What Is Gravitational Potential Energy?
Gravitational potential energy (PE) is the energy stored in an object due to its position above a reference point in a gravitational field. When released, this stored energy converts to kinetic energy as the object falls. PE is one of the two components of mechanical energy.
Potential Energy Formula: PE = mgh
Where m is mass (kg), g is gravitational acceleration (m/s²), and h is height above the reference point (m). The result is in joules. This formula is valid near the surface of a planet where g is approximately constant.
Gravitational Potential Energy
Gravity on Different Worlds
| World | g (m/s²) | Relative to Earth |
|---|---|---|
| Earth | 9.807 | 1.00× |
| Moon | 1.625 | 0.17× |
| Mars | 3.721 | 0.38× |
| Jupiter | 24.79 | 2.53× |
The Reference Point
PE is always relative. You can choose any height as zero. What matters in physics problems is the change in PE (ΔPE = mgΔh). Negative PE simply means the object is below the reference point.
How to Use the Calculator
- Choose what to calculate: PE, mass, height, gravity, or compare worlds.
- Enter values. Change gravity for non-Earth calculations.
- Click Calculate.
- Review the result, formula substitution, and interpretation.
Example Calculations
10 kg, 5 m, Earth
PE = 10 × 9.807 × 5 = 490.3 J
70 kg, 10 m, Moon
PE = 70 × 1.625 × 10 = 1 137.5 J
PE = 980 J, m = 10 kg → h (Earth)
h = 980 / (10 × 9.807) = 9.997 m
Typical Potential Energy Values
| Scenario | Approximate PE |
|---|---|
| Book on a shelf (1 kg, 1.5 m) | ≈ 14.7 J |
| Cliff diver (60 kg, 25 m) | ≈ 14.7 kJ |
| Roller coaster at top (500 kg, 40 m) | ≈ 196 kJ |
| Elevator at 50th floor (1000 kg, 150 m) | ≈ 1.47 MJ |
| Water behind a 100 m dam (1 m³) | ≈ 981 kJ |
| Skier at top of run (80 kg, 500 m) | ≈ 392 kJ |
Real-World Applications of Potential Energy
| Application | How PE Is Used | Example |
|---|---|---|
| Hydroelectric power | PE of water converts to KE, then electricity | Hoover Dam: 221 m head, 2,080 MW |
| Roller coasters | PE at top → KE at bottom | 40 m drop ≈ 28 m/s at bottom |
| Pumped-storage energy | Water pumped uphill stores energy as PE | Bath County: 1,200 m elevation, 3 GW |
| Pile drivers & drop hammers | Heavy mass dropped from height | 500 kg from 5 m = 24.5 kJ impact |
| Gravitational slingshot | Spacecraft gains KE from planetary PE | Voyager used Jupiter’s gravity |
Common Mistakes
- Using cm without converting to metres.
- Forgetting to specify the reference height.
- Using weight (in Newtons) instead of mass (in kg).
- Using Earth's gravity for a different planet.
- Applying PE = mgh at very high altitudes where g varies.
Accuracy and Limitations
PE = mgh is an approximation valid near a planet's surface where gravitational acceleration is approximately constant. For large heights (comparable to the planet's radius), the general formula PE = −GMm/r is needed. This calculator does not account for general relativity, atmospheric buoyancy, or non-uniform gravity fields. It is educational and should not replace professional engineering calculations.
FAQ
What is gravitational potential energy?›
It is the energy stored due to an object’s position in a gravitational field. PE = mgh near a planet’s surface.
Can potential energy be negative?›
Yes. PE is relative to a reference point. If the object is below that point, h is negative and PE is negative.
Why does gravity differ on other planets?›
Surface gravity depends on the planet’s mass and radius. Larger and denser planets have stronger gravity.
Does PE = mgh work at very high altitudes?›
Only approximately. For large heights (compared to the planet’s radius), the general formula PE = −GMm/r is needed.
What unit is PE in?›
The SI unit is the joule (J). 1 J = 1 kg·m²/s².
How does PE relate to KE?›
When an object falls, PE converts to KE. At the bottom (ignoring friction), all PE becomes KE: ½mv² = mgh.
What is the standard gravity value?›
g = 9.80665 m/s² (standard gravity). Actual surface values vary slightly by latitude and altitude.
Sources
Author & technical reviewer
Manish Kumar
PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.
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