Potential Energy Calculator - Energy, Mass, Height & Gravity
Use this gravitational potential energy calculator to solve PE = mgh for potential energy, mass, height, or gravitational acceleration.
Potential Energy Calculator
Results
PE = mgh assumes gravity is constant across the height change.
What is a Potential Energy Calculator?
A potential energy calculator finds the energy stored by an object because of its vertical position in a gravitational field. It uses mass, height, and gravitational acceleration to estimate gravitational potential energy near the surface of a planet or moon.
This PE mgh calculator works in either direction. Enter mass, height, and gravity to find energy, or enter potential energy with two known values to solve for the missing mass, height, or gravity.
- Check physics homework that uses PE = mgh.
- Compare the same lift on Earth, the Moon, Mars, or Jupiter.
- Convert pounds, feet, joules, calories, watt-hours, and foot-pounds.
- Work backward from a target energy to a required height or mass.
To compare energy units after solving, use our Energy Converter for joules, calories, watt-hours, and related units.
For motion energy instead of stored height energy, use the Kinetic Energy Calculator to solve K = 1/2mv^2.
How the Potential Energy Calculator Works
The gravitational potential energy formula is:
PE is potential energy in joules, m is mass in kilograms, g is gravitational acceleration in m/s^2, and h is vertical height in meters. The calculator converts every input to SI units before applying the formula, then converts the result back to your selected unit. The joule, meter, and kilogram are SI units defined by the National Institute of Standards and Technology.
For reverse calculations, the formula becomes m = PE / (g x h), h = PE / (m x g), or g = PE / (m x h).
If the problem gives force rather than mass and gravity separately, use the Force Converter to normalize newtons, pounds-force, and related force units before comparing results.
Key Potential Energy Concepts
Gravitational potential energy depends on three quantities. Changing any one of them changes the stored energy in direct proportion.
Mass
Twice the mass means twice the potential energy at the same height and gravity.
Height
Height means vertical change, not slope distance along a ramp or path.
Gravity
The same object stores less energy on the Moon and more on Jupiter for the same height.
Joules
One joule equals one kg m^2/s^2, so PE = mgh naturally returns joules in SI units.
For heat energy problems that use mass and temperature change instead of height, compare this formula with the Specific Heat Calculator.
How to Use This Calculator
- 1Choose whether to solve for potential energy, mass, height, or gravity.
- 2Enter the known values and select their units.
- 3Use a gravity preset for Earth, Moon, Mars, or Jupiter, or choose custom.
- 4Pick the output unit for the unknown value.
- 5Review the SI base values and formula row to confirm the calculation path.
To convert rates of energy use after solving, use the Power Converter for watts, horsepower, BTU per hour, and related power units.
Benefits of Using This Calculator
This calculator reduces unit mistakes by converting all known values into SI base units before solving. That is useful when a problem mixes pounds with feet, calories with meters, or classroom values with engineering-style precision.
For wave examples where energy is discussed alongside frequency, wavelength, or speed, use the Wave Speed Calculator to solve the motion relationship separately.
Factors That Affect Your Results
Potential energy calculations are linear, but the assumptions behind the inputs matter. Use consistent units and make sure height is the vertical height change.
For reference gravity values across planets, NASA keeps a public planetary fact sheet that can help when setting custom gravity for non-Earth examples. Use the custom gravity field when a classroom problem or reference source gives a different value.
Potential Energy Calculator FAQ
Q: What is the gravitational potential energy formula?
A: The gravitational potential energy formula near a surface is PE = mgh, where PE is energy, m is mass, g is gravitational acceleration, and h is vertical height.
Q: How do you calculate potential energy?
A: Convert mass to kilograms, height to meters, and gravity to meters per second squared. Then multiply mass by gravity by height to get potential energy in joules.
Q: Can this calculator solve for mass, height, or gravity?
A: Yes. It rearranges PE = mgh to m = PE / (g x h), h = PE / (m x g), or g = PE / (m x h) depending on the value you choose to solve for.
Q: What units does this potential energy calculator support?
A: It supports energy in J, kJ, cal, kcal, Wh, and ft-lb; mass in kg, g, lb, and oz; height in m, cm, ft, and in; and gravity in m/s^2 or ft/s^2.
Q: What gravity value should I use on Earth?
A: For most school and engineering estimates near Earth surface, use 9.80665 m/s^2. Some classroom problems round this to 9.8 m/s^2.
Q: Does PE = mgh work for all heights?
A: No. PE = mgh is a near-surface approximation where gravity is treated as constant. For very large altitude changes, use the universal gravitational potential energy equation.