Quick answer
Kinetic energy is KE = ½mv², and momentum p = mv. A 10 kg mass at 5 m/s has 125 J of kinetic energy and a momentum of 50 kg·m/s.
Enter mass and speed. The calculator returns kinetic energy and momentum.
Related tools: Density Calculator: Solve mass, density or volume. Charles's Law Calculator: V₁/T₁ = V₂/T₂ at constant pressure. Boyle's Law Calculator: P₁V₁ = P₂V₂ at constant temperature.
How to use the Kinetic Energy Calculator
- Enter mass (kg) (above 0).
- Enter speed (m/s) (0 or more).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Mass | A number, in kg | > 0 |
| Speed | A number, in m/s | ≥ 0 |
Formula and method
Formula
KE = ½ m v²; p = m v
IEEE-754 double precision; shown to at most 6 decimal places.
Classical (non-relativistic) mechanics; valid well below the speed of light.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Mass = 10; Speed = 5.
| Result | Value |
|---|---|
| Kinetic energy | 125 J |
| Momentum | 50 |
Example 2
Inputs: Mass = 1500; Speed = 20.
| Result | Value |
|---|---|
| Kinetic energy | 300,000 J |
| Momentum | 30,000 |
The first line is the headline result (kinetic energy). Below it the kinetic Energy Calculator lists momentum, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Speed is squared
Doubling the speed quadruples the energy: 10 m/s gives 500 J. That is why stopping distance rises so quickly with speed and why a 60 mph crash is far worse than a 30 mph one.
Units
Mass in kg and speed in m/s give joules. A speed of 0 gives 0 J. Kinetic energy is a scalar and always non-negative, while momentum carries direction.
How the result changes with mass
Holding every other input at the first worked example, this table changes only mass. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Mass | Kinetic energy | Momentum |
|---|---|---|
| 5 | 62.5 J | 25 |
| 10 | 125 J | 50 |
| 20 | 250 J | 100 |
| 40 | 500 J | 200 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Mass: entering "0" shows "Mass must be greater than 0." beside that field and no result.
Choosing between the Kinetic Energy Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Density Calculator](/science/density-calculator/) | Mass | |
| [Charles's Law Calculator](/science/charles-law/) | Final volume | |
| [Boyle's Law Calculator](/science/boyles-law/) | Final volume | |
| [Coulomb's Law Calculator](/science/coulombs-law-charge/) | charge 1, charge 2 and distance | Force |
| [Speed Distance Time Calculator](/science/speed-distance-time-calculator/) | Distance |
Background: motion and mechanics
For constant acceleration the standard relations are v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t. Pick the equation that contains your three known quantities and the one you want. Use SI units (metres, seconds, kilograms, newtons, joules) throughout or the answer will be off by a factor.
These equations stop applying when acceleration changes during the motion, as with a rocket burning fuel; that needs calculus or numerical methods.
Assumptions and limitations
- Speed 0 gives 0 J
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for mass to confirm this.
Frequently asked questions
How much KE does a 1,000 kg car at 20 m/s have?
200,000 J, or 200 kJ.
What is the work-energy theorem?
Work done equals the change in KE.
Is KE conserved?
Not in inelastic collisions.
What does the Kinetic Energy Calculator calculate?
Kinetic energy and momentum of a moving mass. It returns Kinetic energy and Momentum.
What formula does the Kinetic Energy Calculator use?
KE = ½ m v²; p = m v. Classical (non-relativistic) mechanics; valid well below the speed of light.
What do I need to enter in the kinetic Energy Calculator?
You enter Mass (kg) and Speed (m/s).
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Speed 0 gives 0 J.
What is an example of a kinetic Energy result?
With mass 10 and speed 5, the kinetic energy is 125 J.
Related calculators
- Density Calculator — Solve mass, density or volume.
- Charles's Law Calculator — V₁/T₁ = V₂/T₂ at constant pressure.
- Boyle's Law Calculator — P₁V₁ = P₂V₂ at constant temperature.
- Coulomb's Law Calculator — Electrostatic force between two point charges.
- Speed Distance Time Calculator — Solve distance, speed or time.
- Potential Energy Calculator — Gravitational potential energy from mass, height and gravity.
- Photon Energy Calculator — Photon energy from wavelength or frequency.
Sources
- OpenStax, University Physics Volume 2 (Rice University): electricity, circuits and thermodynamics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.