The potential energy formula
Gravitational potential energy is PE = m·g·h, where m is mass in kilograms, g is gravitational acceleration (9.8 m/s²), and h is height in meters. A 2 kg mass raised 10 m stores 196 J. This energy converts to motion as the object falls. To see the work needed to lift it, use the work calculator.
The formula is really just work in disguise. Lifting an object at steady speed means pushing up with a force equal to its weight, m·g, through a distance h — and force times distance is work. The energy you spend does not vanish; it is stored in the object's raised position and comes straight back as kinetic energy if the object is released.
How to use this calculator
Enter the mass in kilograms and the height above the reference point in meters. The calculator uses g = 9.8 m/s² and returns energy in joules (J). Height is measured from whatever level you call zero. For the force of that same mass, see the weight calculator.
- Only the vertical drop counts. Sliding along a ramp or a curved path changes nothing — horizontal distance contributes no gravitational PE.
- Negative heights are allowed and give negative PE, meaning the object sits below your chosen zero.
- Grams are not kilograms — divide by 1,000 before entering a mass in grams.
Worked example
Lift a 2 kg book onto a 10 m high shelf: 2 × 9.8 × 10 = 196 J. Raise it twice as high to 20 m and the stored energy doubles to 392 J, because PE rises in proportion to height. As the object falls, that stored energy turns into the kinetic energy of motion.
Frequently asked questions
- How do I calculate potential energy?
- Multiply mass by gravity (9.8) by height: PE = m·g·h.
- What value of g does this use?
- It uses g = 9.8 m/s², the standard gravitational acceleration near Earth's surface.
- What are the units of potential energy?
- Joules (J), the same energy unit as work and kinetic energy.
- Where is the zero of potential energy?
- Wherever you choose. Height is measured relative to that reference level.
- What if my mass is in pounds or my height in feet?
- Convert to SI units first, or the joule result will be wrong. Divide pounds by 2.205 to get kilograms and multiply feet by 0.3048 to get metres before entering them.