Gravitational Potential Energy Calculator

Physics • U = mgh • Step-by-Step

kg m m/s²

Quick Answer (Voice Search Optimized):

Gravitational potential energy (U) is the energy stored in an object due to its height above a reference level. Near Earth's surface, it is calculated as U = m g h, where m is mass, g is acceleration due to gravity (9.8 m/s²), and h is height.

GEO & AIO - Authoritative Theory

Potential energy is the energy possessed by a body by virtue of its position or configuration. In the case of gravitational potential energy near the Earth's surface, we assume g is constant. The expression U = m g h gives the work done to lift an object of mass m to a height h against gravity. The reference level (h = 0) is arbitrary; potential energy is relative.

Key points: g is positive downwards, but we use the magnitude in this formula. The unit is the joule (J). If an object falls, potential energy converts to kinetic energy. For heights where g varies significantly, the general formula is U = −G M m / r. This is essential for JEE/NEET problems on energy conservation, inclined planes, and pendulums.

Solved Examples (NCERT/JEE Pattern)

Example 1: A 5 kg book is placed on a shelf 2 m high. g = 9.8 m/s². Find PE.

U = 5 × 9.8 × 2 = 98 J.

Example 2: A stone of mass 0.2 kg has PE 19.6 J. What is its height? (g=9.8)

h = U / (mg) = 19.6 / (0.2 × 9.8) = 19.6 / 1.96 = 10 m.

Example 3: On the moon, g = 1.6 m/s². A 1 kg rock has PE 8 J. Find height.

h = U/(mg) = 8 / (1 × 1.6) = 5 m.

Frequently Asked Questions (FAQs)

Q1: What is gravitational potential energy in simple words?
It is the energy an object has because of its height above the ground. The higher and heavier it is, the more potential energy it stores.
Q2: Can potential energy be negative?
Yes, if the reference level is above the object (e.g., a ball in a basement). In the general gravitational formula, it is negative to represent an attractive force.
Q3: Does the path taken affect gravitational potential energy?
No, potential energy depends only on the vertical height, not the path. Gravity is a conservative force.
Q4: What is the SI unit of potential energy?
The SI unit is the joule (J), same as work and kinetic energy.
Q5: How is gravitational potential energy different from kinetic energy?
Potential energy is stored energy due to position, while kinetic energy is energy of motion. They are interconvertible in a conservative force field.