Potential Energy Calculator
Gravitational potential energy is the energy stored in an object due to its height above a reference point. This calculator uses PE = mgh to compute potential energy in Joules, and also shows the velocity the object would reach if it fell from that height.
Advertisement
Calculator
See your Potential Energy Calculator results
Enter your email to unlock results — free forever.
No spam, ever. Unsubscribe at any time.
Advertisement
Formula
PE = mgh
Potential energy (PE) equals mass (m) times gravitational acceleration (g) times height (h). On Earth, g = 9.81 m/s². Result is in Joules. Impact velocity if dropped from height h is derived from energy conservation: all PE converts to KE, so ½mv² = mgh, giving v = √(2gh). Note mass cancels — all objects fall at the same speed regardless of mass.
How to use the Potential Energy Calculator
- 1
Enter your mass
Value should be in kg.
- 2
Enter your height
Value should be in m.
- 3
Enter your gravitational acceleration
Value should be in m/s².
- 4
Read your results instantly
Results update in real time as you type.
Advertisement
Gravitational potential energy and reference points
Potential energy is always measured relative to a reference height — usually the ground or some convenient baseline. Only changes in potential energy matter; the absolute value depends on where you set zero. A book on a table has more potential energy than the same book on the floor, but less than the same book on a shelf — all relative to whatever reference you choose.
This is why potential energy can be 'negative': if you set sea level as zero and measure an object in Death Valley (below sea level), its potential energy relative to sea level is negative. What matters physically is ΔPE = mgΔh — the change when height changes.
Conservation of energy in action
Energy conservation is one of the most fundamental principles in physics. When an object falls (ignoring air resistance), potential energy converts to kinetic energy with perfect efficiency: PE lost = KE gained. A 10 kg ball dropped from 10 m converts 981 J of PE into 981 J of KE, reaching √(2 × 9.81 × 10) ≈ 14 m/s just before hitting the ground.
This same principle powers hydroelectric dams: water at height h has potential energy that converts to kinetic energy as it falls, spinning turbines to generate electricity. A dam 100 m tall with 1,000 kg/s of water flow generates about 981 kW of mechanical power (before efficiency losses).
Advertisement
Potential energy on other planets
The gravity field value (g) changes the calculation significantly. On the Moon (g ≈ 1.62 m/s²), the same 10 kg object at 10 m height has only 162 J of PE — about one-sixth of Earth's 981 J. On Jupiter (g ≈ 24.8 m/s²), it would be 2,480 J — over twice Earth's value.
This matters for space mission planning: the energy cost to launch a rocket depends on the planet's gravity. Mars (g ≈ 3.72 m/s²) requires far less fuel to escape than Earth (g = 9.81 m/s²). The Moon landing was partly enabled by the ease of lunar liftoff — the ascent stage needed only a small engine to reach escape velocity.
Tips & Insights
Use g = 9.81 for Earth
Standard gravitational acceleration on Earth is 9.81 m/s². Some textbooks use 9.8 or 10 for simplicity. This calculator defaults to 9.81 for accuracy.
Height is relative
Set your reference height consistently. If you're calculating PE for an object on a ramp, measure height as the vertical rise above the lowest point of interest, not the slope length.
PE converts to KE in free fall
The impact velocity formula v = √(2gh) applies to any free-falling object regardless of mass. All objects fall at the same rate in a vacuum — a feather and a hammer hit the ground at the same time (as demonstrated on the Moon).
Worked Examples
Diver on a 10m platform
PE = 70 × 9.81 × 10 = 6,867 J. Impact speed (entering water): √(2 × 9.81 × 10) ≈ 14 m/s (50 km/h).
Water behind a dam
PE = 1,000 × 9.81 × 50 = 490,500 J ≈ 490.5 kJ per cubic meter of water at 50 m height.
Advertisement
Frequently Asked Questions
What is potential energy?
Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. It equals mgh — mass times gravity times height.
What is the unit of potential energy?
Joules (J) in SI units, same as all forms of energy. 1 J = 1 kg·m²/s².
Why does impact speed not depend on mass?
In PE = mgh and KE = ½mv², mass appears on both sides and cancels: ½v² = gh, so v = √(2gh). All objects (in vacuum) hit the same speed when dropped from the same height.
What is elastic potential energy?
Elastic PE is energy stored in stretched or compressed materials (springs, rubber bands). It follows PE = ½kx², where k is the spring constant and x is displacement. This calculator covers gravitational PE only.
Can potential energy be negative?
Yes — it depends on your reference point. If you set zero at a height above the object, PE is negative. Only changes in PE have physical significance.
Advertisement