Quick answer: Kinetic energy = ½ × mass × velocity2 (KE = ½mv2), in joules when mass is in kg and velocity in m/s. Enter any two of the three values and this kinetic energy calculator solves for the third, with unit conversion built in.
Last reviewed: September 2026
Key facts
- KE = ½mv2 — half the mass times velocity squared, in joules (kg·m2/s2).
- Rearranged: m = 2KE ÷ v2 and v = √(2KE ÷ m) — enter any two, solve the third.
- Speed dominates: doubling velocity quadruples energy; doubling mass only doubles it.
- Kinetic energy is a scalar — only speed matters, not direction.
Kinetic energy is the energy an object carries because it is moving: KE = ½mv², half the mass times the velocity squared. This free kinetic energy calculator solves for KE, mass or velocity from the other two values, converting between kg, g, lb, m/s, km/h, mph, J, kJ and kcal.
Pick the value to solve for, enter the two known values, and get the answer with the working shown. No sign-up, works on mobile and desktop.
How to use this kinetic energy calculator
- Choose what to solve for: kinetic energy, mass or velocity.
- Enter the two known values and pick their units.
- The unknown field is ignored — read the answer and the steps below.
Background: from vis viva to ½mv²
In the 17th and 18th centuries, natural philosophers debated the correct measure of a moving body's "living force": some held it scaled with velocity, others with the square of velocity. Experiments — notably dropping balls into soft clay and measuring penetration depth — showed the effect grew with the square of speed, settling the debate in favor of the v² view.
The modern form comes from the work–energy theorem, formalized in 19th-century mechanics: the work done accelerating a mass from rest equals the integral of force over distance, ∫F·dx, which evaluates to ½mv². That is also why the ½ appears — it is the area of the triangle under the force–distance curve — and why the joule (kg·m²/s²) is simultaneously the unit of work and of energy.
The kinetic energy formula
| Term | Meaning |
|---|---|
| KE | Kinetic energy in joules (J) = kg·m2/s2. |
| m | Mass of the object in kilograms. |
| v | Speed of the object in meters per second. |
The ½ comes from the work-energy theorem: the work of accelerating a mass from rest equals the area under the force–distance curve, which integrates to ½mv2.
Kinetic energy at everyday scales
The kinetic energy calculator above handles any of these in one step — try entering the sprinter's numbers yourself:
| Object | Mass | Speed | Kinetic energy |
|---|---|---|---|
| Walking adult | 70 kg | 1.5 m/s | ≈ 79 J |
| Sprinter | 80 kg | 10 m/s | 4,000 J |
| Rifle bullet | 10 g | 800 m/s | 3,200 J |
| Family car | 1,500 kg | 100 km/h | ≈ 579 kJ |
| Airliner | 70,000 kg | 250 m/s | ≈ 2.19 GJ |
| Earth orbiting the Sun | 5.97 × 1024 kg | 29.78 km/s | ≈ 2.6 × 1033 J |
Notice the bullet carries less energy than the sprinter despite its far greater speed — mass still counts — while the car at highway speed holds over a hundred times the sprinter's energy, which is why speed limits save lives.
Classical vs relativistic: the honest caveat
½mv² is the classical (Newtonian) formula, valid when speed is far below the speed of light c. At relativistic speeds the correct kinetic energy is (γ − 1)mc², where γ = 1/√(1 − v²/c²). The classical form is simply its low-speed approximation.
Worked comparison — a 1 kg object at half the speed of light (0.5c ≈ 1.50 × 108 m/s):
- Classical: KE = ½(1)(1.50 × 108)² ≈ 1.12 × 1016 J
- Relativistic: KE = (1.1547 − 1)(1)(2.998 × 108)² ≈ 1.39 × 1016 J
The classical formula underestimates by about 19% at 0.5c. At 10% of light speed the error is under 1%, and for every everyday speed it is utterly negligible — so this kinetic energy calculator, like all classical ones, is exact for practical purposes but should not be used for particle-physics or astrophysical speeds.
Worked examples
80 kg runner at 10 m/s
KE = 0.5 × 80 × 102 = 0.5 × 80 × 100.
KE = 4,000 J (4 kJ).
Speed of a 50 kg object with 2,000 J
v = √(2 × 2,000 ÷ 50) = √80.
v = 8.944 m/s (about 32.2 km/h).
Energy unit equivalents
| Unit | Equals |
|---|---|
| 1 joule (J) | 1 kg·m2/s2 |
| 1 kilojoule (kJ) | 1,000 J |
| 1 kilocalorie (kcal) | 4,184 J |
| 1 km/h | 0.2778 m/s |
| 1 mph | 0.4470 m/s |
Limitations
- Classical mechanics only — see the relativistic caveat above; near light speed, use (γ − 1)mc².
- Translational energy only. Spinning or rolling objects carry additional rotational kinetic energy that this tool does not include.
- Speed, not velocity direction. Two objects moving at the same speed in opposite directions have equal kinetic energy.
- Frame of reference matters. Enter the object's speed relative to your chosen frame — kinetic energy is frame-dependent.
Frequently asked questions
What is the kinetic energy formula?
KE = ½mv²: kinetic energy equals half the mass times the velocity squared. With mass in kilograms and velocity in meters per second, the answer is in joules. Example: 80 kg at 10 m/s gives 0.5 × 80 × 100 = 4,000 J.
Why is velocity squared in the formula?
It follows from the work-energy theorem: accelerating an object requires force over distance, and integrating that work gives ½mv². The practical effect is that doubling speed quadruples kinetic energy, which is why speed matters so much in vehicle safety.
How do you find velocity from kinetic energy?
Rearrange the formula: v = √(2KE ÷ m). Example: 2,000 J of energy in a 50 kg object gives v = √(80) ≈ 8.94 m/s.
Is kinetic energy affected by direction?
No. Kinetic energy is a scalar quantity — it depends only on speed, not on the direction of motion. A ball moving up at 10 m/s has the same kinetic energy as one moving down at 10 m/s.
What is the difference between kinetic and potential energy?
Kinetic energy is energy of motion (½mv²); potential energy is stored energy of position, such as gravitational PE = mgh. A falling object converts potential energy into kinetic energy as it speeds up.
Sources
- HyperPhysics: Kinetic Energy — the ½mv² formula, its classical limit (v ≪ c), and the relativistic expression
- OpenStax: College Physics — free college physics textbook covering work, energy and the work–energy theorem
Key takeaways
- KE = ½mv2, with mass in kg and speed in m/s giving joules.
- Enter any two of KE, m, v to solve for the third.
- Doubling speed quadruples energy; doubling mass only doubles it.
- Kinetic energy is scalar — direction does not matter.
- Classical formula only; use (γ − 1)mc² near light speed.
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