What is the kinetic energy?
Type a mass and a speed to get the kinetic energy, or type the energy to find the mass or the speed. The kinetic energy calculator works in metric and US units and shows joules, kilojoules, foot-pounds and kilocalories.
- Kinetic energy (J)
- 312,500
A mass of 2,204.62 lb at 55.9234 mph has 312,500 J of kinetic energy.
- Kinetic energy (kJ)
- 312.5
- Kinetic energy (ft·lbf)
- 230,488
- Kinetic energy (kcal)
- 74.6893
- Mass (kg)
- 1,000
- Mass (lb)
- 2,204.62
- Speed (m/s)
- 25
- Speed (km/h)
- 90
- Speed (mph)
- 55.9234
Kinetic energy (J): 312,500. A mass of 2,204.62 lb at 55.9234 mph has 312,500 J of kinetic energy.
How to calculate
Computes kinetic energy from mass and speed (KE = ½ m v²), or the mass or speed from the other two, in metric or US units.
Example with the default inputs (Find Kinetic energy, Mass 2,204.62262184878 lb, Speed 55.9234073013601 mph): A mass of 2,204.62 lb at 55.9234 mph has 312,500 J of kinetic energy.
Method: KE = ½ × m × v²; m = 2 × KE ÷ v²; v = √(2 × KE ÷ m). Mass in kg and speed in m/s give the energy in joules.
- Classical (Newtonian) mechanics: the speed is below 10% of the speed of light, where KE = ½ m v² is within about 0.75% of the relativistic value.
- The energy is the translational kinetic energy of the whole object; spin (rotational energy) is not included.
- Units are converted with exact factors: 1 lb = 0.45359237 kg, 1 mph = 0.44704 m/s, 1 km/h = 1/3.6 m/s, 1 ft·lbf = 1.3558179483314004 J, 1 kcal = 4,184 J.
Worked examples
Each example is checked against the calculator on every build.
- Find Kinetic energy, Mass 176.4 lb, Speed 22.37 mph gives Kinetic energy (J) 4,000, Kinetic energy (kJ) 4.Source: OpenStax, University Physics Volume 1, §7.2 Kinetic Energy, Example 7.6(a): ½ × 80 kg × (10 m/s)² = 4.0 kJ. https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy
- Find Kinetic energy, Mass 2,205 lb, Speed 55.92 mph gives Kinetic energy (J) 312,500, Kinetic energy (kJ) 312.5, Speed (km/h) 90.Source: OpenStax, University Physics Volume 1, §7.2 Kinetic Energy (K = ½mv²). https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy
- Find Kinetic energy, Mass 0.3197 lb, Speed 90 mph gives Kinetic energy (J) 117.358836, Speed (m/s) 40.2336.Source: NIST Handbook 44 Appendix C (1 mi = 1,609.344 m). https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy
- Find Speed, Kinetic energy 1,000 J, Mass 44.09 lb gives Speed (m/s) 10, Speed (km/h) 36.Source: OpenStax, University Physics Volume 1, §7.2 Kinetic Energy (K = ½mv², so v = √(2K ÷ m)). https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy
- Find Mass, Kinetic energy 450 J, Speed 6.711 mph gives Mass (kg) 100, Mass (lb) 220.462262.Source: OpenStax, University Physics Volume 1, §7.2 Kinetic Energy (K = ½mv², so m = 2K ÷ v²). https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy
How it works
Pick what to find, then type the other two values.
- Kinetic energy: KE = ½ × m × v²
- Mass: m = 2 × KE ÷ v²
- Speed: v = √(2 × KE ÷ m)
The page works in kilograms, metres per second and joules, then converts:
- 1 kJ = 1,000 J; 1 ft·lbf = 0.3048 × 4.4482216152605 = 1.3558179483314004 J; 1 kcal = 4,184 J
- 1 lb = 0.45359237 kg
- 1 km/h = 1/3.6 m/s; 1 mph = 0.44704 m/s; 1 ft/s = 0.3048 m/s; 1 knot = 1,852/3,600 m/s
- Energy units you can type: J, kJ, MJ, cal (4.184 J), kcal, Wh (3,600 J), kWh, BTU (1,055.05585262 J) and ft·lbf
Exact arithmetic. Each value is read as the exact decimal you typed, in the unit you typed it in. The energy and the mass are exact fractions of those decimals; the speed is an exact square root when 2 × KE ÷ m is the square of a fraction, and a 64-bit float otherwise.
Output format. Every result shows 6 significant figures, rounded half up from its exact value, with trailing zeros left off. The answer sentence names pounds and miles per hour in US units, and kilograms and kilometres per hour in Metric.
When there is no answer.
- Finding the mass at a speed of 0: no mass has kinetic energy at rest.
- A solved mass over 10¹² kg.
- A speed (typed or solved) at or above 10% of the speed of light, 29,979,245.8 m/s.
Assumptions
- Classical (Newtonian) mechanics; the energy is the motion of the whole object in a line, not its spin.
- Mass: more than 0 and at most 10¹² kg. Speed: 0 to 10⁸ m/s as typed. Energy: more than 0 and at most 10¹⁸ J.
Worked examples by hand
An 80 kg athlete at 10 m/s (OpenStax Example 7.6). ½ × 80 × 10² = 4,000 J = 4 kJ.
A 1,000 kg car at 25 m/s. ½ × 1,000 × 25² = 312,500 J = 312.5 kJ; 25 m/s × 3.6 = 90 km/h.
A 0.145 kg baseball at 90 mph. 90 × 0.44704 = 40.2336 m/s; ½ × 0.145 × 40.2336² = 117.359 J.
Speed from 1,000 J and 20 kg. √(2 × 1,000 ÷ 20) = √100 = 10 m/s = 36 km/h.
Mass from 450 J at 3 m/s. 2 × 450 ÷ 3² = 100 kg = 100 ÷ 0.45359237 = 220.462 lb.
Other questions people ask
What is the formula for kinetic energy?
Kinetic energy is KE = ½ × m × v², where m is the mass and v the speed. With the mass in kilograms and the speed in metres per second, the energy is in joules. An 80 kg runner at 10 m/s has ½ × 80 × 10² = 4,000 J, or 4 kJ.
How do I find speed from kinetic energy?
Rearrange the formula: v = √(2 × KE ÷ m). A 20 kg object with 1,000 J of kinetic energy moves at √(2 × 1,000 ÷ 20) = √100 = 10 m/s.
How do I find mass from kinetic energy?
Use m = 2 × KE ÷ v². An object with 450 J of kinetic energy at 3 m/s has a mass of 2 × 450 ÷ 9 = 100 kg.
What happens to kinetic energy when speed doubles?
It goes up four times, because the speed is squared. A car at 50 mph has four times the kinetic energy it has at 25 mph, which is why braking distance grows so fast with speed.
Can kinetic energy be negative?
No. The mass is positive and the speed is squared, so kinetic energy is zero for an object at rest and positive for any moving object.
What units is kinetic energy measured in?
The SI unit is the joule: 1 J = 1 kg·m²/s². The page also shows kilojoules, foot-pounds (1 ft·lbf = 1.3558179483314004 J) and kilocalories (1 kcal = 4,184 J).
When does KE = ½mv² stop working?
Near the speed of light. Below 10% of light speed the classical formula is within 0.75% of the relativistic value. The page gives no answer at or above 10% of light speed (29,979,245.8 m/s).