Calculators
Kinetic Energy Calculator
Solve kinetic energy, mass, or speed with unit conversion.
Use KE = ½mv² to calculate kinetic energy, or rearrange the formula to solve for mass or speed. Common mass and speed units are converted automatically.
Calculated kinetic energy
9 J
KE = ½mv²
About This Tool
Kinetic energy is the energy an object has because it is moving. For ordinary non-relativistic motion, it depends on mass and on the square of speed, so doubling speed produces four times the kinetic energy when mass stays the same. This calculator solves KE = ½mv² in all three directions: find kinetic energy from mass and speed, find mass from kinetic energy and speed, or find speed from kinetic energy and mass. Common units are converted automatically and calculations run locally in your browser.
How To Use It
- Choose whether to solve for kinetic energy, mass, or speed.
- Enter the two known positive values and select their units.
- Choose the desired result unit and review the formula shown with the result.
- Use the result as an ideal classical-physics calculation; measurement uncertainty and real-world losses are not modeled.
Examples
2 kg moving at 3 m/s
KE = ½ × 2 × 3² = 9 J.
1000 kg at 36 km/h
36 km/h equals 10 m/s, so KE = ½ × 1000 × 10² = 50,000 J, or 50 kJ.
Find speed
An object with mass 2 kg and kinetic energy 9 J has speed √(2 × 9 ÷ 2) = 3 m/s.
Why speed matters strongly
For the same mass, increasing speed from 10 m/s to 20 m/s multiplies kinetic energy by four because speed is squared.
Useful Notes
Kinetic energy formula
The classical translational kinetic-energy formula is KE = ½mv², where KE is energy in joules, m is mass in kilograms, and v is speed in metres per second.
Solving for mass or speed
Rearranging the same equation gives m = 2KE/v² and v = √(2KE/m). The calculator converts your selected units before applying these formulas.
Unit conversions
Mass inputs can use kilograms, grams, or pounds; speed can use metres per second, kilometres per hour, or miles per hour; and energy can be displayed in joules or kilojoules.
Classical model limitation
KE = ½mv² is the standard classical formula and is an excellent approximation for everyday speeds. At speeds approaching the speed of light, relativistic kinetic energy is required instead and this calculator is not appropriate.
What the result does not include
The calculation represents translational kinetic energy from the supplied mass and speed. It does not automatically include rotational energy, potential energy, deformation, friction, drag, heat, or other forms of energy.
FAQ
Why is speed squared in the kinetic energy formula?
In classical mechanics, the work required to accelerate an object leads to the relationship KE = ½mv². Because speed is squared, kinetic energy changes faster than speed.
What is the SI unit of kinetic energy?
The SI unit is the joule (J). One joule is one kilogram metre squared per second squared.
Can kinetic energy be negative?
In this classical translational formula, mass is positive and speed is squared, so kinetic energy is non-negative. This calculator requires positive values for the quantities used to solve the equation.
Does direction affect kinetic energy?
No. Kinetic energy depends on speed, which is the magnitude of velocity, so reversing direction without changing speed does not change the kinetic energy.
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