Potential Energy Calculator
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Gravitational potential energy is \(PE = mgh\): lifting 2 kg by 10 m stores 2 × 9.80665 × 10 ≈ 196 J. A spring stretched x meters stores \(\tfrac{1}{2}kx^{2}\): with k = 200 N/m and x = 0.1 m, that is 1 J.
| Joules | 196.133 J |
| Kilojoules | 0.196133 kJ |
| Calories | 46.8769 cal |
| Kilowatt-hours | 0.0000544814 kWh |
| Speed if it falls the full height | \(v = \sqrt{2gh} = \) 14.0047 m/s |
Show steps
- \(PE = mgh = 2\ \text{kg} \times 9.80665\ \text{m/s}^{2} \times 10\ \text{m} = 196.133\ \text{J}\)
How to use the potential energy calculator
- Choose gravitational or spring (elastic) energy.
- Enter mass and height, or the spring constant and the stretch, with units.
- Press Calculate to get the energy in joules and other units.
Formulas
- Gravitational: \(PE = mgh\) (m in kg, g in m/s², h in m)
- Elastic: \(PE = \tfrac{1}{2}kx^{2}\) (k in N/m, x in m)
Energy is measured in joules: 1 J = 1 N·m = 1 kg·m²/s².
Energy conservation
Without friction, potential energy turns into kinetic energy: \(mgh = \tfrac{1}{2}mv^{2}\), so an object dropped from h reaches \(v = \sqrt{2gh}\), whatever its mass.
Choosing the zero level
Only changes in potential energy matter physically. You can measure h from the floor, the ground or a tabletop, as long as you use the same reference for every value.
Potential energy practice quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
Quiz complete
Frequently asked questions
What is the formula for potential energy?
Gravitational PE = mgh; elastic PE in a spring = ½kx².
What units should I use?
Mass in kilograms, height and stretch in meters, g in m/s² and k in N/m give joules. The calculator converts other units for you.
Can potential energy be negative?
Yes, if the object is below your chosen zero level. Only differences in PE have physical meaning.
How is potential energy related to kinetic energy?
In the absence of friction, mechanical energy is conserved: PE lost equals KE gained.
What is the spring constant?
k measures stiffness: the force in newtons needed to stretch the spring one meter (Hooke’s law F = kx).
Sources
- OpenStax University Physics Volume 1
- OpenStax College Physics 2e
- NIST Special Publication 811: Guide for the Use of the SI
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