Kinetic Energy Calculator
Calculate kinetic energy from mass and velocity (KE = ½mv²) in joules, kJ or kcal, plus momentum — or solve for the velocity or mass that gives a known energy.
Kinetic Energy Calculator: with the default inputs, kinetic energy is 200,000 J.
Not used when solving for mass.
Direction doesn't matter for energy (v is squared). Not used when solving for velocity.
Used when solving for velocity or mass.
- Momentum (kg·m/s)
- 20,000
- Velocity
- 20 m/s
- Mass
- 1,000 kg
- Equivalent drop height
- 20.39 mHeight of a free fall (no air) that reaches this speed: h = v² ÷ 2g.
Assumptions
- Classical (non-relativistic) mechanics — speeds well below c.
- Translational motion only; rotational energy is not included.
- Equivalent drop height uses standard gravity 9.80665 m/s² and ignores air resistance.
| Speed(m/s) | Kinetic energy(J) | Versus your speed | Equivalent drop(m) |
|---|---|---|---|
| 5 m/s | 12,500 J | 0.06× | 1.27 m |
| 10 m/s | 50,000 J | 0.25× | 5.1 m |
| 15 m/s | 112,500 J | 0.56× | 11.47 m |
| 20 m/s | 200,000 J | 1× | 20.39 m |
| 25 m/s | 312,500 J | 1.56× | 31.87 m |
| 30 m/s | 450,000 J | 2.25× | 45.89 m |
| 40 m/s | 800,000 J | 4× | 81.58 m |
Double the speed and the energy quadruples — the ratio column is just the speed ratio squared. The last column is the height you would have to drop the object from, in a vacuum, to reach that speed.
How this is worked out
The formula
KE = ½ × m × v² p = m × v KE = kinetic energy (J) m = mass (kg) v = velocity (m/s) p = momentum (kg·m/s) Rearranged: v = √(2·KE ÷ m), m = 2·KE ÷ v²
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Solve for
- Choose one of 3 options.Kinetic energy — from mass & velocity · Velocity — from kinetic energy & mass · Mass — from kinetic energy & velocity
- Mass
- Not used when solving for mass.in kg · 0 or more · defaults to 1000
- Velocity
- Direction doesn't matter for energy (v is squared). Not used when solving for velocity.in m/s · defaults to 20
- Kinetic energy
- Used when solving for velocity or mass.in J · 0 or more · defaults to 200000
What you get back
- Kinetic energymain answer
- Momentum (kg·m/s)
- Velocity
- Mass
- Equivalent drop height
- Height of a free fall (no air) that reaches this speed: h = v² ÷ 2g.
What this assumes
- Classical (non-relativistic) mechanics — speeds well below c.
- Translational motion only; rotational energy is not included.
- Equivalent drop height uses standard gravity 9.80665 m/s² and ignores air resistance.
About this calculator
Kinetic energy is the energy an object has because it is moving: KE = ½mv². Enter mass and velocity in any units — pounds and mph work as well as kilograms and m/s — and get the energy in joules, kilojoules, kilocalories or kWh, along with the object's momentum. Switch Solve for to find how fast something must move to carry a given energy, or how heavy it must be.
The square matters
Energy grows with the square of speed. A car at 60 mph has four times the kinetic energy it had at 30 mph, which is why stopping distance quadruples and why crash severity climbs so steeply with speed. Doubling mass only doubles the energy. Momentum (p = mv) grows linearly with both, so it is the quantity that matters in a collision's impulse, while kinetic energy is what turns into crumpled metal and heat.
Reading the results
- Kinetic energy in J. 1 kJ is roughly the energy of a 1 kg book dropped from 100 m; 1 kcal (4,184 J) is a food calorie.
- Momentum in kg·m/s. Direction follows the velocity's sign.
- Equivalent drop height — the free-fall height (ignoring air) that produces this speed, from v² = 2gh. It is a good intuition check: a 20 m/s car impact is like driving off a six-storey building.
Common mistakes
- Forgetting the ½. It comes from integrating F·dx with F = ma, and dropping it doubles your answer.
- Using km/h or mph in the formula. The joule is defined with m/s; the calculator converts, but hand calculations must too (1 m/s = 3.6 km/h = 2.237 mph).
- Treating velocity's sign as meaningful: it is squared, so a negative velocity gives the same energy (momentum, however, keeps the sign).
Where the formula breaks
½mv² is the low-speed limit of the relativistic energy (γ − 1)mc². Below a few percent of light speed the error is negligible; at 0.1c it is about 0.75%, and at 0.5c the classical formula is 40% low. For rotating bodies add rotational kinetic energy ½Iω² — a rolling ball carries more energy than a sliding one at the same speed.
Frequently asked questions
▸What is the kinetic energy formula?
KE = ½mv², with mass in kilograms and velocity in meters per second giving joules. It applies to any object moving in a straight line at everyday speeds.
▸Why is kinetic energy proportional to velocity squared?
Work equals force times distance. Accelerating an object to speed v takes a distance proportional to v² (from v² = 2ad), so the work done — and the energy stored as motion — scales with v².
▸How do I find velocity from kinetic energy?
Rearrange to v = √(2·KE ÷ m). For 200,000 J and 1,000 kg: √(400,000 ÷ 1,000) = √400 = 20 m/s.
▸What is the difference between kinetic energy and momentum?
Momentum (mv) is a vector conserved in every collision; kinetic energy (½mv²) is a scalar conserved only in elastic collisions. A bullet and a slow truck can have equal momentum but wildly different kinetic energies.
▸Can kinetic energy be negative?
No. Mass is positive and v² is never negative, so kinetic energy is always zero or positive. Only changes in kinetic energy can be negative, when an object slows down.
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