Potential Energy Calculator
Calculate gravitational potential energy (PE=mgh) and elastic potential energy (PE=½kx²). Find the stored energy of objects based on height or spring compression.
Potential Energy
490.5000 J
Potential Energy
490.5000 J
Mass
10.0000 kg
Height
5.0000 m
Weight (Force)
98.1000 N
Energy Conversions
Joules: 490.5000 J
Kilojoules: 0.490500 kJ
Calories: 117.2323 cal
Kilocalories: 0.117232 kcal
BTU: 0.464902 BTU
ft·lbf: 361.7737
Height Reference Examples
- • Book on shelf (1kg, 2m): ~19.6 J
- • Person on diving board (70kg, 10m): ~6,867 J
- • Car on hill (1500kg, 50m): ~735,750 J
- • Water behind dam (1000kg, 100m): ~981,000 J
About This Calculator
Potential energy is stored energy that an object has due to its position or configuration. Unlike kinetic energy (energy of motion), potential energy is "waiting" to be converted into other forms. This calculator helps you find gravitational and elastic potential energy for physics problems and real-world applications.
What is Potential Energy? Potential energy (PE) is the energy stored in an object due to its position relative to other objects, internal stresses, electric charge, or other factors. The two most common types are gravitational potential energy (PE = mgh) and elastic potential energy (PE = ½kx²).
The Formulas:
- Gravitational: PE = mgh (mass × gravity × height)
- Elastic: PE = ½kx² (spring constant × displacement squared)
Why Potential Energy Matters:
- Designing roller coasters and water slides
- Calculating energy storage in springs and bows
- Understanding hydroelectric power generation
- Analyzing pendulums and oscillating systems
- Engineering safety systems
This calculator handles both gravitational and elastic potential energy calculations. For related calculations, see our Kinetic Energy Calculator and Force Calculator.
How to Use the Potential Energy Calculator
- 1Choose the energy type: gravitational or elastic.
- 2Select what you want to calculate from the dropdown.
- 3For gravitational PE: Enter mass, height, and gravity.
- 4For elastic PE: Enter spring constant and displacement.
- 5Use the unit selectors for mass and height inputs.
- 6Adjust gravity for different planets if needed.
- 7Review the calculated result in standard units.
- 8Check the energy conversions for other units.
- 9Compare with reference values for context.
- 10Use results in energy conservation problems.
Gravitational Potential Energy
Energy stored due to height above a reference point.
The Formula
PE = mgh
Where:
- PE = potential energy (Joules, J)
- m = mass (kilograms, kg)
- g = gravitational acceleration (m/s²)
- h = height above reference (meters, m)
Understanding the Variables
Mass (m): The amount of matter in the object.
Gravity (g): On Earth, approximately 9.81 m/s². Varies by location and altitude.
Height (h): Measured from a chosen reference point (often ground level).
Example
Person on a diving board: m = 70 kg, g = 9.81 m/s², h = 10 m
PE = 70 × 9.81 × 10 PE = 6,867 J
Reference Point Matters
PE is relative to your chosen reference. A ball 2m above a table has different PE values depending on whether you measure from the table or the floor.
Elastic Potential Energy
Energy stored in stretched or compressed elastic materials.
The Formula
PE = ½kx²
Where:
- PE = potential energy (Joules, J)
- k = spring constant (N/m)
- x = displacement from equilibrium (meters, m)
Understanding Spring Constant
The spring constant (k) measures stiffness:
- High k = stiff spring (car suspension: ~50,000 N/m)
- Low k = soft spring (slinky: ~1 N/m)
Hooke's Law Connection
Force and displacement: F = kx
Work done to stretch: W = ½kx² = PE stored
Example
Compressed car spring: k = 50,000 N/m, x = 0.05 m (5 cm)
PE = ½ × 50,000 × 0.05² PE = ½ × 50,000 × 0.0025 PE = 62.5 J
Applications
- Bow and arrow (elastic PE → kinetic energy)
- Vehicle suspension
- Trampolines and diving boards
- Mechanical watches (mainspring)
Energy Conservation
Potential energy converts to other forms.
The Principle
Total mechanical energy is conserved (in absence of friction):
PE + KE = constant
Falling Object
At top: All PE, no KE Falling: PE decreases, KE increases At bottom: All KE, no PE
mgh = ½mv² v = √(2gh)
Example: Roller Coaster
At top (h = 30 m, v = 0): PE = mgh = m × 9.81 × 30 = 294.3m J
At bottom (h = 0): KE = 294.3m J ½mv² = 294.3m v = √(588.6) = 24.3 m/s (87 km/h)
Pendulum Motion
Swinging pendulum continuously converts between PE (at ends) and KE (at bottom).
Height determines maximum speed: v_max = √(2gh)
Gravitational Potential on Other Planets
Different gravity means different potential energy.
Gravity Values
| Location | g (m/s²) | Relative to Earth |
|---|---|---|
| Earth | 9.81 | 1.00 |
| Moon | 1.62 | 0.17 |
| Mars | 3.71 | 0.38 |
| Jupiter | 24.79 | 2.53 |
| Sun | 274 | 27.9 |
Example: 70 kg Person, 10 m Height
Earth: PE = 70 × 9.81 × 10 = 6,867 J Moon: PE = 70 × 1.62 × 10 = 1,134 J Mars: PE = 70 × 3.71 × 10 = 2,597 J Jupiter: PE = 70 × 24.79 × 10 = 17,353 J
Implications
- Moon: Jumping is easier (less PE needed)
- Jupiter: Very hard to climb (more PE stored per meter)
- Escape velocity depends on gravitational PE
Real-World Applications
Potential energy in everyday life and engineering.
Hydroelectric Power
Water behind a dam has gravitational PE:
Large reservoir: 10⁹ kg of water, 100 m height PE = 10⁹ × 9.81 × 100 = 981 GJ
This converts to electricity when water falls through turbines.
Pumped Storage
- Pump water uphill when electricity is cheap
- Release water to generate power during peak demand
- Efficiency: ~70-85%
Sports and Recreation
High Jump: Athlete converts kinetic energy to PE at peak Bungee Jumping: PE → KE → elastic PE in cord Archery: Elastic PE in bow → KE of arrow
Construction
Pile Drivers: PE of raised weight drives piles into ground Counterweights: Elevators use counterweights to balance PE
Safety Systems
Circuit Breakers: Spring-loaded mechanisms store elastic PE Airbags: Compressed gas has potential energy
Advanced Concepts
Beyond basic PE calculations.
General Gravitational PE
Near Earth's surface: PE = mgh (linear approximation)
More precisely: PE = -GMm/r
Where:
- G = gravitational constant
- M = mass of Earth
- r = distance from center
Escape Velocity
Energy needed to escape Earth's gravity: ½mv² = GMm/r v = √(2GM/r) ≈ 11.2 km/s
Chemical Potential Energy
Bonds store potential energy:
- Food: ~17 kJ/g (carbs)
- Gasoline: ~46 kJ/g
- TNT: ~4.6 kJ/g
Electrical Potential Energy
PE = qV (charge × voltage)
A 1.5V battery stores ~4.5 kJ per amp-hour.
Nuclear Potential Energy
E = mc²
1 gram of matter = 90 trillion joules (Nuclear binding energy)
Pro Tips
- 💡PE = mgh for gravitational; PE = ½kx² for elastic.
- 💡Height is measured from your chosen reference point.
- 💡On Earth, use g = 9.81 m/s² (or 10 for quick estimates).
- 💡Total mechanical energy (PE + KE) is conserved without friction.
- 💡Double the height = double the PE (linear relationship).
- 💡Double the spring stretch = quadruple the PE (squared relationship).
- 💡Falling speed depends only on height: v = √(2gh).
- 💡Spring constant has units N/m (force per displacement).
- 💡Energy units: 1 J = 1 N·m = 1 kg·m²/s².
- 💡Reference point choice doesn't affect energy changes.
- 💡Negative PE just means below your reference point.
- 💡Conservation: PE_top = KE_bottom (frictionless fall).
Frequently Asked Questions
Potential energy is stored energy based on position or configuration—it's energy "waiting" to be used. Kinetic energy is energy of motion. A ball held high has PE; when dropped, that PE converts to KE. Total mechanical energy (PE + KE) is conserved in ideal systems.
