The Potential Energy Calculator solves energy problems in physics with full step-by-step working. Calculate gravitational potential energy (PE = mgh), elastic potential energy (PE = 1/2 kx squared), kinetic energy (KE = 1/2 mv squared), and energy conservation between potential and kinetic energy.
Enter your values in any mode and get instant results. The calculator includes detailed formula breakdowns and interpretations for each calculation.
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Potential energy is stored energy due to an object's position or configuration. Gravitational potential energy (PE = mgh) depends on mass, gravitational field strength, and height above a reference point.
Elastic potential energy (PE = 0.5 times k times x squared) is stored in a deformed elastic object such as a spring. It depends on the spring constant k (stiffness) and the displacement x from the natural length.
Kinetic energy (KE = 0.5 times m times v squared) is the energy of motion. It depends on mass and the square of velocity, so doubling the speed quadruples the kinetic energy.
The law of conservation of energy states that in an isolated system, total energy remains constant. For mechanical systems without friction, the sum of potential and kinetic energy stays the same: PE_i + KE_i = PE_f + KE_f. This lets you find unknown velocities or heights.
Problem: A 10 kg object is 5 m above the ground. What is its gravitational PE? (g = 9.81)
Solution: PE = mgh = 10 * 9.81 * 5 = 490.5.
Answer: 490.5 J
Problem: A spring with k = 200 N/m is compressed by 0.1 m. What is the elastic PE?
Solution: PE = 0.5 * k * x^2 = 0.5 * 200 * (0.1)^2 = 0.5 * 200 * 0.01 = 1.
Answer: 1 J
Problem: A 2 kg ball moves at 8 m/s. What is its kinetic energy?
Solution: KE = 0.5 * m * v^2 = 0.5 * 2 * 64 = 64.
Answer: 64 J
Problem: A 3 kg ball is dropped from 20 m. What is its speed just before hitting the ground?
Solution: mgh = 0.5mv^2. v = sqrt(2gh) = sqrt(2 * 9.81 * 20) = sqrt(392.4) = 19.81.
Answer: 19.81 m/s
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