Potential Energy Calculator
Calculate gravitational (PE=mgh), elastic (PE=½kx²), and electric potential energy
Calculate gravitational potential energy from mass, gravity, and height.
Quick Reference:
- Gravitational PE: Energy due to position in a gravitational field
- Elastic PE: Energy stored in a stretched or compressed spring
- Electric PE: Energy due to position of charges (k = 8.99×10⁹ N·m²/C²)
- Earth's gravity: g = 9.80665 m/s² (standard)
- Moon's gravity: g = 1.62 m/s²
- Mars's gravity: g = 3.72 m/s²
Understanding Potential Energy
Potential energy is stored energy that an object has due to its position, configuration, or condition. Unlike kinetic energy which depends on motion, potential energy represents the potential for doing work.
Gravitational Potential Energy
The formula PE = mgh calculates the energy stored in an object due to its height above a reference point. Here, m is mass, g is gravitational acceleration (9.8 m/s² on Earth), and h is height. The higher an object is lifted, the more potential energy it stores.
Elastic Potential Energy
Springs and elastic materials store energy when stretched or compressed. The formula PE = ½kx² shows that elastic potential energy depends on the spring constant (k) and the displacement (x) from the equilibrium position. Note that energy increases with the square of displacement.
Electric Potential Energy
Two charged particles have potential energy due to their electrostatic interaction. The formula PE = kq₁q₂/r uses Coulomb's constant (k ≈ 8.99×10⁹ N·m²/C²), the two charges, and the distance between them. Like charges result in positive (repulsive) energy, while opposite charges give negative (attractive) energy.
Conservation of Energy
Potential energy can be converted to kinetic energy and vice versa. A falling object converts gravitational PE to kinetic energy. A compressed spring releases its elastic PE as kinetic energy. Total mechanical energy (PE + KE) remains constant in an isolated system.
Examples of Potential Energy
- Water behind a dam: Gravitational PE converted to electrical energy
- Drawn bow: Elastic PE stored in the bent limbs
- Roller coaster at top: Maximum gravitational PE
- Compressed car spring: Elastic PE for suspension
Gravity on Different Bodies
Gravitational potential energy varies with location. On the Moon (g = 1.62 m/s²), an object has less gravitational PE at the same height compared to Earth. On Jupiter (g = 24.79 m/s²), it would have much more.
Worked Example: Lifting a Box
Suppose you lift a 12 kg box onto a shelf 1.5 m above the floor. Using PE = mgh with g = 9.8 m/s²: PE = 12 × 9.8 × 1.5 = 176.4 joules. That is the work you did against gravity, and exactly the kinetic energy the box would have just before hitting the floor if it fell back down (ignoring air resistance).
Frequently Asked Questions
How do I calculate gravitational potential energy?+
Enter the object's mass, its height above the reference point, and the gravitational acceleration (9.8 m/s² on Earth by default). The calculator multiplies them using PE = mgh and returns the result in joules. For example, a 2 kg book on a 1 m shelf stores 2 × 9.8 × 1 = 19.6 J.
What units should I use for potential energy calculations?+
Use SI units: kilograms for mass, meters for height or spring displacement, newtons per meter for spring constant, and coulombs for charge. The result is then in joules (1 J = 1 kg·m²/s²). If you have pounds or feet, convert them first — 1 lb is about 0.4536 kg and 1 ft is 0.3048 m.
What is the difference between gravitational and elastic potential energy?+
Gravitational PE (mgh) grows linearly with height, while elastic PE (½kx²) grows with the square of displacement — doubling a spring's stretch quadruples the stored energy. Both represent stored work that can convert to kinetic energy, but they arise from different forces: gravity versus a spring's restoring force.
Can potential energy be negative?+
Yes. Gravitational PE is negative if the object sits below your chosen reference level, since height h is measured relative to that level. Electric potential energy is negative for opposite charges because they attract — you must add energy to separate them. Only elastic PE (½kx²) is always non-negative.
Is this potential energy calculator free to use?+
Yes, it is completely free with no sign-up required. All calculations run entirely in your browser, so nothing is sent to a server, and the responsive layout works on phones and tablets — convenient for physics homework or lab work on any device.
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