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Formula
KE = ½ × m × v²
- KE
- kinetic energy, in joules (J)
- m
- mass of the object, in kilograms (kg)
- v
- speed of the object, in meters per second (m/s)
What kinetic energy is
Kinetic energy is the energy an object has because it is moving. It equals the work needed to bring the object from rest up to its current speed. It is also the work the object can do, such as denting a fender or driving a nail, as it slows back down to rest. For anything moving at everyday speeds it is given by:
KE = ½ × m × v²
The mass counts once, but the speed counts twice. That squared term is the most important thing to understand about kinetic energy. A small increase in speed means a large increase in energy.
How to use the kinetic energy calculator
- Choose what you want to find: Kinetic energy, Mass or Velocity.
- Enter the two known values and pick their units. Mass can be in grams, kilograms, metric tons, ounces, pounds or US tons. Speed can be in m/s, km/h, mph, ft/s or knots. Energy can be in joules, kilojoules, foot-pounds, calories, kilocalories, watt-hours, kilowatt-hours or BTU.
- Choose the unit for the answer. The same result in other units appears below it.
- Read the working. If you entered non-SI units, the first line shows the conversion to kilograms and meters per second, then the formula with your numbers.
How to calculate kinetic energy by hand
Take a 2 kg ball moving at 6 m/s:
- Square the speed: 6² = 36
- Multiply by the mass: 2 × 36 = 72
- Halve it: 72 ÷ 2 = 36 J
With US units, convert first. A 10 lb object is 4.536 kg, and 30 mph is 13.41 m/s. KE = 0.5 × 4.536 × 13.41² ≈ 408 J, or about 301 ft·lbf. Mixing pounds with miles per hour directly gives a number with no meaningful unit.
Solving for speed or mass
- Speed: v = √(2KE ÷ m). Double the energy, divide by the mass, then take the square root.
- Mass: m = 2KE ÷ v². Double the energy and divide by the speed squared.
Kinetic energy of a car at different speeds
The table shows the kinetic energy of a 1,500 kg (about 3,300 lb) car, calculated with KE = ½mv². All of this energy must be absorbed by the brakes, or by the crash structure, to bring the car to a stop.
| Speed | Speed (m/s) | Kinetic energy | In foot-pounds |
|---|---|---|---|
| 25 mph | 11.18 | 93.68 kJ | 69,090 ft·lbf |
| 35 mph | 15.65 | 183.6 kJ | 135,400 ft·lbf |
| 45 mph | 20.12 | 303.5 kJ | 223,900 ft·lbf |
| 55 mph | 24.59 | 453.4 kJ | 334,400 ft·lbf |
| 70 mph | 31.29 | 734.4 kJ | 541,700 ft·lbf |
| 80 mph | 35.76 | 959.3 kJ | 707,500 ft·lbf |
Going from 35 mph to 70 mph doubles the speed but quadruples the energy, from 184 kJ to 734 kJ. With the same braking force, the stopping distance also roughly quadruples.
Real-life uses
Road safety
Kinetic energy explains why speed limits near schools are so low and why highway crashes are so much more severe. The energy a crash has to dissipate grows with the square of the speed.
Sports and ballistics
Projectile energy is usually quoted in joules or foot-pounds. Coaches and engineers use it to compare thrown balls, hockey pucks and arrows, and to rate protective equipment.
Machines and flywheels
Engineers estimate the energy stored in moving parts to design brakes, guards and shock absorbers. For spinning parts, rotational kinetic energy must be added separately.
Physics homework
Most kinetic energy problems combine this formula with others. The velocity calculator gives a speed from distance and time, the acceleration calculator gives the rate of speed change, and the force calculator links force, mass and acceleration through F = ma.
Common mistakes
- Forgetting to square the speed. ½ × 2 × 6 = 6 is wrong. The answer is ½ × 2 × 36 = 36 J.
- Squaring the whole product. Only v is squared, not m × v.
- Mixing units. Grams with m/s, or pounds with mph, give wrong answers. Convert to kilograms and meters per second first, as the calculator does.
- Confusing pounds of mass with pounds-force. In KE = ½mv², the mass must be in kilograms (or slugs in the old US engineering system), not pounds-force.
- Using it for rolling objects. A rolling ball also stores rotational energy, so ½mv² underestimates its total energy.
Glossary
- Joule (J): the SI unit of energy, 1 kg·m²/s². Lifting an apple about 1 m takes roughly 1 J.
- Foot-pound (ft·lbf): the work done by a 1 lbf force over 1 ft, about 1.356 J.
- Work-energy theorem: the net work done on an object equals its change in kinetic energy.
- Momentum: mass × velocity (p = mv). It is related to kinetic energy by KE = p² ÷ 2m.
Worked examples
A car on the highway
A 1,500 kg car traveling at 65 mph. Its speed is converted to m/s (29.0576 m/s) before squaring.
Inputs (Kinetic energy): Mass = 1500; Mass unit = Kilograms; Velocity = 65; Velocity unit = Miles per hour; Show energy in = Kilojoules (kJ)
Convert to SI units: 65 mph = 29.0576 m/s KE = ½ × m × v² = 0.5 × 1,500 kg × (29.0576 m/s)² = 633,258 J 633,258 J = 633.258 kJ
Answer: A 1,500 kg object moving at 65 mph has 633.258 kJ of kinetic energy.
A baseball pitch
A 145 g baseball thrown at 40 m/s (about 89.5 mph).
Inputs (Kinetic energy): Mass = 145; Mass unit = Grams; Velocity = 40; Velocity unit = Meters per second; Show energy in = Joules (J)
Convert to SI units: 145 g = 0.145 kg KE = ½ × m × v² = 0.5 × 0.145 kg × (40 m/s)² = 116 J
Answer: A 145 g object moving at 40 m/s has 116 J of kinetic energy.
Mass from energy and speed
A runner moving at 8 m/s carries 2,400 J of kinetic energy. What is their mass?
Inputs (Mass): Kinetic energy = 2400; Kinetic energy unit = Joules; Velocity = 8; Velocity unit = Meters per second; Show mass in = Kilograms (kg)
m = 2 × KE ÷ v² = 2 × 2,400 J ÷ (8 m/s)² = 75 kg
Answer: An object with 2,400 J of kinetic energy at 8 m/s has a mass of 75 kg.
Edge case: speed from a tiny energy
A 0.25 kg toy with just 0.5 J of kinetic energy. The square root gives v = √(2 × 0.5 ÷ 0.25) = 2 m/s.
Inputs (Velocity): Kinetic energy = 0.5; Kinetic energy unit = Joules; Mass = 0.25; Mass unit = Kilograms; Show velocity in = Meters per second (m/s)
v = √(2 × KE ÷ m) = √(2 × 0.5 J ÷ 0.25 kg) = 2 m/s
Answer: A 0.25 kg object with 0.5 J of kinetic energy moves at 2 m/s.
Assumptions and limitations
- Uses the classical formula KE = ½mv² for translational motion. It is accurate for everyday speeds. Above about 10% of the speed of light, the result shows a note, because the relativistic formula is needed there.
- Rotational kinetic energy (spinning wheels, rolling balls) is not included. A rolling object has more total kinetic energy than ½mv² alone.
- Inputs are converted to SI units (kg, m/s) before calculating. Foot-pounds use 1 ft·lbf = 1.3558179483 J, and calories are thermochemical (1 cal = 4.184 J).
- Speed is a magnitude. Direction does not matter because v is squared, so kinetic energy is never negative.
- Results are shown to 6 significant figures.
Frequently asked questions
What is the formula for kinetic energy?
KE = ½mv², one half of the mass times the speed squared. With mass in kilograms and speed in meters per second, the answer is in joules.
How do you find velocity from kinetic energy?
Rearrange the formula to v = √(2KE ÷ m). An object of 4 kg with 200 J of kinetic energy moves at √(2 × 200 ÷ 4) = √100 = 10 m/s. Use the Velocity tab to do this with any units.
How do you find mass from kinetic energy?
Use m = 2KE ÷ v². If something moving at 5 m/s has 150 J of kinetic energy, its mass is 2 × 150 ÷ 25 = 12 kg.
Why does doubling the speed quadruple the kinetic energy?
Because speed is squared. 2² = 4, so twice the speed means four times the energy, and three times the speed means nine times the energy. This is why braking distances grow so quickly with speed.
What unit is kinetic energy measured in?
The SI unit is the joule (J), equal to 1 kg·m²/s². In the US, foot-pounds (ft·lbf) are common for firearms and machinery. 1 ft·lbf is about 1.356 J.
Can kinetic energy be negative?
No. Mass is positive and the square of the speed is never negative, so kinetic energy is zero for an object at rest and positive otherwise.
What is the difference between kinetic and potential energy?
Kinetic energy is energy of motion. Potential energy is stored energy due to position, such as height in a gravitational field (mgh). A falling object converts potential energy into kinetic energy.
Sources
- University Physics Volume 1, 7.2 Kinetic Energy — OpenStax (Rice University). Checked October 12, 2026.
- NIST Guide to the SI, Appendix B.9: Factors for units listed by kind of quantity — National Institute of Standards and Technology (NIST). Checked October 12, 2026.