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Physics

Gravitational Potential Energy

PE = mgh. Free online Gravitational Potential Energy. Calculate gravitational potential energy online — fast, accurate, mobile-friendly, no signup needed.

PE = m·g·h.
PE
490.5 J

Derivation

  1. ├── 01Givenm = 10, h = 5, g = 9.81
  2. ├── 02Formulat × e.g × a
  3. ├── 03Substitutet × e.9.81 × a
  4. └── 04Compute PE490.5 J
Did you know?

The phrase "kinetic energy" was coined by William Thomson (Lord Kelvin) and Peter Guthrie Tait in 1867 — before that physicists called it vis viva, "living force".

§01What is

Understanding the Gravitational Potential Energy

The Gravitational Potential Energy computes PE from 3 inputs: mass (kg), height (m), gravity (m/s²). PE = mgh.

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Gravitational Potential Energy sits in that toolkit — it PE = mgh. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

t × e.g × a

Where

m
Mass (kg)
h
Height (m)
g
Gravity (m/s²)
result
PE — in J
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Mass (kg) = 10, Height (m) = 5, Gravity (m/s²) = 9.81.

  1. 01Start by noting the input — Mass (kg): 10.
  2. 02Start by noting the input — Height (m): 5.
  3. 03Start by noting the input — Gravity (m/s²): 9.81.
  4. 04Substitute these values into the formula: t × e.g × a
  5. 05Compute PE: the calculator returns 490.5 J.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Gravitational Potential Energy Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Mass (kg) halved

m = 5 (from 10)

Keep every other input at its default and halve the mass (kg). See how pe responds.

  1. 01New Mass (kg): 5
  2. 02Baseline PE: 490.5 J
  3. 03New PE: 245.25 J
  4. 04PE decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Mass (kg) doubled

m = 20 (from 10)

Keep every other input at its default and double the mass (kg). See how pe responds.

  1. 01New Mass (kg): 20
  2. 02Baseline PE: 490.5 J
  3. 03New PE: 981 J
  4. 04PE increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Height (m) halved

h = 2.5 (from 5)

Keep every other input at its default and halve the height (m). See how pe responds.

  1. 01New Height (m): 2.5
  2. 02Baseline PE: 490.5 J
  3. 03New PE: 245.25 J
  4. 04PE decreases by 50% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Height (m) doubled

h = 10 (from 5)

Keep every other input at its default and double the height (m). See how pe responds.

  1. 01New Height (m): 10
  2. 02Baseline PE: 490.5 J
  3. 03New PE: 981 J
  4. 04PE increases by 100% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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