Potential Energy Calculator
Potential energy is the energy stored in an object because of its position or configuration. This calculator covers the two forms most commonly encountered in physics: gravitational potential energy and elastic (spring) potential energy. Gravitational PE arises when an object is raised above a reference level in a gravitational field. The formula is PE = m * g * h, where m is mass in kilograms, g is gravitational acceleration (9.81 m/s² at Earth's surface), and h is height in metres. Elastic PE is the energy stored in a compressed or stretched spring, calculated as PE = 0.5 * k * x², where k is the spring constant in newtons per metre and x is the displacement from the equilibrium position in metres. Both forms follow from the principle of conservation of energy: potential energy converts to kinetic energy (and vice versa) in a frictionless system, keeping total mechanical energy constant. Results are shown in joules (J) and kilojoules (kJ). Select the mode below to switch between gravitational and elastic calculations.
Potential energy: -- J (-- kJ)
How potential energy is calculated
Both gravitational and elastic potential energy can be derived from first principles using the work-energy theorem. In each case, the stored energy equals the work done against the relevant force to achieve the given configuration.
Gravitational potential energy
PE = m × g × h
where PE = potential energy (J), m = mass (kg), g = gravitational acceleration (m/s²), h = height (m)
Elastic potential energy (spring)
PE = 0.5 × k × x²
where PE = potential energy (J), k = spring constant (N/m), x = displacement (m)
Worked example: gravitational
A 10 kg object lifted 5 m on Earth (g = 9.81 m/s²):
- PE = 10 × 9.81 × 5 = 490.50 J
- In kilojoules: 490.50 / 1,000 = 0.49 kJ
Worked example: elastic
A spring with k = 200 N/m compressed by 0.1 m:
- PE = 0.5 × 200 × 0.1² = 0.5 × 200 × 0.01 = 1.00 J
Potential energy calculator: frequently asked questions
What is potential energy?
Potential energy is stored energy that an object possesses due to its position or configuration. The two most common forms in introductory physics are gravitational potential energy (energy stored by height in a gravitational field) and elastic potential energy (energy stored in a stretched or compressed spring). Both are measured in joules (J).
What is gravitational potential energy?
Gravitational potential energy (GPE) is the energy stored by an object due to its height above a reference point: GPE = m * g * h. Here m is mass (kg), g is gravitational acceleration (9.81 m/s² at Earth's surface), and h is height (m). It represents the work that gravity would do if the object fell to the reference level.
What is elastic potential energy?
Elastic potential energy is the energy stored in a spring or elastic object when it is stretched or compressed from its equilibrium position: EPE = 0.5 * k * x². Here k is the spring constant (N/m) and x is the displacement from equilibrium (m). This follows from Hooke's Law, where the restoring force is F = -k * x.
How does conservation of energy connect kinetic and potential energy?
In a frictionless system, total mechanical energy (KE + PE) is constant. As an object falls, gravitational PE decreases and kinetic energy increases by the same amount. Similarly, a compressed spring releases its elastic PE as kinetic energy when released. This principle is called conservation of mechanical energy.
What is the standard value of g used in the formula?
The standard acceleration due to gravity is defined by NIST and the BIPM as exactly 9.80665 m/s², which is rounded to 9.81 m/s² for most calculations. The actual local value of g varies slightly with latitude and altitude, from about 9.78 m/s² at the equator to 9.83 m/s² at the poles. This calculator uses 9.81 m/s² by default but allows you to enter a custom value.
Official sources
- NIST SP 330 (2019) "The International System of Units (SI)": NIST SP 330 PDF.
- NIST SI Unit definitions: nist.gov SI units.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology. General information only.