Potential Energy Calculator
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A potential energy calculator estimates near-Earth gravitational potential energy from mass, gravitational acceleration and vertical height relative to a chosen reference.
Potential Energy Calculator Formula and Reference Height
PE = mgh. Use kilograms, m/s² and metres to obtain joules. Rearranged forms can solve for mass, gravity or height.
Potential Energy Calculator and the Zero Level
Potential energy depends on a reference. The absolute zero is arbitrary for many problems; the meaningful quantity is usually the change between two heights.
Worked example
Raising a 12 kg object by 3 m using g = 9.81 m/s² increases potential energy by 353.16 J.
Use vertical height
An object moved along a ramp gains energy according to vertical elevation change, not the longer path distance. Friction affects required work but not the mgh change itself.
When constant g is reasonable
The formula approximates a uniform gravitational field near Earth’s surface. Large altitude or planetary-scale problems should use gravitational potential based on distance from the body’s centre.
Energy conversion
In an ideal system, lost potential energy can become kinetic energy. Real systems also transfer energy to heat, sound, deformation and rotation.
Calculate a change rather than an arbitrary total
For most near-Earth problems, the useful relationship is ΔPE = mg(h₂ − h₁). Choosing the floor, table or starting point as zero changes the reported potential energy but not the energy difference between two heights. Write the reference level beside the result so another reader can reproduce it.
Relation to work and lifting force
In an ideal slow lift with no losses, external work against gravity equals the increase in gravitational potential energy. Lifting faster changes average power, not the mgh energy change for the same mass and height. Real machines also lose energy through friction, deformation and heat.
Ramps, stairs and vertical rise
A longer ramp can reduce required force while increasing travel distance, but the vertical height determines ΔPE. Similarly, climbing two staircases with the same elevation gain produces the same ideal gravitational-energy increase for the same mass, even if the horizontal layout differs.
Beyond the constant-gravity approximation
For satellites or very large altitude changes, gravitational acceleration is not constant. The more general gravitational potential depends on masses and distance from the center of the attracting body. Do not extend mgh to orbital scales without checking that its near-surface assumption remains valid.
Input checks
- Use total lifted mass, including any carried load.
- Enter vertical height change in metres for SI joules.
- Use the specified local value of g when provided.
- Keep the sign consistent with the chosen reference.
- Separate energy from power and force.
Potential energy is a property of the system and its configuration, not a substance stored inside one object in isolation. State the model and reference level when comparing answers.
Sign conventions in falling motion
If upward is positive, height and potential-energy change decrease while an object falls. The lost gravitational potential energy may appear as kinetic energy and other transfers. Avoid changing the zero level midway through a problem. A negative final value is not automatically wrong; verify the difference between states and the direction defined at the start. When presenting an answer, state both the zero height and whether the number represents a total or a change. Keep that convention in every later energy equation.
See OpenStax University Physics Volume 1 for a fuller treatment of gravitational energy.
potential energy calculator FAQs
Can potential energy be negative?
Yes relative to the chosen zero; only differences must remain physically consistent.
Is height measured along a slope?
No. Use vertical elevation change.
Which value of gravity should I use?
9.81 m/s² is a common Earth approximation; use the problem’s specified value when provided.
Pair this with the Kinetic Energy Calculator for mechanical-energy comparisons.
