Kinetic energy calculator

How do I calculate kinetic energy?

KE = ½ × mass × speed². A 1,000 kg car at 20 m/s (45 mph) has ½ × 1,000 × 400 = 200,000 joules.

Why does speed matter so much?

Because it is squared: doubling the speed quadruples the energy. That car at 40 m/s carries 800,000 J — four times as much to stop.

What units is kinetic energy in?

Joules when mass is in kilograms and speed in meters per second. 1 foot-pound is 1.356 J, and 1 food Calorie (kcal) is 4,184 J.

How do I find speed from kinetic energy?

v = √(2 × KE ÷ m): 200,000 J in a 1,000 kg car means √400 = 20 m/s.

Is this the same as momentum?

No — momentum is mass × speed (kg·m/s) and grows in step with speed; kinetic energy grows with its square.

How much work does it take to stop a moving object?

By the work-energy theorem, the net work equals the change in kinetic energy, W = K₂ − K₁ (OpenStax University Physics, Volume 1, section 7.3, Eq. 7.9). To stop the car of the example below from 60 mph in 40 m, the brakes must remove 489.5 kJ, an average force of 489,500 ÷ 40 = 12,237 N (2,751 lbf). OpenStax Example 7.10 does the same for a 2.60 g bullet at 335 m/s: 145.9 J and, over 15.2 cm, about 960 N.

Does kinetic energy depend on who is measuring the speed?

Yes, because speed depends on the frame of reference (OpenStax, section 7.2). A 75.0 kg person walking at 1.50 m/s along a train has 84.4 J relative to the train. If the train moves at 15.0 m/s relative to the tracks, the person’s speed over the tracks is 16.5 m/s or 13.5 m/s, depending on whether they walk toward the front or the back, and the energy is 10.21 kJ or 6.83 kJ (OpenStax Example 7.7). The same person has no kinetic energy in their own frame.

The formula and what it assumes

Kinetic energy is K = ½mv² (OpenStax University Physics, Volume 1, section 7.2, Eq. 7.6). It is measured in joules, 1 J = 1 kg·m²/s², and it can never be negative. Because it depends on v², the speed must be in m/s and the mass in kg for joules; the calculator converts mph, km/h, ft/s, pounds and grams first. It is the classical formula, valid when the speed is much less than the speed of light (section 7.2); the same quantity can be written K = p² ÷ 2m using the momentum.

Worked example: a 3,000 lb car at 60 mph and at 30 mph

The mass is 3,000 × 0.45359237 = 1,360.8 kg and 60 mph is 60 × 0.44704 = 26.82 m/s. Then K = ½ × 1,360.8 × 26.82² = 489,500 J, or 489.5 kJ, which is 361,036 ft·lbf. At 30 mph the speed is half and the energy is 122.4 kJ, a quarter of that.

Common mistakes

Forgetting to square the speed is the usual one: doubling the speed quadruples the energy, and tripling it multiplies the energy by nine. Using mph in the formula without converting to m/s gives a number that is not in joules. Mixing up pounds and pounds-force is another: the 3,000 lb above is a mass, so there is no further division by 32.174. Finally, energy does not add the way speed does: two identical cars each at half the speed carry together only half the energy of one car at full speed.

Sources: OpenStax University Physics, Volume 1, section 7.2 (kinetic energy, Eq. 7.6; Example 7.7) and section 7.3 (work-energy theorem, Eq. 7.9; Example 7.10); the pound (0.45359237 kg), mile per hour (0.44704 m/s) and foot-pound force (1.355818 J) are from NIST SP 811, Appendix B.8. Related: potential energy calculator, momentum calculator, work calculator and stopping distance calculator.