Kinematics

6 calculators

Mechanics

25 calculators
Newton's laws

Newton's Second Law

F = m·a

Force, mass and acceleration — the heart of dynamics.

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Elasticity

Hooke's Law

F = −k·x

Spring force, stiffness, extension and stored elastic energy.

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Rotation

Torque

τ = r·F·sinθ

Turning effect of a force about a pivot.

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Circular motion

Circular Motion

a_c = v² / r

Centripetal acceleration and force for motion in a circle.

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Energy

Kinetic Energy

KE = ½·m·v²

Energy of motion — note the v² dependence.

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Energy

Gravitational Potential Energy

PE = m·g·h

Stored energy of a raised mass, on any world.

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Energy

Work & Power

W = F·d, P = W / t

Work done by a force and how fast it is delivered.

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Momentum

Momentum

p = m·v

Mass in motion, impulse and the change in momentum.

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Momentum

Center of Mass

x_cm = (m1·x1 + m2·x2 + m3·x3) / (m1 + m2 + m3)

Weighted-average balance point of two or three point masses.

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Friction

Friction

F = μ·N

Friction force from the coefficient of friction and the normal force.

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Forces

Inclined Plane

a = g(sinθ - μ·cosθ)

Full force set on a ramp — mg sinθ, mg cosθ, N, friction and acceleration — from mass, angle and friction.

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Rotation

Angular Velocity

ω = θ / t

How fast an angle is swept out — plus rpm to rad/s.

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Momentum

Collision

m1u1 + m2u2 = m1v1 + m2v2

Final velocities in elastic and inelastic collisions.

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Circular motion

Centripetal Force

F = m·v² / r

Inward force keeping an object moving in a circle.

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Elasticity

Spring Constant

k = F / x

Spring stiffness from force and extension, plus elastic energy.

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Energy

Power

P = W / t

Rate of doing work or transferring energy.

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Rotation

Moment of Inertia

I = k·m·r²

Rotational inertia for spheres, cylinders, rods and hoops.

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Momentum

Impulse

J = F·Δt

Impulse from force and time, equal to change in momentum.

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Circular motion

Banked Curve

tanθ = v² / (r·g)

Ideal banking angle or speed for a curve.

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Simple machines

Mechanical Advantage

MA = F_load / F_effort

The force-for-distance trade of a lever, pulley or ramp — MA, IMA and efficiency.

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Elasticity

Young's Modulus

E = (F·L0) / (A·ΔL)

Modulus of elasticity from stress and strain — E = stress/strain.

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Power

Power-to-Weight Ratio

PWR = P / m

Power divided by mass — the key performance ratio for engines and vehicles.

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Rotation

Coriolis Force

F = 2·m·ω·v·sinφ

The deflecting force felt in a rotating frame such as the spinning Earth.

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Rotation

Nm to ft-lb Converter

1 N·m = 0.73756 ft·lb

Convert torque between newton-metres and foot-pounds, both ways.

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Units and prefixes

SI Prefix Converter

result = v · 10^(a - b)

Convert a value between any two SI prefixes, quetta to quecto, or straight to the coherent SI unit.

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Gravitation

4 calculators

Fluid Mechanics

11 calculators

Waves & Oscillations

3 calculators

Waves & Optics

4 calculators

Optics

4 calculators

Thermodynamics

17 calculators
Gas laws

Ideal Gas Law

P·V = n·R·T

The four state variables of an ideal gas.

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Gas laws

Charles's Law

V1/T1 = V2/T2

Volume-temperature ratio of a gas at constant pressure.

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Gas laws

Boyle's Law

P1·V1 = P2·V2

Pressure-volume product of a gas at constant temperature.

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Thermal

Thermal Expansion

ΔL = α·L0·ΔT

How materials grow when heated.

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Calorimetry

Specific Heat

Q = m·c·ΔT

Heat energy to change a material temperature, Q = mcΔT.

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Calorimetry

Latent Heat Calculator

Q = mL

Energy for a phase change, Q = mL.

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Heat engines

Carnot Efficiency

η = 1 − T_c / T_h

Maximum efficiency of a heat engine between two temperatures.

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Radiation

Stefan-Boltzmann

P = σ·A·ε·T^4

Power radiated by a black body, P = σAεT^4.

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Conduction

Thermal Conduction (Fourier's Law)

Q/t = k·A·ΔT / d

Steady-state heat-conduction rate through a slab, Q/t = kAΔT/d.

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Gas laws

Gay-Lussac's Law

P1/T1 = P2/T2

Pressure-temperature ratio of a gas at constant volume.

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Radiation

Wien's Law

λ_max = b / T

Peak wavelength of black-body radiation, λmax = b/T.

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Gas laws

Gas Density

ρ = P·M / (R·T)

Density of an ideal gas from its pressure, molar mass and temperature.

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Thermochemistry

Enthalpy of Reaction

q = n · ΔH

Heat released or absorbed by a reaction from moles and molar enthalpy.

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Entropy

Entropy Change

ΔS = Q / T

Entropy change for reversible heat transfer at constant temperature.

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Reaction kinetics

Activation Energy

Ea = R·ln(k2/k1) / (1/T1 − 1/T2)

Arrhenius activation energy from two rate constants at two temperatures.

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Heat

Water Heating Energy

q = m·c·ΔT, t = q / P

Energy and time to heat water, from q = mcΔT.

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Psychrometrics

Wet-Bulb Temperature

Tw = f(T, RH) (Stull 2011)

Wet-bulb temperature from air temperature and relative humidity.

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Electromagnetism

16 calculators
Circuits

Ohm's Law

V = I·R, P = I·V

Voltage, current, resistance and power in a circuit.

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Circuits

Electric Current

I = Q/t

Current as the rate of charge flow, I = Q/t, with the electron count.

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Circuits

Potential Difference

V = W/Q

Potential difference as energy per unit charge, V = W/Q.

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Resistance

Resistivity

R = ρL / A

Wire resistance from material resistivity and geometry, R = ρL/A.

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Circuits

Kirchhoff's Law

Sum I = 0, Sum V = 0

Solves the two-loop circuit for all three branch currents.

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Circuits

RMS Voltage

Vrms = V0 / sqrt(2)

Convert between peak, peak-to-peak and RMS voltage, plus AC power.

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Electrostatics

Coulomb's Law

F = k·q1·q2 / r²

Electrostatic force between two point charges.

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Circuits

Resistor

Series: ΣR · Parallel: 1/Σ(1/R)

Total resistance of resistors wired in series or parallel.

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Energy use

Electricity Cost

Cost = kWh × rate

Running cost of an appliance from wattage, hours and rate.

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Electrostatics

Electric Field

E = k·Q / r²

Electric field strength around a point charge.

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Capacitors

Capacitance

C = Q / V

Capacitance from charge and voltage, plus stored energy.

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Magnetism

Magnetic Force

F = q·v·B·sinθ

Lorentz force on a moving charge in a magnetic field.

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Magnetism

Magnetic Field

B = μ0·n·I

Magnetic field inside a solenoid, B = μ0nI.

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Induction

Faraday's Law Calculator

ε = −N ΔΦ/Δt

Induced EMF from a changing magnetic flux, ε = −N ΔΦ/Δt.

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Circuits

RC Time Constant

τ = R·C

Charging time constant of an RC circuit, τ = RC.

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Circuits

Cutoff Frequency

fc = 1 / (2π·R·C)

The -3 dB corner frequency of an RC filter.

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Modern Physics

8 calculators