Reduced Mass Calculator (μ = m₁·m₂ / (m₁ + m₂))

Enter any two of voltage, current, resistance, or power — the calculator solves for the other two using V = IR and P = VI.

Enter any two of distance, time and speed to get the third — with km/h, mph, m/s, km, miles, hours and minutes supported.

Compute density from mass and volume (ρ = m / V), or solve for the missing variable. Built-in reference table for 19 common substances.

Enter launch speed, angle and height to compute projectile range, peak height and flight time (no air resistance). Pick from Earth, Moon, Mars and more.

Compute the wind chill (feels-like temperature) from air temperature and wind speed using the 2001 Environment Canada / US NWS formula, with frostbite risk levels.

Compute dew point from air temperature and relative humidity using the Magnus formula — handy for HVAC, photography and weather analysis.

Compute kinetic energy KE = ½ m v² with mixed units (kg / g / lb and m/s / km/h / mph) and see the result in joules, kilojoules, food calories, foot-pounds and watt-hours.

Enter any three of initial amount, remaining amount, elapsed time and half-life to solve for the fourth — useful for radioactive decay, drug pharmacokinetics and radiometric dating.

Pick the colour bands and instantly read the resistance and tolerance — 4-band and 5-band notations supported, with Ω / kΩ / MΩ formatting and a closest E12 / E24 preferred-value check.

Enter two latitude/longitude pairs to compute the great-circle distance using the haversine formula (km, miles, nautical miles), with bearing and midpoint.

Solve any one of C₁, V₁, C₂, V₂ from the dilution equation C₁V₁ = C₂V₂ — a daily lab essential for chemistry, biology and pharmacy work.

Two 80 dB sound sources do not equal 160 dB. Enter multiple dB values to compute the combined SPL, and subtract background noise to recover the signal alone.

Enter up to 8 resistor values to see the series total (R₁ + R₂ + …) and the parallel total (1 / Σ(1/Rᵢ)) at the same time.

Convert between electromagnetic wavelength and frequency via c = λf, with the matching spectrum band (radio / microwave / visible / X-ray / γ) and photon energy.

Compute the capacity of vertical or horizontal cylindrical, rectangular and spherical tanks, including partial-fill volumes at a given liquid level.

Enter the pendulum length and local gravity to get the period, frequency and angular frequency, with Earth/Moon/Mars/Jupiter presets — and reverse-solve for the length needed to hit a target period.

Enter air temperature and relative humidity to get the apparent temperature (NOAA Rothfusz heat index) and the corresponding heat-stress risk band.

Enter speed, reaction time and road friction to estimate reaction, braking and total stopping distance.

Enter the refractive indices of two media and an angle of incidence — get the refraction angle and critical angle from Snell's law (n₁ sin θ₁ = n₂ sin θ₂).

Enter capacitance (F, mF, µF, nF, pF) and voltage to compute the stored energy (E = ½CV²) and charge (Q = CV) on a capacitor.

Enter altitude to compute the boiling point of water (°C / °F) and local air pressure using the ICAO standard atmosphere and the Antoine equation — useful for hiking, cooking and high-altitude baking.

Solve Q = m × c × ΔT for any one of heat energy, mass, specific heat capacity or temperature change — with presets for water, aluminium, iron, copper, glass, air and more.

Convert between pH, pOH, hydrogen-ion concentration [H⁺] and hydroxide concentration [OH⁻] — with acid / neutral / alkaline classification.

Pick the unknown (P, V, n or T), enter the other three and PV = nRT is solved instantly — works in Pa / kPa / atm / bar / mmHg / psi, m³ / L / mL, mol / mmol / kmol and K / °C / °F.

Enter two point charges and the separation distance to compute the electrostatic force between them via F = kₑ·q₁·q₂/r² (attractive or repulsive).

Enter two masses and the distance between them to compute the gravitational attraction via F = G·m₁·m₂/r².

Given any two of the three quantities (object distance u, image distance v, focal length f), solve for the remaining one and the lateral magnification.

Enter the observer eye height above the surface to compute the distance to the geometric and refraction-corrected horizon.

Given any two of spring constant k, displacement x or restoring force F, solve for the third and the elastic potential energy U = ½kx².

Enter fluid density, submerged volume and gravitational acceleration to compute the buoyant force F = ρ V g, plus whether the object floats, sinks or stays neutral.

Enter the input voltage and two series resistor values to find the divider output voltage, current and power dissipated in each resistor.

Enter the mass and radius of a celestial body (or pick Earth, Moon, Mars and other presets) to compute the minimum surface launch speed v = √(2GM/r) needed to escape its gravity.

Enter the source frequency, observer/source velocities and wave speed (sound or light) to compute the observed frequency shift due to the Doppler effect.

Enter initial temperature, ambient temperature, cooling constant and elapsed time to estimate an object's temperature with T(t) = T∞ + (T₀ − T∞)·e^(−kt), plus half-cooling time and time constant.

Enter mass and radius, then linear speed, angular speed or period, and instantly read off centripetal force F = m·v²/r, centripetal acceleration, tangential speed, angular speed, period and frequency.

Enter inductance L (H) and capacitance C (F) to compute the resonant frequency f = 1 / (2π√(LC)) of an LC tank circuit, plus its period and angular frequency.

Enter the air temperature and compute the speed of sound in dry air using v = 331.3 × √(1 + T/273.15) — output in m/s, km/h, mph, ft/s plus the "count-the-seconds" thunder distance rule.

Enter fluid density, velocity, characteristic length and viscosity to compute the Reynolds number and classify the flow as laminar, transitional or turbulent.

Enter the spring constant k and displacement x to instantly compute the elastic potential energy stored in a Hookean spring via U = ½·k·x², with conversions to kJ, kcal, ft·lbf and Wh for easy comparison.

Use A = ε·c·ℓ to compute absorbance, transmittance and concentration — any three of the four inputs determines the fourth.

Compute orbital period from semi-major axis and central body mass via T² = 4π²·a³/GM, or invert to recover the semi-major axis — with presets for the Sun, Earth, Moon and Jupiter.

Enter fluid density, velocity, drag coefficient Cd and frontal area and compute the drag force from Fd = ½·ρ·v²·Cd·A — handy for cycling, automotive, ballistic and skydiving scenarios.

Compute the hydrostatic pressure P = ρ·g·h from fluid density, depth and gravity, and convert it to kPa, bar, psi, atm, mmHg and metres of water — useful for diving, aquariums and piping.

Enter pKa together with the conjugate-base [A⁻] and weak-acid [HA] concentrations and apply the Henderson–Hasselbalch equation to compute buffer pH, the buffer ratio and the effective buffering range.

Enter mass, incline angle and friction coefficients (or pick a preset like steel-on-steel or rubber-on-concrete) to compute normal force N, maximum static friction fs,max = μs·N, kinetic friction fk = μk·N and the critical angle θc — and instantly see whether the block stays at rest or slides down the slope.

Enter driving and driven gear tooth counts plus input RPM and torque to compute gear ratio, output RPM, output torque and mechanical advantage.

Enter solute mass, molecular weight and solution volume to compute molarity (mol/L); solve for any one unknown.

Convert moment magnitude (Mw) to released energy (joules and TNT equivalent) via the Gutenberg–Richter relation log₁₀E = 1.5M + 4.8, with a comparison to landmark historical earthquakes.

Enter the actual mass of product recovered and the theoretical yield to compute % yield = actual ÷ theoretical × 100%, with an indicative classification (poor / moderate / good / excellent).

Pick a common shape (solid sphere, hollow sphere, solid cylinder, thin-walled cylinder, thin disk, slender rod about centre or end, rectangular plate) and enter mass and dimensions to get the rotational moment of inertia I = k·m·r² / k·m·L².

Enter air temperature, barometric pressure and relative humidity to compute air density (kg/m³) via the CIPM partial-pressure form and the Magnus-Tetens saturation vapour pressure — useful for cyclists, runners, pilots and aerodynamics estimates.

Enter a fall height (and optional mass / gravity) to compute fall time, impact velocity and kinetic energy via h = ½·g·t² and v = √(2·g·h). Preset gravities for Earth, Moon, Mars and more.

Enter a chemical formula (e.g. H2SO4, Ca(OH)2, CuSO4·5H2O) and the tool sums the IUPAC standard atomic weights element by element to return the molar mass in g/mol — useful for chemistry homework and lab weighing.

Enter any two of force, mass and acceleration and the tool solves for the third — handy for high-school physics, machine design, vehicle braking and elevator safety factors.

Enter mass and molar mass (g/mol), or moles, and the tool converts via n = m / M, also reporting the particle count N = n · Nₐ — the everyday workhorse of chemistry lab weighing and stoichiometry problems.

Enter a velocity v (as a fraction of c or in m/s) and compute the special-relativity Lorentz factor γ = 1/√(1 − v²/c²), together with the time-dilation factor, the length-contraction ratio and the relativistic kinetic energy.

Enter surface area A, temperature T (kelvin) and emissivity ε, then compute the radiant power P = ε σ A T⁴ under the Stefan–Boltzmann law — the standard formula for thermal radiation, the solar constant and stellar luminosity estimates.

Enter the moles (or mass + molar mass) of each component in a mixture and compute the mole fraction xᵢ = nᵢ / Σ nⱼ for every component, with the total checked to equal 1 — used in Raoult's law, gas mixtures and thermodynamic analysis.

Enter mass, frontal area, drag coefficient and air density and the tool returns the terminal velocity v_t = √(2mg / (ρ·A·Cd)) — the speed at which drag balances gravity, with presets for skydivers, raindrops, baseballs and feathers.

Enter applied force, cross-sectional area, original length and the change in length. The tool returns the engineering stress σ, strain ε, Young's modulus E = σ/ε and the elongation, alongside a reference table of common materials (steel, copper, aluminium, concrete, rubber).

Enter a mass (or energy) and the tool uses Einstein's E = mc² to compute the other side, expressing the result in joules, kilowatt-hours, megatonnes of TNT and electron-volts — and showing just how staggering even 1 g of fully-converted matter is.

Enter elevation, velocity and pressure at two points and the tool applies P + ½ρv² + ρgh = constant from Bernoulli's equation to solve for the missing variable — the foundation of pipe flow, Venturi meters, Pitot tubes and aerofoil lift.

Enter the spring constant k and mass m; the tool returns the simple-harmonic period T = 2π√(m/k), frequency f and angular frequency ω, and can also solve for k — the foundation of physics labs, mechanical vibration and MEMS sensor design.

Enter resistance R and capacitance C; the tool returns the RC circuit time constant τ = R × C, the 63.2% / 99.3% charging times (1τ / 5τ) and the voltage percentage at any time t during charging or discharging — the workhorse for electronics design, RC filters, oscillator timing and Arduino debounce.

Enter hot-reservoir temperature T_h and cold-reservoir T_c (units auto-handled in °C / K / °F); the tool returns the Carnot maximum efficiency η = 1 − T_c / T_h, the thermodynamic upper bound for any real heat engine — IC engines, thermal power stations and refrigerators.

Enter any one of linear speed, radius, period, frequency or RPM; the tool interconverts angular velocity ω (rad/s), frequency f (Hz), period T, revolutions per minute (RPM) and rim speed v — for circular motion problems, motor specs, orbital mechanics, centrifuges and any spinning object.

Enter a wavelength or frequency; the tool applies the Planck relation E = hf = hc/λ to return the energy of a single photon in joules and electron-volts (eV), plus the visible-light colour band where applicable — the foundation of physics, chemistry and spectroscopy problems.