Potential Energy Calculator (PE = mgh)

Frequently Asked Questions

What is the formula for gravitational potential energy?

PE = mgh: mass × gravitational acceleration × height above a chosen reference. On Earth, g = 9.81 m/s². Choose any convenient zero level: only differences in PE matter.

Why does PE depend on a chosen reference height?

Only changes in PE affect the physics. Whether ground level or sea level is "zero" is arbitrary; what matters is how much PE changes between two heights.

How does PE differ on other planets?

g varies: Moon ≈ 1.62 m/s², Mars ≈ 3.71, Jupiter ≈ 24.79, Sun ≈ 274. The same mass at the same height has very different PE on each.

How does PE convert to KE?

In a frictionless drop, all PE converts to KE: ½mv² = mgh, so v = √(2gh). A 10 m drop on Earth gives v ≈ 14 m/s regardless of mass.

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How This Calculator Works

You choose what to solve for, potential energy, mass, or height, pick a gravitational body (or type a custom g), and supply the other two values. The tool returns the potential energy in joules and kilojoules along with the mass and height that satisfy the equation, so you can check the relationship from any direction.

Formula

Gravitational potential energy is PE = m × g × h, where m is mass in kilograms, g is the gravitational acceleration in m/s², and h is height in meters above the reference, giving PE in joules. Rearranged, m = PE ÷ (g × h) and h = PE ÷ (m × g). Built-in presets: Earth 9.81, Moon 1.62, Mars 3.71, Jupiter 24.79, and Sun 274 m/s².

Worked Example

A 10 kg mass lifted 5 m on Earth: PE = 10 × 9.81 × 5 = 490.5 J (0.4905 kJ). On the Moon the same lift stores only 10 × 1.62 × 5 = 81 J, because the Moon's gravity is about one sixth of Earth's. Solving for height given 490.5 J: h = 490.5 ÷ (10 × 9.81) = 5 m. If that 10 kg mass then falls back 5 m in a frictionless drop, it lands at v = √(2 × 9.81 × 5) ≈ 9.9 m/s, converting all PE back into kinetic energy.

Common Mistakes

Using grams or pounds for mass instead of kilograms.

Measuring height in feet rather than meters.

Keeping Earth's g when the scenario takes place on another body.

Entering a zero mass or zero height when solving the inverse, which is undefined.

Forgetting that only the height difference from the chosen reference matters, not the absolute height.

Tips & FAQ

Where is PE zero? At whatever ground level you pick: only differences in PE are physically meaningful.

What happens as it falls? Gravitational PE converts to kinetic energy (½mv²), conserving total mechanical energy when drag is negligible.

Why does the body matter? g scales the energy directly, so lower-gravity worlds store far less PE for the same lift. See the kinetic energy calculator for the conversion that completes the picture.

Potential Energy Calculator (PE = mgh)

Frequently Asked Questions

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