Physics
Motion with constant acceleration, projectiles and free fall, force, energy, momentum, torque, work and power, pressure, waves, refraction and the Doppler effect.
Acceleration Calculator
Acceleration from a change in velocity over a time, or any two of initial velocity, final velocity, acceleration, displacement and time from the other three.
Kinetic Energy Calculator
The kinetic energy of a moving mass, ½mv², or the mass or speed that gives a kinetic energy, with its momentum.
Potential Energy Calculator
Gravitational potential energy, mgh, or the energy stored in a spring, ½kx², and the mass, height, spring constant or stretch from an energy.
Force Calculator
Force from mass and acceleration by Newton’s second law, F = ma, or the mass or acceleration from the other two, in newtons or pounds-force.
Projectile Motion Calculator
How far, how high and how long a projectile flies from its launch speed, angle and height, with the speed and angle it lands at, ignoring air resistance.
Free Fall Calculator
How long something dropped from a height takes to fall and how fast it lands, or how far it falls in a time, with no air resistance.
Torque Calculator
Torque from a force and a lever arm at any angle, τ = rF sin θ, or the force or arm length needed for a torque, in newton metres or pound-feet.
Momentum Calculator
Momentum from mass and velocity, p = mv, or the mass or velocity from a momentum, plus impulse, FΔt, and the average force behind a change in velocity.
Work and Power Calculator
The work a force does over a distance, W = Fd cos θ, and the average power, P = W ÷ t, or the energy or time from a power.
Wavelength Calculator
Wavelength from frequency, or frequency from wavelength, for light and radio at the speed of light or any wave at a speed you enter, with the photon energy.
Pressure Calculator
Pressure from a force spread over an area, P = F ÷ A, or the force a pressure exerts on an area, or the area a force needs to reach a pressure.
Snell’s Law Calculator
The angle light bends to as it crosses from one material into another, n₁ sin θ₁ = n₂ sin θ₂, or either index or the incident angle, with the critical angle.
Doppler Effect Calculator
The frequency you hear from a moving source or while moving yourself, from the emitted frequency, the speed of sound and each speed and direction.
Each page here solves one relationship from an introductory mechanics or waves course, from whichever values you know, and shows the formula with your numbers in it. Units are converted on the way in and the arithmetic runs in SI, so pounds, feet and miles per hour mix freely with kilograms and metres. The motion pages assume constant acceleration and no air resistance, which is exact on paper and close for a dense, slow object over a short distance, but not for a feather, a parachute or a long-range shot. Where gravity enters, the pages start from standard gravity, 9.80665 m/s², and let you change it for a textbook's 9.8, a precise local value or another planet. Signs carry direction: a negative acceleration slows something moving the positive way, and a displacement below the start is negative. Refractive indices and the speed of sound are entered rather than assumed, because both depend on the material and the temperature. Nothing here rates a part, a load or a structure; that needs a qualified engineer and the rules that apply where you are.