Potential Energy Calculator (PE = mgh)
By Santaji GadepatilinUpdated October 27, 2026
Gravitational potential energy is the energy an object has because of its height. Lifting a mass stores energy that is released as it falls — the principle behind hydropower and pumped storage.
Potential energy (kJ) vs Height (m) — other inputs held at your current values.
How to use the potential energy calculator
Enter the mass and height to get the potential energy, or enter the energy to find the height. Choose J, kJ, kWh or other energy units.
Potential energy formula
PE = m × g × h (g = 9.80665 m/s²)
Worked example
1,000 kg (1 m³) of water held 50 m above a turbine:
PE = 1,000 × 9.81 × 50 = 490 kJ = 0.136 kWh
Potential energy examples
| Situation | Mass | Height | Energy |
|---|---|---|---|
| Book on a shelf | 1 kg | 2 m | 20 J (0.0000 kWh) |
| Person climbing a floor | 70 kg | 3 m | 2,059 J (0.0006 kWh) |
| Water in a rooftop tank | 1,000 kg | 15 m | 147,100 J (0.0409 kWh) |
| Lift car with passengers | 1,500 kg | 30 m | 441,299 J (0.1226 kWh) |
| Water behind a 100 m dam (1 m³) | 1,000 kg | 100 m | 980,665 J (0.2724 kWh) |
Hydroelectric power
Hydro plants turn water’s potential energy into electricity:
P = ρ × g × Q × h × η
with Q the flow in m³/s, h the head in metres and η the efficiency (often 0.85–0.9). A flow of 10 m³/s through a 50 m head at 88% efficiency gives about 4.3 MW.
Pumped storage
Pumped-storage hydro stores energy by pumping water uphill when electricity is cheap and releasing it through turbines when demand is high. 1 m³ of water raised 100 m stores only about 0.27 kWh, so these schemes move very large volumes.
Elastic potential energy
Springs store energy too: E = ½ × k × x², where k is the spring constant and x the stretch or compression. A spring with k = 2,000 N/m compressed by 5 cm stores 2.5 J.
Energy conservation
If dropped, the object’s potential energy turns into kinetic energy. Ignoring air resistance, its speed at the bottom is v = √(2gh) — for 50 m that is 31.3 m/s. Check it with the free fall calculator.
Height is measured from a reference
Potential energy is always relative to a chosen zero level, such as the floor or the turbine.
Frequently asked questions
What is gravitational potential energy?
The energy an object has because of its height. Lifting it stores energy that is released when it falls.
Why is it m × g × h?
Lifting a mass m against gravity g through height h takes force mg over distance h, and work = force × distance.
Can it be converted to electricity?
Yes. Hydropower and pumped-storage plants turn falling water's potential energy into electricity at around 80–90% efficiency.
What is the formula for potential energy?
PE = m × g × h: mass × gravitational acceleration (9.81 m/s²) × height.
How much energy is needed to lift 1 kg by 1 m?
About 9.81 joules.