Potential Energy Calculator

Calculate gravitational potential energy from mass, gravitational acceleration, and height. Also computes equivalent kinetic energy velocity and power generation potential.

GRAVITATIONAL POTENTIAL ENERGY
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Energy (kJ)
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Energy (cal)
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Equiv. Velocity (m/s)
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Weight Force (N)
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What Is Potential Energy?

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. When you lift a book off the floor, you do work against gravity, and that energy is stored as potential energy. When the book falls, that stored energy converts to kinetic energy (energy of motion). This fundamental concept is central to mechanics, engineering, and energy generation.

The concept extends beyond gravity. Elastic potential energy is stored in stretched springs and compressed materials. Chemical potential energy is stored in molecular bonds. Electrical potential energy exists in charged particles within electric fields. All forms of potential energy share the common principle of stored energy due to position or configuration within a force field.

Formula

PE = m × g × h
Equivalent velocity: v = √(2gh)

Where PE is potential energy in Joules, m is mass in kg, g is gravitational acceleration (9.81 m/s² on Earth), and h is height in meters above the reference point. The equivalent velocity is the speed the object would reach if all PE converted to kinetic energy during free fall.

Real-World Examples

  • Hydroelectric dams: Water stored at height has PE that converts to kinetic energy as it flows through turbines, generating electricity. The Hoover Dam stores water 180 m high.
  • Roller coasters: The initial climb stores PE that powers the entire ride through successive conversions between PE and KE.
  • Pendulum clocks: A raised weight provides PE that slowly converts to kinetic energy, driving the clock mechanism.
  • Pumped-storage hydroelectricity: Excess grid power pumps water uphill, storing energy as PE for later release during peak demand.

Energy Comparisons

ScenarioMassHeightEnergy
Apple on table0.2 kg1 m1.96 J
Person on 10th floor75 kg30 m22,073 J
Car on mountain pass1500 kg2000 m29.4 MJ
Water in reservoir1,000,000 kg100 m981 MJ

Frequently Asked Questions

Does the path matter for potential energy?

No. Gravitational potential energy depends only on the vertical height difference between two points, not the path taken. Whether you carry an object straight up or along a winding ramp, the PE change is identical. This is because gravity is a conservative force, meaning work done depends only on initial and final positions.

What is the reference point for height?

The reference point (zero height) is arbitrary and chosen for convenience. Often it is ground level, the floor, or sea level. Only changes in potential energy have physical meaning, so the choice of reference does not affect calculations of energy conversion or work done.

How does gravity vary by location?

Standard gravity is 9.80665 m/s², but actual values range from 9.78 at the equator to 9.83 at the poles due to Earth's rotation and oblate shape. At high altitude, gravity decreases by about 0.003 m/s² per kilometer. On the Moon, g = 1.62 m/s²; on Mars, g = 3.72 m/s².