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Kinetic Energy Calculator

Kinetic energy is one half times mass times the square of speed. The square is what makes the formula interesting: it is why doubling your speed quadruples the energy you have to lose, and why momentum tells a different story.

Kinetic energy in joules

578,703.7037

Speed in metres per second
27.7778
The same energy in kilojoules
578.7037
Momentum in kilogram metres per second
41,666.6667

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

The formula this calculator uses

KE = 1/2 x m x v^2

m
Mass in kilograms
v
Speed in metres per second — divide km/h by 3.6 first
KE
Kinetic energy in joules, a scalar with no direction
p
Momentum, equal to m v, a vector along the direction of motion

How to check the result by hand

  1. 1

    Convert the speed to metres per second

    Divide the kilometres-per-hour figure by 3.6: 100 km/h becomes 27.7777778 m/s. Skipping this step is the most damaging error available, because the answer then comes out 12.96 times too large.

  2. 2

    Square the speed

    27.7777778^2 = 771.604938. This squaring is what makes kinetic energy grow so much faster than momentum, and it is the reason small speed increases matter disproportionately.

  3. 3

    Multiply by the mass and halve

    0.5 x 1500 x 771.604938 = 578703.7037 joules. The mass must be in kilograms; the half belongs to the formula and must not be dropped.

  4. 4

    Read momentum alongside as a cross-check

    Momentum is simply mass times speed: 1500 x 27.7777778 = 41666.6666667 kg m/s. Having both numbers lets you confirm that energy scaled with the square while momentum scaled only linearly.

  5. 5

    Convert to kilojoules and sanity-check by doubling

    578703.7037 joules is 578.7037037 kilojoules. Doubling the speed should quadruple that energy to 2314814.814814815 joules; if it does not, the conversion or the squaring has gone wrong.

For worked examples, common mistakes and the limits of this formula, read the full How To Calculate Kinetic Energy page.