Science Calculators

Newton's second law: enter mass and acceleration, get force in newtons. Step-by-step working and pound-force conversion shown.

Compute mechanical work from force, displacement, and the angle between them. Result in joules with calorie and foot-pound conversions.

Compute the kinetic energy of a moving object from its mass and speed. Result in joules with kcal and ft·lb conversions.

Energy stored in an object lifted to a height. Enter mass, height, and (optionally) the gravity of another planet.

Compute linear momentum from mass and velocity. Result in kg·m/s, with a comparison to a typical small car at highway speed.

Compute impulse from force and contact time, or use it to find the change in velocity for a given mass.

Compute average velocity from total displacement and elapsed time. Result in m/s with km/h and mph conversions.

V = IR, P = IV = I²R = V²/R. Pick which two values you know and solve for the others.

P = IV — compute power from voltage and current, or from voltage and resistance, or current and resistance.

Compute electric field from a point charge: E = kQ/r², or from force/charge: E = F/q.

C = Q/V or parallel-plate C = ε₀A/d. Compute capacitance, charge stored, or energy.

L = μ₀N²A/ℓ for an ideal solenoid, or V = L(dI/dt) for the defining equation.

τ = RC. Time for an RC circuit to charge to ~63% (or discharge to ~37%) of final value.

1/R = 1/R₁ + 1/R₂ + … — find equivalent resistance of resistors in parallel.

R_total = R₁ + R₂ + R₃ + … — find equivalent resistance of resistors in series.

Sum of voltages around a closed loop = 0. Solve a 2-loop circuit with two batteries and three resistors.

M = moles solute / liters solution. The most common solution-concentration unit in chemistry.

m = moles solute / kg solvent. Used in colligative-property calculations (boiling-point elevation, freezing-point depression).

Compute molar mass from a chemical formula. Supports common elements; multi-character symbols and subscripts.

Convert between moles and grams using molar mass.

Find target volume or concentration when diluting a stock solution.

pH = -log[H⁺]. Compute pH from hydrogen-ion concentration in mol/L.

pH + pOH = 14 at 25°C. Convert one to the other.

Percent yield = (actual / theoretical) × 100. Quantifies reaction efficiency.

Compute theoretical yield (g) from moles of limiting reactant, stoichiometric ratio, and product molar mass.

For a reaction with two reactants A and B in ratio a:b, find which one runs out first.

Convert mechanical (imperial) horsepower to watts. 1 hp = 745.7 W.

Convert watts to horsepower. 1000 W ≈ 1.341 hp (mechanical).

Convert British thermal units to kilowatt-hours. 1 BTU ≈ 0.000293 kWh.

Convert kilowatt-hours to BTU. 1 kWh = 3,412 BTU.

1 cal (thermochemical) = 4.184 J. 1 kcal (food calorie) = 4,184 J.

1 J ≈ 0.239 cal (small) ≈ 0.000239 kcal (food calorie).

Watts = lumens / efficacy. Modern LEDs hit 100-150 lm/W, vs incandescent ~15 lm/W.

c = λν. Convert between wavelength and frequency for any electromagnetic wave.

For atomic and particle-physics scales: 1 eV = 1.602176634 × 10⁻¹⁹ J.

Bidirectional conversion among Hz / kHz / MHz / GHz / THz.

a = (v_f − v_i) / t. Average acceleration from initial + final velocity over time.

f = μ × N. Force resisting motion between contacting surfaces.

N = m × g × cos(θ). Component of weight perpendicular to incline surface.

W = m × g_planet. Earth weight × planet gravity ratio.

F = −k × x. Spring force is proportional to displacement from equilibrium.

k = F / x. Determine spring stiffness from a known force and displacement.

F_c = m × v² / r. Force required to keep object in circular motion.

Range, max height, time of flight from launch speed and angle (level ground, no air drag).

d = ½ g t² and v = g t. Distance and final velocity for an object falling from rest.

v_e = √(2GM/r). Speed needed to escape gravitational pull of body.

T = 2π √(L/g). Period of a simple pendulum (small angles).

ω = Δθ / Δt = 2π·f. Conversion between rad/s, rev/min, and Hz.

τ = r × F × sin(θ). Rotational force = lever arm × applied force × angle.

n₁ sin θ₁ = n₂ sin θ₂. Refraction angle from indices and incidence.

1/f = 1/d_o + 1/d_i. Solve for any of focal length, object distance, image distance.

1/f = 1/d_o + 1/d_i. Same form as lens but with mirror sign conventions.

For spherical mirror: f = R/2. For thin lens: 1/f = (n−1)(1/R₁ − 1/R₂) (lensmaker).

M = -d_i/d_o = h_i/h_o. Linear magnification of a lens or mirror.

c = λ × ν. Wavelength in vacuum from frequency or vice versa. c = 3×10⁸ m/s.

Solve for any of P, V, n, T given the other three. R = 8.314 J/(mol·K).

Constant T, constant n: pressure × volume = constant.

Constant P: volume scales linearly with absolute temperature.

At constant T, P: volume scales with number of moles.

When n is constant, all of P, V, T can change. Solve for any one.

Σ (isotope mass × abundance fraction). Periodic-table atomic mass from isotope mix.

t½ = ln(2) / k. Convert between half-life and decay constant; predict remaining fraction.

Quantity remaining after time t given decay constant k or half-life.

pH = pKa + log([A⁻]/[HA]). Predict buffer pH from acid + conjugate base concentrations.

Given a balanced equation's coefficients + moles of one species, compute moles of all others.

1 knot = 1.15078 mph = 1.852 km/h. Bidirectional, also m/s.

Beaufort 0-12: from "calm" (0 mph) to "hurricane" (>72 mph).

Surface gravity table for solar system bodies.

R = F + 459.67. Rankine is absolute (0 = absolute zero); Fahrenheit + 460.

1 bar = 14.5038 psi = 100 kPa = 0.987 atm.

1 atm = 1.01325 bar = 14.696 psi.

Convert seconds to days/hours/minutes/seconds; auto-format hh:mm:ss.

1 g/cm³ = 1000 kg/m³. Water = 1 g/cm³ = 1000 kg/m³.

Pa·s ↔ cP (centipoise) ↔ Poise. 1 Pa·s = 1000 cP = 10 Poise.

Resize an image to a new width or height while preserving the original aspect ratio — with preset 16:9, 4:3, 1:1, 21:9.

Estimate annual tCO₂e from electricity, gas, driving, flights, and diet — EPA / DEFRA emission factors.

One-way and round-trip light-time across interplanetary distances. c = 299,792,458 m/s exactly (SI defining constant).

Apparent temperature when wind cools exposed skin. Uses the NWS / Environment Canada 2001 formula (valid for T ≤ 50 °F, V ≥ 3 mph).

Apparent temperature combining air temperature and relative humidity. NWS Rothfusz regression with Steadman 1979 baseline.

Temperature at which air becomes saturated (100% RH). Magnus / August-Roche-Magnus equation — accurate to ±0.4 °C over normal range.

Decode resistance, tolerance, and (6-band) temperature coefficient from IEC 60062 color rings.

Vout = Vin · R2 / (R1 + R2). Solve for any one of Vin/R1/R2/Vout given the other three.

R = (V_supply − V_LED) / I_LED. Required series-resistor value to safely drive an LED at a target current.

dB = 10·log₁₀(P₂/P₁) for power; 20·log₁₀(V₂/V₁) for voltage; absolute scales dBSPL / dBm / dBW / dBV / dBu.

Illuminance (lux) = luminous flux (lm) ÷ area. Inverse-square law for point sources at distance.

Estimate how long a battery lasts from its capacity (mAh) and the device load current (mA), with an adjustable efficiency factor.

Calculate total dynamic head from static lift plus pipe friction loss using the Hazen-Williams equation, with flow velocity and pressure output.

How long you can safely listen at a given dB SPL level before hearing damage risk — per NIOSH (3 dB exchange) and OSHA (5 dB exchange) limits.

Source + load impedance — power transfer efficiency, mismatch loss in dB, and pass/fail vs the 1:1 ideal.

First-order passive crossover: solve for fc, capacitance, or inductance given driver impedance and the other two values.

Frequency → physical antenna length for quarter-wave and half-wave designs, with velocity-factor correction for thin-wire construction.

Cable type + frequency + length → total RF loss in dB and percent of power surviving the run.

Forward + reflected power → SWR, reflection coefficient ρ, and return loss — the three standard antenna-matching metrics.

Coax or parallel-wire dimensions + dielectric → characteristic impedance Z₀.

Input watts + output watts → efficiency η, heat dissipation, and 80 PLUS-style rating.

Load watts + desired runtime hours + battery voltage → required battery capacity in Ah and Wh (with safety margin).

Cell voltage + cell capacity + series count + parallel count → pack voltage, capacity, and total energy.

Primary V + secondary V → turns ratio. Also computes secondary current and reflected impedance.