Science & engineering calculators
Established scientific relationships with consistent SI units. Each page names the equation it uses and the conditions where it applies.
Chemistry
- Molarity CalculatorFind the grams of solute needed for a solution of given molarity and volume, or the molarity or volume from the others, in mol/L or mmol/L.
- Molecular Weight CalculatorType a chemical formula such as C6H12O6, Ca(OH)2 or CuSO4·5H2O to get its molar mass in g/mol and the mass percentage of each element.
- Mole to Mass CalculatorConvert moles to grams or grams to moles with the molar mass, and see the number of particles using the exact Avogadro constant.
- Limiting Reagent CalculatorFind which reactant runs out first in aA + bB → cP, the theoretical yield of product in grams and how much of the excess reactant is left over.
- Solution Dilution CalculatorWork out how much stock solution to dilute, the final volume or either concentration with C₁V₁ = C₂V₂, plus the diluent to add and the dilution factor.
- Solution pH CalculatorCalculate pH, pOH, [H⁺] and percent ionisation for strong or weak acids and bases from concentration and pKa or pKb, solving the full charge balance.
- Acid–Base Titration CalculatorFind the concentration of an acid or base from a titration: titrant molarity, end-point volume, sample volume and the mole ratio in the balanced equation.
Electrical
- Voltage Drop CalculatorEstimate the voltage drop along a copper or aluminium cable from its size (mm² or AWG), length and current, for DC, single-phase or three-phase.
- Resistor CalculatorDecode the colour bands on a 4-, 5- or 6-band resistor into its resistance, tolerance, minimum and maximum value and temperature coefficient.
- Ohm’s Law CalculatorEnter any two of voltage, current, resistance and power to calculate the other two with Ohm’s law (V = I × R) and the power law (P = V × I).
- Electric Power CalculatorCalculate real power in watts, apparent power in VA and reactive power in var from voltage, current and power factor, with daily energy in kWh.
- Capacitor Energy CalculatorCalculate the energy stored in a capacitor and its charge from capacitance in F, mF, µF, nF or pF and the voltage across it, using E = ½CV² and Q = CV.
- Resistors in Series and Parallel CalculatorEnter any list of resistor values to get the equivalent resistance in series and in parallel, using R = R₁ + R₂ + … and 1/R = 1/R₁ + 1/R₂ + ….
- Inductive Reactance CalculatorFind the reactance of an inductor in ohms at any frequency from its inductance in H, mH or µH and the frequency in Hz, kHz or MHz, with angular frequency.
- AC Impedance CalculatorCalculate the impedance, phase angle, power factor and current of a series RLC circuit from R, L, C, frequency and voltage, with the resonant frequency.
- RC Time Constant CalculatorFind the time constant τ = R × C of a resistor–capacitor circuit, the capacitor voltage at any time while charging or discharging, and the RC cut-off frequency.
- RL Time Constant CalculatorCalculate the time constant τ = L ÷ R of a resistor–inductor circuit, the inductor current at any time as it rises or decays, and the RL cut-off frequency.
Electrochemistry
Growth & decay
- Exponential Population Growth CalculatorProject a population with exponential growth, continuous (N₀e^(rt)) or per-period ((1 + r)^t), with the doubling or halving time and a growth curve.
- Logistic Growth CalculatorProject an S-shaped logistic population curve from the starting size, carrying capacity and growth rate, with the time of fastest growth and a chart.
Heat transfer
- Conduction Heat Flow CalculatorCalculate steady heat flow through a flat layer from its thermal conductivity, area, thickness and temperatures, with heat flux, R-value and U-value.
- Convection Heat Transfer CalculatorFind the convective heat flow between a surface and the surrounding air or liquid from the heat transfer coefficient, area and temperature difference.
- Stefan–Boltzmann Radiation CalculatorCalculate net thermal radiation between a grey surface and large surroundings with Q = εσA(Ts⁴ − Tsur⁴), plus emitted power and radiative coefficient.
Mechanics
- Horsepower CalculatorCalculate power in horsepower, metric horsepower (PS), kilowatts and watts from torque and engine speed, or from force, distance and time.
- Engine Horsepower CalculatorEstimate a car’s engine horsepower from its weight and quarter-mile elapsed time or trap speed, using Patrick Hale’s drag-racing formulas.
- Kinetic Energy CalculatorFind kinetic energy from mass and speed, or the speed or mass behind a given energy, with J, kJ, kWh, kcal and ft·lbf and km/h, mph or m/s.
- Potential Energy CalculatorWork out gravitational potential energy from mass and height, or the height or mass for a given energy, with any value of g and common units.
- Force Calculator (F = ma)Use Newton’s second law to find force from mass and acceleration, or mass or acceleration from the other two, in N, kN, lbf, kgf, m/s² or g.
- Momentum CalculatorCalculate linear momentum from mass and velocity, or find the mass or speed for a given momentum, plus the matching kinetic energy.
- Impulse CalculatorFind impulse from force and contact time, or from a mass’s change in velocity, and the average force during an impact or push.
- Centripetal Force CalculatorFind the centripetal force for an object moving in a circle, or the speed or radius it allows, with speed in m/s, km/h, mph, rpm or rad/s.
- Projectile Range CalculatorCalculate how far a projectile travels from launch speed, angle and launch height, with flight time, peak height, impact speed and a range-by-angle table.
- Projectile Maximum Height CalculatorFind the highest point of a projectile’s path from launch speed and angle, or the launch speed needed to reach a chosen peak height.
- Hooke’s Law CalculatorFind a spring’s constant from a load and its stretch, or the force or extension from the other two, with the elastic energy stored in the spring.
Mechanics of materials
- Beam Deflection CalculatorMaximum deflection, bending moment and shear for a simply supported or cantilever beam under a point load or uniform load, from E, I and span.
- Euler Buckling Load CalculatorFind the Euler critical buckling load π²EI ÷ (KL)² of a slender column, its slenderness ratio and critical stress, and check it against yield strength.
- Torsion Stress CalculatorCalculate the maximum shear stress τ = Tr ÷ J and the angle of twist of a solid or hollow circular shaft under torque, with the polar moment J.
- Young’s Modulus, Stress and Strain CalculatorCalculate stress, strain and Young’s modulus from a tensile test, or predict how far a bar stretches under load from its modulus, with σ = F/A and E = σ/ε.
- Poisson’s Ratio CalculatorCalculate Poisson’s ratio ν = −ε_lateral ÷ ε_axial from dimension changes or measured strains, plus volumetric strain and shear and bulk moduli from E.
- Factor of Safety CalculatorWork out the factor of safety (strength ÷ applied stress or load), the margin of safety against a required factor, utilisation and the allowable value.
- Bolt Torque CalculatorConvert between bolt tightening torque and clamp preload with T = K × F × d, and check the bolt stress as a percentage of its proof load.
Oscillations
- Simple Harmonic Motion Period CalculatorFind the period and frequency of a mass on a spring, or the mass or spring constant for a target period, with peak speed, acceleration and energy.
- Pendulum Period CalculatorFind a simple pendulum’s period from its length, or the length for a target period, using the exact large-swing correction as well as 2π√(L/g).
Physics & materials
- Density CalculatorFind density from mass and volume, or the mass or volume from the other two, with results in kg/m³, g/cm³ and lb/ft³ and mixed metric and imperial units.
- Weight CalculatorConvert a mass in kg or lb into weight (the force of gravity) in newtons, kilogram-force and pound-force on Earth, the Moon and the planets.
Pressure & fluids
- Pressure CalculatorCalculate pressure from a force spread over an area, or the force or area for a given pressure, in Pa, kPa, MPa, bar, psi, atm or mmHg.
- Hydrostatic Pressure CalculatorWork out gauge and absolute pressure at a depth in water or any liquid, or the depth that gives a chosen pressure, from density, depth and g.
- Buoyancy CalculatorCalculate the buoyant force on a submerged volume with Archimedes’ principle, and compare it with an object’s weight to see whether it floats or sinks.
- Flow Rate CalculatorFind the volumetric flow rate in a round pipe from its bore and flow velocity, or the velocity or bore for a given flow, in L/s, L/min, m³/h or US gpm.
- Reynolds Number CalculatorCalculate the Reynolds number from velocity, pipe diameter and dynamic or kinematic viscosity, and see whether pipe flow is laminar, transitional or turbulent.
- Bernoulli Equation CalculatorApply Bernoulli’s equation between two points in a flow to find the downstream pressure and pressure difference, or the velocity at the second point.
Signals
- Signal-to-Noise Ratio CalculatorCalculate signal-to-noise ratio in decibels from signal and noise powers, RMS voltages or dBm levels, with the equivalent power and amplitude ratios.
- Decibel to Power Ratio ConverterConvert two power levels into decibels, or a gain or loss in dB into power and voltage ratios, and apply it to a reference power to find the output.
- FFT Frequency Bin CalculatorFind the FFT bin spacing fs ÷ N, the Nyquist frequency, the number of bins and record length, and which bin a given frequency falls into.
- Nyquist Rate CalculatorFind the Nyquist rate (twice the highest frequency) for a signal, check whether a sample rate is high enough, and see where an undersampled tone aliases.
Thermodynamics
- Ideal Gas Law CalculatorSolve the ideal gas law for pressure, volume, amount of gas or temperature, with kPa, bar, atm or psi, litres or m³, and kelvin, °C or °F.
- Gas Density CalculatorFind the density of any gas from its pressure, temperature and molar mass using the ideal gas law, with molar volume and specific volume.
- Heat Capacity CalculatorWork out the heat needed to warm or cool a mass, or find a material’s specific heat from measured heat and temperature change, using Q = mcΔT.
- Calorimetry Heat Transfer CalculatorFind the equilibrium temperature when a hot object meets water or another body, and the heat exchanged, with an optional calorimeter heat capacity.
- Thermal Expansion CalculatorCalculate how much a rod, pipe, rail or volume of liquid grows or shrinks with temperature, from its expansion coefficient and temperature change.
Waves & optics
- Frequency and Wavelength CalculatorConvert between frequency and wavelength with λ = v ÷ f, using the exact speed of light in vacuum or your own wave speed, such as sound in air.
- Thin Lens Equation CalculatorSolve the thin lens equation 1/f = 1/do + 1/di for image distance, object distance or focal length, with magnification, image type and lens power.
- Photon Energy CalculatorFind the energy of a photon from its wavelength, frequency or energy in eV with E = hf = hc/λ, using the exact SI values of h, c and the elementary charge.
Work, energy & power
- Work CalculatorCalculate the mechanical work done by a force over a distance at any angle, or the force or distance for a given amount of work, in J, kJ or ft·lbf.
- Mechanical Power CalculatorFind power from work and time or from force and speed, or the work done or time needed at a given power, in watts, kilowatts and horsepower.