🧮Calculators

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ASTM Grain Size

Compute the number of grains per square inch at 100× magnification from the ASTM grain-size number, N = 2^(G−1). The higher the G number, the smaller and more numerous the grains. Grain size is decisive in metal properties: fine grains (high G) increase strength and toughness (Hall-Petch relation), while coarse grains reduce them. It is measured by metallography. Enter the ASTM grain-size number (G).

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Welding Travel Speed

Compute the welding travel speed (arc advance) by dividing the bead length by the time taken, in mm/min. It is a fundamental parameter that, together with voltage and current, defines the heat input: welding too fast produces narrow beads with little penetration; too slow overheats and deposits excess material. Enter the bead length and the welding time.

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Shielding Gas Consumption

Compute the shielding gas consumption of a MIG/MAG or TIG weld by multiplying the flow rate (L/min) by the welding time (min), in liters. The gas (argon, CO₂, mixtures) protects the molten pool from atmospheric contamination. Knowing the consumption lets you size cylinders and budget — and adjust the flow, since excess wastes gas and can cause turbulence and porosity. Enter the gas flow rate and the welding time.

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Tensile Strength from Brinell Hardness

Estimate a carbon steel's tensile strength (Rm) from the Brinell hardness, Rm ≈ 3.45·HB, in MPa. There is a remarkably robust empirical correlation between hardness and strength in steels, which lets you estimate strength from a hardness test — fast, cheap and almost non-destructive — instead of a tensile test. Useful in inspection and quality control. Enter the Brinell hardness (HB).

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Mold Clamping Force

Compute the clamping force needed on a plastic injection machine, F = projected area · cavity pressure, to keep the mold closed against the molten plastic pressure. If the force is insufficient, the mold opens during injection and plastic leaks out at the parting lines (flash). It is the parameter that defines the machine tonnage required for a part. Enter the part's projected area (mm²) and the cavity pressure (MPa).

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Plastic Mold Shrinkage

Compute the final dimension of a plastic part after molding shrinkage, part_dim = mold_dim · (1 − shrinkage%/100). Every thermoplastic shrinks as it cools and solidifies in the mold — from ~0.5% (amorphous like ABS) to 2–3% (semicrystalline like PP and PA). That is why the mold cavity is machined larger than the final part, compensating exactly for this shrinkage. Getting it wrong ruins an expensive mold. Enter the mold dimension and the material's shrinkage rate.

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Injection Shot Volume

Compute the shot volume of a plastic part by dividing the injected mass by the molten material density. The shot is the total volume of plastic injected per cycle (parts + runners), a parameter that must fit the injection barrel capacity. Together with the machine capacity, it defines how many cavities can be filled per cycle. Enter the injected mass (g) and the material density (g/cm³).

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Screw L/D Ratio (Injection)

Compute the L/D (length/diameter) ratio of an injection or extrusion screw by dividing the effective length by the diameter. It is a central parameter of the plasticizing design: long screws (L/D 20–24) give better melt mixing and homogenization; short ones (L/D < 18) plasticize less but are more robust. It defines melt quality and the ability to process different materials. Enter the screw length and diameter.

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Mold Cavity Count

Compute the maximum number of mold cavities the machine can fill per cycle by dividing the machine's injection capacity by each part's mass (rounding down). More cavities increase productivity but require a larger machine and a more expensive, complex mold. It is a key calculation in production planning and mold selection. Enter the machine injection capacity and each part's mass.

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Injection Cycle Time

Compute the total cycle time of a plastic injection by adding the injection time (fill + pack), the cooling time and the mold open/eject time. Cooling is usually the largest share (50–80% of the cycle). The cycle time directly determines productivity: parts/hour = 3600/cycle × cavities. Reducing it is the constant focus of optimization. Enter the injection, cooling and opening times.

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Mold Cavity Pressure

Estimate the pressure that actually reaches the mold cavity by multiplying the injection pressure (at the screw tip) by the pressure transmission factor, which accounts for pressure losses along the runners, nozzle and gates to the cavity. Typically only 40–60% of the machine pressure reaches the part. It is the cavity pressure that defines the clamping force and fill quality. Enter the injection pressure and the transmission factor.

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Shear Rate (Injection)

Compute the shear rate of the molten plastic in a rectangular channel, γ = 6Q/(W·H²), from the flow rate (Q), the channel width (W) and height (H). It is a critical parameter of polymer processing: thermoplastic viscosity drops with shear rate (pseudoplastic behavior), and excessive rates degrade the material. It guides the design of runners and gates. Enter the flow rate, the width and the height of the channel.

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Injection Capacity (PS Equivalent)

Convert a machine's nominal injection capacity (always specified in polystyrene, PS, density ~1.05) to the equivalent capacity in another material by multiplying by the density ratio. Since the barrel has a fixed volume, the mass it injects changes with the plastic's density — denser materials yield more grams per shot. Essential to size the machine for the real material. Enter the nominal PS capacity and the material density.

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Plastic Injection Flow Rate

Compute the injection flow rate by dividing the injected volume by the fill time, in cm³/s. It is the speed at which the molten plastic enters the mold — a parameter that controls the shear rate, molecular orientation, surface finish and defects such as jetting or flow marks. High flow fills fast but may degrade; low flow may solidify before filling. Enter the injected volume and the fill time.

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Radioactive Activity

Compute the activity of a radioactive sample, A = λ·N, the product of the decay constant (λ) and the number of radioactive nuclei present (N). Activity, measured in becquerel (Bq = 1 disintegration/s) or curie, expresses how many nuclei decay per second. It is the fundamental quantity quantifying a radioactive source, and it decreases over time as nuclei decay. Enter the decay constant and the number of nuclei.

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Decay Constant

Compute the radioactive decay constant, λ = ln(2)/T½, from the half-life (T½). The constant λ is the probability of a nucleus decaying per unit time — the larger it is, the more unstable the isotope and the shorter its half-life. It links the half-life (time for half the nuclei to decay) to the activity and to the exponential decay law. Enter the isotope's half-life.

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Number of Half-Lives

Compute how many half-lives have elapsed, n = t/T½, and the fraction of radioactive material remaining, (1/2)ⁿ, from the elapsed time and the half-life. With each half-life the amount halves: after 1 half-life 50% remains, after 2 it is 25%, after 10 less than 0.1%. It is the intuitive way to assess how much of a source (or contamination) is left. Enter the elapsed time and the half-life.

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Effective Half-Life

Compute the effective half-life of a radionuclide in the body, 1/Teff = 1/Tbio + 1/Tphys, combining the physical half-life (radioactive decay) with the biological one (elimination by the organism). Since both processes reduce the amount simultaneously, the effective half-life is always shorter than either. It is essential in internal dosimetry in nuclear medicine and radiation protection. Enter the biological and physical half-lives.

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Half-Value Layer (HVL)

Compute the half-value layer (HVL), HVL = ln(2)/μ, the material thickness that reduces the radiation intensity by half, from the linear attenuation coefficient (μ). It is the practical way to specify shielding: one HVL cuts 50% of the radiation, two HVLs cut 75%, and so on. Dense materials like lead have a small HVL. Enter the linear attenuation coefficient.

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Radiation Shielding Attenuation

Compute the radiation intensity after passing through shielding, I = I₀·e^(−μ·x), by the exponential attenuation law, from the initial intensity (I₀), the material's linear attenuation coefficient (μ) and the thickness (x). Unlike alpha and beta particles (which have a finite range), gamma rays and X-rays are only exponentially attenuated — never fully blocked. It is the basis of shielding calculation. Enter the initial intensity, the attenuation coefficient and the thickness.

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Inverse Square Law (Radiation)

Compute the radiation intensity at a new distance from a point source, I₂ = I₁·(d₁/d₂)², by the inverse square law: intensity falls with the square of distance. Doubling the distance reduces the dose to a quarter — which is why distance is one of the three basic radiation-protection defenses (time, distance and shielding) and the most effective and cheapest. Enter the initial intensity and distance and the new distance.

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Effective Dose

Compute the effective dose, E = H·wT, multiplying the equivalent dose in an organ (H, in mSv) by the tissue weighting factor (wT) reflecting the tissue's radiosensitivity. While the equivalent dose accounts for the radiation type, the effective dose weights the risk by the irradiated organ (gonads and marrow are more sensitive than skin or bone). It is the quantity used in occupational dose limits. Enter the equivalent dose and the tissue weighting factor.

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Gamma Exposure Rate

Compute the exposure (or dose) rate of a point gamma source, X = Γ·A/d², from the exposure-rate constant (Γ, specific to the radionuclide), the source activity (A) and the distance (d). It combines the source strength with the inverse square law, allowing you to estimate the dose received at a given distance — fundamental in planning tasks with radioactive sources. Enter the gamma constant, the activity and the distance.

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Collective Dose

Compute the collective dose, S = mean individual dose · number of people, in person-sievert (person-Sv), summing the dose received by an entire exposed group. It is the quantity used to assess the total impact of an exposure on a population — in radiation protection, practice optimization and epidemiological studies. Even small individual doses, multiplied by many people, produce a significant collective dose. Enter the mean individual dose and the number of people.

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Oil in Place (OOIP)

Compute a reservoir's original oil in place (OOIP) by the volumetric method, OOIP = 7758·A·h·φ·(1−Sw)/Boi, in stock-tank barrels (STB). It combines the reservoir area (acres), the porous thickness (ft), the porosity (φ), the water saturation (Sw) and the oil formation volume factor (Boi). The constant 7758 converts acre-feet into barrels. It is the basis of any oil-field evaluation. Enter the area, thickness, porosity, water saturation and Boi.

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Water Saturation (Archie)

Compute a reservoir's water saturation (Sw) by Archie's equation (with a=1, m=2, n=2), Sw = √(Rw/(φ²·Rt)), from the formation-water resistivity (Rw), the rock's true resistivity (Rt) and the porosity (φ). It is the fundamental petrophysics equation: it relates the resistivity measured by electric logs to the fraction of pores filled with water — and, by complement (1−Sw), with hydrocarbons. Enter Rw, Rt and the porosity.

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Density-Log Porosity

Compute a reservoir rock's porosity from the density log, φ = (ρma − ρb)/(ρma − ρf), where ρma is the matrix (mineral) density, ρb the bulk density read by the log and ρf the pore-fluid density. It is one of the most used petrophysical methods to estimate porosity in wells, since the bulk density drops as the pore volume (filled by less dense fluid) increases. Enter the matrix, bulk (log) and fluid densities.

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Gas-Oil Ratio (GOR)

Compute the gas-oil ratio (GOR) by dividing the produced gas volume by the oil volume, in scf/STB (standard cubic feet per barrel). It is a central petroleum-production parameter: it indicates how much gas accompanies the oil, characterizes the reservoir fluid type (black oil, volatile, gas-condensate) and sizes the surface separation equipment. A rising GOR can signal gas-cap breakthrough at the well. Enter the gas and oil volumes.

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Well Productivity Index

Compute an oil well's productivity index (PI), PI = Q/(Pr − Pwf), the ratio of the produced rate to the pressure differential (drawdown) between the reservoir (Pr) and the bottomhole (Pwf). It measures how easily the well produces: a high PI indicates good permeability and reservoir connection. It is the basis of lift design and production forecasting. Enter the rate and the reservoir and bottomhole pressures.

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Reservoir Recovery Factor

Compute a reservoir's recovery factor, RF = (Np/N)·100%, the fraction of the original oil (N, or OOIP) that will actually be produced (Np). It is one of the most important — and uncertain — numbers in the industry: primary recovery (natural energy) is usually 5–15%; with secondary recovery (water/gas injection) it rises to 30–50%; and advanced methods (EOR) can go further. It defines the field's economic value. Enter the cumulative production and the original oil in place.

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Recoverable Oil Reserves

Compute the recoverable oil reserves by multiplying the original oil in place (OOIP) by the recovery factor (%). While the OOIP is the total volume present in the rock, only a fraction is technically and economically extractable — those are the reserves that actually have value and enter oil companies' books. It is the number behind asset valuations and investment decisions. Enter the OOIP and the recovery factor.

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Reservoir Net Pay

Compute a reservoir's net pay (net productive thickness) by multiplying the gross interval thickness by the net-to-gross ratio (N/G), the fraction of rock with enough porosity and permeability to produce. Shale layers, tight rock or water zones are discounted. The net pay, not the total thickness, is what enters the oil and gas volume calculations. Enter the gross thickness and the net-to-gross ratio.

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Oil Formation Volume Factor (Bo)

Compute the oil formation volume factor (Bo) by dividing the volume the oil occupies at reservoir conditions by the volume it occupies at the surface (stock-tank barrels). Bo is always greater than 1 because, in the reservoir, the oil is hot and has dissolved gas, occupying more space; as it rises and loses gas and heat, it shrinks. It is essential to convert reservoir volumes into surface production. Enter the volumes at reservoir and surface conditions.

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Pore Pressure Gradient

Compute a formation's pore pressure gradient by dividing the pore pressure by the vertical depth, in psi/ft (or kPa/m). The normal saltwater gradient is ~0.465 psi/ft; higher values indicate overpressure (dangerous, can cause kicks and blowouts) and lower ones, underpressure. It is a critical drilling-safety parameter, since it sets the mud weight needed to balance the formation. Enter the pore pressure and the vertical depth.

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Reactor Conversion (Batch)

Compute a reactant's conversion, X = (C₀ − C)/C₀·100%, the fraction of reactant consumed in the reaction, from the initial (C₀) and final (C) concentrations. Conversion is the fundamental measure of a chemical reaction's progress: 0% means nothing reacted, 100% that the reactant is exhausted. Together with selectivity and yield, it defines a reactor's performance. Enter the initial and final concentrations.

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Chemical Reaction Yield

Compute a chemical reaction's yield, Y = (actual mass obtained / theoretical mass)·100%, comparing what was actually produced with the maximum predicted by stoichiometry. Real reactions rarely reach 100%: there are incomplete reactions, side reactions, purification losses. Yield is the efficiency indicator that separates paper chemistry from lab and industrial chemistry. Enter the actual mass obtained and the theoretical mass.

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Reaction Selectivity

Compute a reaction's selectivity, S = moles of desired product / moles of undesired product, when parallel reactions compete for the same reactant. In a chemical plant it is not enough to convert the reactant — it must be steered to the valuable product, not to byproducts. High selectivity reduces waste, separation cost and environmental impact. It is optimized by the choice of catalyst, temperature and time. Enter the moles of desired and undesired product.

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Number of Transfer Units (NTU)

Compute the number of transfer units (NTU) of an absorption or stripping column (dilute case), NTU = ln(C_in/C_out), from the inlet and outlet concentrations. NTU measures the 'difficulty' of the separation: the greater the removal desired, the more transfer units are needed. Together with the height of a unit (HTU), it defines the total packing height. Enter the inlet and outlet concentrations.

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Packing Height (HTU·NTU)

Compute the packing height of an absorption or distillation column, Z = HTU·NTU, multiplying the height of a transfer unit (HTU, which depends on hydrodynamics and packing type) by the number of transfer units (NTU, which depends on the desired separation). It is the HTU-NTU method of sizing packed columns — it separates the 'kinetic' part (HTU) from the 'thermodynamic' (NTU). Enter the HTU and the NTU.

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Minimum Reflux (Underwood)

Estimate the minimum reflux ratio of a binary distillation by Underwood's equation (saturated-liquid feed), Rmin = [xD/xF − α·(1−xD)/(1−xF)]/(α − 1), from the relative volatility (α) and the light-component mole fractions in the distillate (xD) and feed (xF). At minimum reflux, the column would need infinite plates; the operating reflux is a multiple of it (1.1–1.5×). It is a key number in column design. Enter α, xD and xF.

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Distribution Coefficient (Extraction)

Compute the distribution (or partition) coefficient of a liquid-liquid extraction, KD = concentration in the extract / concentration in the raffinate, the ratio of how the solute distributes between the two immiscible phases at equilibrium. A high KD means the solvent extracts the solute well, requiring fewer stages and less solvent. It is the central parameter of extractor design and solvent choice. Enter the extract and raffinate concentrations.

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Equilibrium Constant from Conversion

Compute the equilibrium constant of a simple A ⇌ B reaction from the equilibrium conversion, Keq = X/(1 − X), where X is the fraction of reactant converted when the reaction reaches equilibrium. It shows the direct relation between how far a reaction 'goes' and its Keq: high conversions (X→1) imply a large Keq (favorable reaction); X = 0.5 gives Keq = 1 (equilibrium in the middle). Enter the equilibrium conversion (fraction).

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Actual Plates (Efficiency)

Compute the number of actual plates of a distillation column, N_actual = N_theoretical / (efficiency/100), from the number of theoretical (equilibrium) plates and the column's overall efficiency (%). Since no real plate reaches perfect equilibrium, more actual plates than theoretical are needed: a 50% efficiency doubles the plate count. It is the step that turns the theoretical design into the physical column. Enter the theoretical plates and the overall efficiency.

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Optimum Reflux Ratio

Compute a distillation column's operating reflux ratio, R = factor · Rmin, multiplying the minimum reflux by a factor (typically 1.1 to 1.5). There is a classic economic trade-off: a low reflux (near minimum) requires many plates (more column investment); a high reflux requires fewer plates but much more energy in the reboiler and condenser (more operating cost). The optimum balances the two. Enter the minimum reflux and the factor.

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Decimal Reduction Time (D-Value)

Compute the decimal reduction time (D-value) of a microorganism, D = t/(log N₀ − log N), the time needed, at a given temperature, to destroy 90% of the population (a one-log reduction). It is the fundamental parameter of thermal death kinetics in food processing: the larger the D, the more heat-resistant the microorganism. Enter the heating time and the initial and final populations.

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F₀ Sterilization Value

Compute the F₀ value of a thermal process, F₀ = t·10^((T − 121.1)/z), the equivalent sterilization time at 121.1 °C (250 °F) with z = 10 °C, the reference for Clostridium botulinum. It is the universal 'currency' that compares thermal processes at different temperatures: an F₀ of 3 minutes is the minimum safety for low-acid canned foods (botulinum cook). Enter the time, the process temperature and the z-value.

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z-Value (Thermal Resistance)

Compute a microorganism's z-value, z = (T₂ − T₁)/(log D₁ − log D₂), the temperature change needed to alter the D-value (decimal reduction time) by a factor of 10. The z measures the microorganism's temperature sensitivity: the smaller the z, the more the destruction accelerates with heating. It is the basis of converting between processes at different temperatures (F₀, pasteurization). Enter two temperatures and their corresponding D-values.

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Pasteurization Units (PU)

Compute the pasteurization units (PU) of a process, PU = t·10^((T − Tref)/z), the lethal time equivalent at a reference temperature. Widely used for beer and juice (Tref = 60 °C, z = 7 °C): a beer needs ~15 PU for microbiological stability. It lets you compare and control pasteurizers operating at different time-temperature combinations. Enter the time, the process temperature, the reference temperature and the z-value.

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Moisture: Dry / Wet Basis

Convert a food's moisture from wet basis to dry basis, Xdb = Xwb/(1 − Xwb), where Xwb is the water fraction relative to total mass (wet basis) and Xdb relative to dry mass. The dry basis is preferred in drying calculations because the denominator (dry mass) does not change during the process, unlike the total mass. Confusing the two bases is a common and serious error. Enter the wet-basis moisture (fraction).

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Food Specific Heat (Choi-Okos)

Compute a food's specific heat by the Choi-Okos equations, cp = 4.18·Xwater + 1.55·Xprotein + 1.71·Xfat + 1.42·Xcarbohydrate + 0.91·Xash (kJ/kg·K), from the component mass fractions. Since water has a very high specific heat, wetter foods heat and cool more slowly. It is essential in computing the heat loads of cooking, refrigeration and freezing. Enter the water, protein, fat, carbohydrate and ash fractions.

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Microbial Lethality

Compute the lethality rate (L-value) of a thermal process, L = 10^((T − Tref)/z), the factor indicating how many times faster (or slower) microbial destruction at a temperature T is than at the reference temperature. Integrated over time, the lethality gives the process F-value. It is the basis of the general-method sterilization calculation, which sums the lethality over the product's actual thermal history. Enter the temperature, the reference temperature and the z-value.

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Food Water Activity

Compute a food's water activity (aw) from the equilibrium relative humidity, aw = ERH/100. Water activity — the 'free water' available for reactions and microorganisms — is the most important conservation factor: below aw 0.6 no microorganism grows; bacteria stop at ~0.90, molds at ~0.70. Unlike total moisture, it explains why honey (moist but with low aw) does not spoil. Enter the equilibrium relative humidity (%).

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Extraction Yield (Solid)

Compute the yield of a solid-liquid extraction, Y = (extract mass / sample mass)·100%, the fraction of raw material extracted by the solvent. It is used in processes such as the extraction of oils, caffeine, pectin, dyes and bioactive compounds from plant matrices. The yield assesses extraction efficiency and guides the optimization of solvent, temperature, time and solid-liquid ratio. Enter the extract mass and the sample mass.

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Potential Alcohol from Brix

Estimate the potential alcohol of a must (wine, beer, kombucha) from the sugar content in degrees Brix, %ABV ≈ Brix · 0.55, assuming complete fermentation of the sugars. Brix measures the soluble solids (mostly sugar) of the must; fermentation converts that sugar into alcohol and carbon dioxide. It is a quick estimate used by winemakers and brewers to predict the final strength. Enter the content in degrees Brix.

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Carnot COP (Refrigeration)

Compute the maximum theoretical coefficient of performance (COP) of a refrigerator, COP = Tc/(Th − Tc), with temperatures in kelvin, where Tc is the cold-source (evaporator) temperature and Th the hot-source (condenser). It is the limit set by the 2nd law of thermodynamics: no real refrigerator can exceed it. The smaller the temperature difference between the sources, the higher the possible COP — which is why refrigerating to very low temperatures is so costly. Enter the cold and hot temperatures in kelvin.

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Compressor Work (Isentropic)

Compute the specific compression work in an ideal refrigeration cycle, W = h₂ − h₁, the enthalpy difference between the compressor outlet and inlet (isentropic compression, at constant entropy). It is the energy the compressor adds to the refrigerant per kilogram — the cycle's 'electricity bill'. Together with the refrigerating effect, it defines the COP (COP = refrigerating effect/work). Enter the outlet and inlet enthalpies.

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Compressor Volumetric Efficiency

Compute a compressor's volumetric efficiency, ηv = (actual suction flow / volumetric displacement)·100%, the fraction of the piston-swept volume that actually pumps gas. Losses come from clearance volume (gas that re-expands), suction reheating and leakage. It drops as the compression ratio rises. It is a key indicator of compressor performance. Enter the actual suction flow and the volumetric displacement.

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Compression Ratio (Refrigeration)

Compute a refrigeration system's compression ratio, rc = Pcondensation/Pevaporation, the ratio of the compressor's absolute discharge to suction pressures. High ratios (above ~10) lower volumetric efficiency, raise the discharge temperature (risking oil and refrigerant degradation) and may require two-stage compression — common at low temperatures and in cryogenics. Enter the condensation and evaporation pressures (absolute).

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Superheat Degree

Compute the superheat of a refrigeration system, ΔT = T_suction − T_evaporation(saturation), how much hotter the refrigerant vapor is than its saturation temperature at the evaporator pressure. Proper superheat (typically 5–10 °C) ensures only vapor (no liquid) reaches the compressor, protecting it from liquid slugging. Too much superheat reduces capacity. It is controlled by the expansion valve. Enter the suction and saturated evaporation temperatures.

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Subcooling Degree

Compute the subcooling of a refrigeration system, ΔT = T_condensation(saturation) − T_liquid, how much colder the liquid refrigerant is than its saturation temperature at the condenser pressure. Proper subcooling (typically 4–8 °C) ensures pure liquid (no vapor bubbles) at the expansion-valve inlet, avoiding flash gas that reduces capacity. It increases the refrigerating effect. Enter the saturated condensation temperature and the liquid temperature.