Potential Energy Calculator
Potential energy represents mechanical energy stored within a system by virtue of its spatial configuration or elevation. Gravitational potential energy (PE = m·g·h) measures work stored against a gravity field, converting seamlessly into kinetic energy during free fall. Elastic potential energy (PE = ½·k·x²) measures energy stored when deforming a spring according to Hooke's Law.
Mass of the elevated body in kilograms (kg)
Elevation above the reference datum plane in metres (m)
Local gravitational field strength (Earth: 9.81, Moon: 1.62, Mars: 3.72 m/s²)
Spring stiffness in Newtons per metre (N/m)
Compression or extension stretch from equilibrium in metres (m)
Energy stored in the gravitational field in Joules (J)
How to Use This Calculator
- Enter the mass of the object in kilograms.
- Specify the height elevation above ground level in metres.
- Adjust local gravity if computing for other celestial bodies (e.g. Moon = 1.62 m/s²).
- Enter spring stiffness and compression distance to calculate Hookean elastic storage.
Formula & Calculation Methodology
Gravitational potential energy equals mass times gravitational acceleration times vertical height. By conservation of mechanical energy (PE = KE), a falling body reaches impact speed v = √(2gh). Spring energy integrates Hooke's law F = kx across displacement x.
Worked Example
An 80 kg skydiver perched on a 15-metre dive platform on Earth
Frequently Asked Questions
Why is potential energy defined relative to a reference datum?↓
Only differences in potential energy (ΔPE) have physical significance. You can choose any reference level (such as floor level, sea level, or infinity) as zero potential energy without changing the resulting work or kinetic energy equations.
Does atmospheric air resistance alter potential energy?↓
No. Potential energy depends solely on position within the gravitational field (m·g·h). However, during descent, air drag dissipates some potential energy into atmospheric heat rather than 100% kinetic velocity.
What is Hooke's Law for spring potential energy?↓
Hooke's Law states that restoring force is proportional to displacement (F = -k·x). Integrating this force over displacement produces quadratic stored potential energy: PE = ½·k·x².
What limitation exists when calculating potential energy at astronomical heights?↓
The formula PE = m·g·h assumes a uniform gravitational field where g is constant. For satellites or space probes where elevation h is significant compared to Earth's radius R, the universal formula PE = -G·M·m / r must be used.
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.