Kinetic energy calculator: Eₖ = ½mv²
Solve the classical kinetic-energy equation in all three directions. Enter two values among energy, mass and speed, select units and calculate the third with automatic conversions and worked equations.
Enter exactly two values among kinetic energy, mass and speed. Leave the quantity you want to calculate empty.
The calculator uses the classical formula for translational kinetic energy. It is appropriate at speeds much lower than the speed of light and does not include rotational kinetic energy.
Results
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How does this tool work?
Kinetic energy is the energy associated with motion. In classical mechanics, translational kinetic energy is given by Eₖ = ½mv², where m is mass and v is speed. This calculator solves the equation in all three directions: energy from mass and speed, mass from energy and speed, or speed from energy and mass. Unit conversion is automatic, so kilograms, grams, metres per second, kilometres per hour, miles per hour, joules and kilojoules can be mixed without manual conversion.
The classical formula is Eₖ = ½mv². OpenStax defines translational kinetic energy as one-half the product of mass and speed squared. The SI unit is the joule, equivalent to kg·m²/s². A 1000 kg object moving at 20 m/s therefore has 200,000 J, or 200 kJ, of kinetic energy.
The equation can be inverted. Mass is m = 2Eₖ/v², while speed is v = √(2Eₖ/m). The calculator detects the empty field, selects the correct rearrangement and shows the numerical substitution.
The square on speed is the most important scaling effect. Doubling speed multiplies kinetic energy by four; tripling speed multiplies it by nine. A moderate increase in speed can therefore produce a much larger increase in kinetic energy.
Mass enters linearly. At the same speed, doubling mass doubles kinetic energy. This difference between linear dependence on mass and quadratic dependence on speed is central when comparing moving objects.
The calculation is normalized to coherent SI units: joules, kilograms and metres per second. Inputs may still use J, kJ, Wh, kWh, cal, kcal or BTU; mg, g, kg, tonnes, oz or lb; and m/s, km/h, mph, knots or ft/s. The shared conversion engine handles all conversions.
The equation Eₖ = ½mv² is a classical, non-relativistic result. OpenStax notes that at speeds comparable with the speed of light, special relativity requires a different kinetic-energy expression.
Kinetic energy is also connected to the work-energy theorem: net work done on a system equals the change in its kinetic energy. This calculator does not solve work directly, but that theorem explains how forces that change speed transfer energy.
How to use this tool
Choose the two known quantities
Fill two fields among Eₖ, m and v. Leave only the required result empty.
Select the measurement units
Choose units that match the original data; the output can use a different unit.
Convert internally to SI
Bethemesh converts energy to J, mass to kg and speed to m/s before solving the equation.
Review the worked equation
The details show the rearranged formula, SI substitution and result in your selected unit.
Kinetic energy formulas
Classical translational kinetic energy depends on mass and the square of speed.
Kinetic energy
Eₖ = ½ × m × v²
Kinetic energy is one-half mass multiplied by speed squared.
Mass
m = 2Eₖ ÷ v²
Mass can be recovered from energy and speed.
Speed
v = √(2Eₖ ÷ m)
Speed is the square root of twice the energy divided by mass.
Joule unit
1 J = 1 kg·m²/s²
The joule is the SI unit of energy and work.
- Eₖ
- translational kinetic energy, usually in joules
- m
- mass of the object or system, usually in kilograms
- v
- speed in the chosen reference frame, usually in m/s
The formula is classical and non-relativistic. It does not include rotational kinetic energy or motion near the speed of light.
Use cases
Mechanics exercises
Check kinetic-energy formulas, unit conversion and numerical results.
Compare the effect of speed
See how energy grows with the square of speed for a fixed mass.
Find speed from energy
Determine the classical speed associated with a known kinetic energy and mass.
Compare moving objects
Compare kinetic energies of objects or vehicles with different masses and speeds.
Examples
1000 kg car at 72 km/h
72 km/h = 20 m/s; Eₖ = ½ × 1000 × 20² = 200,000 J.
Input
m = 1000 kg; v = 72 km/hResult
Eₖ = 200 kJFind speed
v = √(2 × 125,000 / 1000).
Input
Eₖ = 125 kJ; m = 1000 kgResult
v ≈ 15.81 m/s ≈ 56.92 km/hFind mass
m = 2 × 90,000 / 15² = 800 kg.
Input
Eₖ = 90 kJ; v = 15 m/sResult
m = 800 kgDoubling speed
Doubling speed quadruples kinetic energy.
Input
m = 1000 kg; v increases from 10 to 20 m/sResult
Eₖ increases from 50 kJ to 200 kJStationary object
A stationary object has zero translational kinetic energy in the chosen reference frame.
Input
m = 2 kg; v = 0 m/sResult
Eₖ = 0 JTips and best practices
- Convert km/h to m/s by dividing by 3.6 before doing a manual calculation.
- Because speed is squared, an error in speed has an amplified effect on the energy result.
- Use the inertial mass of the object or system, expressed in kilograms for SI calculations.
- Zero speed gives zero kinetic energy. Mass, however, must remain strictly positive.
- Kinetic energy depends on the reference frame because speed depends on the reference frame.
- Do not confuse translational kinetic energy with rotational kinetic energy of wheels, disks or rotors.
- For speeds close to the speed of light, do not use the classical ½mv² formula.
Sources and references
- OpenStax, 9.1 Work, Power, and the Work–Energy Theorem (opens in a new tab), PhysicsPage in English
- BIPM — SI Brochure: units of time (opens in a new tab)Page in English
Frequently asked questions
What is the kinetic energy formula?
In classical mechanics, Eₖ = ½mv², where m is mass and v is speed.
What is the SI unit of kinetic energy?
The SI unit is the joule, J. One joule equals 1 kg·m²/s².
How do I calculate speed from kinetic energy?
Use v = √(2Eₖ/m) with coherent units.
How do I calculate mass from kinetic energy?
Use m = 2Eₖ/v². Speed must be nonzero for a finite positive mass.
Why is speed squared?
The classical energy required to accelerate a mass leads to a quantity proportional to v². Therefore doubling speed quadruples kinetic energy.
Can kinetic energy be zero?
Yes. In a reference frame where the object is stationary, translational kinetic energy is zero.
Do work and kinetic energy use the same unit?
Yes. Both are measured in joules, and the work-energy theorem links net work to the change in kinetic energy.
Does the formula work at any speed?
No. It is non-relativistic. At speeds close to light speed, a relativistic expression is required.
Are my values sent to a server?
No. Unit conversion and calculation run locally in your browser.
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