Potential Energy Calculator

Calculate gravitational potential energy, mass, or height. Select what to solve for and enter known values.

Gravitational Potential Energy Formula: PE = mgh Where: • PE = potential energy (joules, J) • m = mass (kilograms, kg) • g = gravitational acceleration (m/s²) - Earth: 9.8 m/s² (standard: 9.80665) - Moon: 1.62 m/s² - Mars: 3.71 m/s² • h = height above reference point (meters, m) Rearrangements: • Mass: m = PE/(gh) • Height: h = PE/(mg)
Example 1 (Energy): A 70 kg person stands on a 10 m platform (Earth) PE = 70 * 9.8 * 10 = 6,860 J ~= 6.86 kJ This is the energy released if they fall to ground level. Example 2 (Mass): An object 5 m high has 980 J of PE on Earth m = 980 / (9.8 * 5) = 980 / 49 = 20 kg Example 3 (Height): A 2 kg object has 500 J of PE on Earth h = 500 / (2 * 9.8) = 500 / 19.6 ~= 25.5 m Example 4 (Moon): A 10 kg object at 6 m height on the Moon (g = 1.62) PE = 10 * 1.62 * 6 = 97.2 J Same object on Earth would have: 10 * 9.8 * 6 = 588 J (6x more!) Example 5 (Energy conversion): Water at top of 100 m dam, mass 1000 kg PE = 1000 * 9.8 * 100 = 980,000 J = 980 kJ Falling to bottom, this converts to kinetic energy: v = sqrt(2gh) ~= 44.3 m/s

What is potential energy?

Potential energy is stored energy due to an object's position or configuration. Gravitational potential energy (PE = mgh) depends on mass, height, and gravity. It represents the work needed to lift an object to that height.

What is the formula for gravitational potential energy?

PE = mgh, where m is mass (kg), g is gravitational acceleration (9.8 m/s² on Earth), and h is height (m). This gives energy in joules (J). The formula assumes constant gravity and a reference point at h = 0.

Why does gravity vary with location?

Earth's gravity varies slightly by location due to altitude, latitude, and local geology. Standard g = 9.80665 m/s². It's weaker at high altitudes (9.78 at Everest) and stronger at poles (9.83) vs equator (9.78) due to Earth's rotation and shape.

Can potential energy be negative?

Yes, if you choose a reference point above the object. PE is relative to a chosen zero point. In gravitational fields extending to infinity, PE is often set to zero at infinity, making all finite-distance PE negative.

What is elastic potential energy?

Elastic PE is energy stored in stretched or compressed elastic materials (springs, rubber bands). Formula: PE = ½kx², where k is spring constant and x is displacement. Different from gravitational PE.

How does potential energy convert to kinetic energy?

When an object falls, PE converts to KE. Starting from rest at height h: PE_initial = mgh becomes KE_final = ½mv². This gives v = √(2gh). Energy conservation: PE_i + KE_i = PE_f + KE_f.

What happens to potential energy at the Moon?

Moon's gravity is ~1.62 m/s² (about 1/6 of Earth's). An object has less PE on the Moon at the same height and mass. This is why astronauts can jump higher there - they need less energy to gain height.

How do you calculate the height from potential energy?

Rearrange PE = mgh to get h = PE/(mg). For example, if a 2 kg object has 196 J of PE on Earth: h = 196/(2 × 9.8) = 196/19.6 = 10 meters.

What are real-world applications of potential energy?

Applications include: hydroelectric dams (water's PE converts to electricity), roller coasters (PE at top converts to KE downhill), pendulums, counterweights in elevators, and gravitational energy storage systems.

Is potential energy a vector or scalar?

Potential energy is a scalar quantity (has magnitude but no direction). However, the gravitational force and field are vectors. PE is the scalar potential from which the force vector can be derived (F = -∇PE).

What is the zero point for potential energy?

The zero point is arbitrary and chosen for convenience. Often set at ground level, but could be anywhere. Only changes in PE matter physically. For Earth-Moon system, zero might be at Earth's center or at infinity.

How does potential energy relate to work?

The work done against gravity to lift an object equals the PE gained: W = Fd = (mg)h = mgh. This is why PE = mgh. Work and energy have the same units (joules) and are interconvertible.