hardness gradients better than Vickers and is less sensitive to microcracking. Enter the load and the long diagonal of the indentation.

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True Strain

Calculate the true (logarithmic) strain, ε = ln(1 + e), from the engineering strain e (dimensionless or fractional). While engineering strain uses the fixed initial length as reference, true strain integrates the instantaneous length changes, being additive and better suited to large plastic deformations such as in metal forming (rolling, extrusion, drawing). The result is the actual strain accumulated by the material. For small strains, ε ≈ e; the difference grows as strain increases. Enter the engineering strain.

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True Stress

Calculate the true stress, σ_t = s × (1 + e), from the engineering stress s (MPa) and the engineering strain e. Engineering stress uses the specimen's initial area, but during a tensile test the real cross-section shrinks; true stress corrects this using the instantaneous area (assuming constant volume in the uniform region), always giving a higher value than engineering stress. It is essential to build the true stress-strain curve and model strain hardening (σ = K·εⁿ). The result is in the same unit as the input stress. Enter the engineering stress and strain.

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Stress Intensity Factor (K)

Calculate the stress intensity factor, K = Y × σ × √(π·a), from the geometry factor Y (dimensionless), the applied stress σ (MPa) and the crack size a (m). The result, in MPa·√m, quantifies the intensity of the stress field at a crack tip, the central concept of fracture mechanics. When K reaches the material's fracture toughness (K_IC), the crack propagates unstably and failure occurs — even at stresses well below the yield strength. It is the basis of damage-tolerant design. Enter the geometry factor, the stress and the crack size.

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Percent Cold Work

Calculate the percent cold work (area reduction), %CW = (A₀ − A_f) ÷ A₀ × 100%, from the initial cross-section area A₀ and the final area A_f after cold plastic deformation (rolling, drawing, stamping). The result, in %, shows how much the material was deformed below the recrystallization temperature. Cold work strain-hardens the metal: it raises the yield strength and hardness and lowers ductility as dislocations multiply and tangle. It is the parameter used to control properties before an anneal. Enter the initial and final areas.

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Fillet Weld Throat

Calculate the effective throat of a fillet weld, a = 0.707 × z, from the leg z of the fillet. For an equal-leg fillet, the throat — the smallest dimension of the resisting section, from root to face — equals the leg times sin(45°) ≈ 0.707. The result, in the same unit as the leg (mm), is the dimension used to calculate the strength of the welded joint, since the weld tends to fail across this minimum section. Sizing the throat correctly ensures the weld carries the design load. Enter the fillet leg.

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Modulus of Resilience

Calculate the modulus of resilience, U_r = σ_y² ÷ (2·E), from the yield strength σ_y (MPa) and the elastic modulus E (MPa). The result, in MJ/m³ (equivalent to MPa), is the strain energy the material absorbs per unit volume up to the elastic limit — the area under the linear part of the stress-strain curve. Materials with high yield strength and low modulus (like spring steels) have high resilience: they store much elastic energy and return it on unloading, with no permanent deformation. Enter the yield strength and the elastic modulus.

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Larson-Miller Parameter (Creep)

Calculate the Larson-Miller parameter, LMP = T × (C + log₁₀ t), from the absolute temperature T (K), the material constant C (typically ~20) and the time to rupture t (hours). The parameter combines temperature and time into a single number that correlates creep behaviour: short high-temperature tests predict service life at lower temperatures over long periods. It is widely used to estimate the life of components operating hot under constant load — turbine blades, boiler tubing, pressure vessels. Enter the temperature, the constant C and the rupture time.

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Percent Elongation

Calculate the percent elongation, A% = (L_f − L₀) ÷ L₀ × 100%, from the initial gauge length L₀ and the final length L_f measured after rupture in a tensile test (fitting the two halves of the specimen back together). The result, in %, is a direct measure of the material's ductility — how much it stretches before breaking. Ductile steels reach 20–40%; brittle materials, a few percent. Elongation depends on the gauge length used, so it is always quoted with it (e.g. A% over 50 mm). Enter the initial and final lengths.

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Corrosion Rate (Mass Loss)

Calculate the corrosion rate by the mass-loss method, CR = 87.6 × W ÷ (D × A × t), from the mass loss W (mg), the material density D (g/cm³), the exposed area A (cm²) and the exposure time t (hours). The result, in mm/year, is the average speed at which the metal is consumed by corrosion — the key parameter to predict the service life of structures, piping and equipment and to set the corrosion allowance in design. Rates below 0.1 mm/year are usually acceptable. Enter the mass loss, density, area and time.

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Electrochemical Equivalent Weight

Calculate the electrochemical equivalent weight, EW = M ÷ n, dividing the element's molar mass M (g/mol) by the number of electrons exchanged n (valence). The result, in g/eq, is the mass associated with transferring one mole of electrons and appears in nearly every electrochemical calculation: Faraday's law, electrochemical corrosion rate, electrodeposition and anode sizing. For divalent iron (Fe²⁺), for example, EW = 55.85 ÷ 2 ≈ 27.9 g/eq. Enter the molar mass and the number of electrons exchanged.

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Pilling-Bedworth Ratio (PBR)

Calculate the Pilling-Bedworth ratio, PBR = (M_oxide × ρ_metal) ÷ (n × M_metal × ρ_oxide), comparing the volume of oxide formed with the volume of metal consumed in oxidation. The dimensionless result predicts whether the oxide layer protects the metal: PBR < 1 gives a porous, non-protective oxide (continuous oxidation, as in alkali metals); 1 < PBR < 2 forms an adherent, protective layer (aluminium and chromium, the basis of passivation); PBR > 2 produces an oxide under compression that tends to crack and spall. Enter the molar masses, densities and the number of metal atoms per oxide molecule.

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Tafel Overpotential

Calculate the activation overpotential by the Tafel equation, η = a + b × log₁₀(i), from the Tafel constant a (V), the Tafel slope b (V/decade) and the current density i. The result, in volts, is the overpotential — how far an electrode's potential departs from equilibrium — needed to sustain a given current density in an activation-controlled electrochemical reaction. The Tafel relation is central to electrode kinetics, corrosion (extrapolation to obtain the corrosion current) and electrolysis. Enter the Tafel constant, slope and current density.

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Corrosion Thickness Loss

Calculate the cumulative thickness lost to corrosion, δ = CR × t, multiplying the corrosion rate CR (mm/year) by the service time t (years). The result, in mm, is the depth of material consumed over the period — direct input to assess the integrity of piping, tanks and structures and to decide on inspection, repair or replacement. Compared with the corrosion allowance set in design, it shows how much of the margin is already used and estimates the component's remaining life. Enter the corrosion rate and the service time.

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Faradaic Efficiency

Calculate the faradaic efficiency (current efficiency), η = (m_actual ÷ m_theoretical) × 100%, comparing the mass of product actually deposited or consumed with the theoretical mass predicted by Faraday's law for the charge that passed. The result, in %, measures what fraction of the current was actually used in the desired reaction; the rest is lost to side reactions (such as hydrogen or oxygen evolution) or short circuits. It is a key indicator in electrodeposition, industrial electrolysis, electroplating and batteries. Enter the actual mass obtained and the theoretical mass.