Kinetic and Potential Energy Calculator

A moving object has kinetic energy; a raised one has potential energy. This calculator works out either in any units, then shows what that energy is worth the other way round: how high a moving object could climb, or how fast a raised one would be going if it fell.

How to Use It

1. Choose Kinetic Energy or Potential Energy.
2. Enter the Mass, then the Speed (kinetic) or the Height (potential), with their units.
3. Leave Gravity at 9.81 m/s² for Earth, or change it for another planet.
4. Pick the energy unit in Answer In and press Calculate.

How It Works

Kinetic energy grows with the square of the speed:

Gravitational potential energy grows with height:

With no friction or air resistance, energy converts fully between the two. Setting them equal gives the height a moving object could climb, $h = \frac{v^2}{2g}$, and the speed a dropped object reaches, $v = \sqrt{2gh}$. Mass cancels out of both.

Worked Example

A 2 kg ball moving at 3 m/s has:

Rolling up a frictionless slope, it could climb $\frac{3^2}{2 \times 9.81} \approx 0.46 \text{ m}$.

The same ball held 10 m up has $PE = 2 \times 9.81 \times 10 = 196.2 \text{ J}$, and dropped, it would hit the ground at about $\sqrt{2 \times 9.81 \times 10} \approx 14 \text{ m/s}$.

Tips and Common Mistakes

• Square the speed, not the half. KE is ½ × m × v², so doubling speed quadruples energy.
• Use kilograms and meters per second for joules, or let the calculator convert for you.
• Height is measured from a reference level you choose; only changes in height matter.
• The conservation figures ignore friction and air resistance, so real objects climb a little less and fall a little slower.
• Mass doesn’t affect the fall speed. A heavier object has more energy, but reaches the same speed.