Library / Foundations: Physics / FPH-09
Foundations: Physics
Gravitational potential energy
Energy gained by lifting a mass through a height.
- Ref
- FPH-09
- Rev
- v1
- Field
- Foundations: Physics
- Result
- ΔEp [kJ]
Height gain Δh increases gravitational energy at constant g.
Lifting something stores energy in it, in proportion to its mass and the height gained.
Calculator
kJ
kg
m
- Speed gained in a fall of this height22.14 m/s
- Energy in kWh0.005448 kWh
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
Potential energy gained (kJ) current value 19.61 kJ
mMassKey driver
0.2451,230
ΔhHeight gained
0.785392
- Only the vertical height gained matters, not the path taken.
- This energy is released as kinetic energy in a fall (ignoring air resistance).
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kJ) | Local step | Change in result |
|---|---|---|---|---|---|---|
| m Mass | 1 to 5,000 kg | 0.2452 | 1,226 | 1,226 | +10% | +10 % |
| Δh Height gained | 1 to 500 m | 0.7845 | 392.3 | 391.5 | +10% | +10 % |
Sweep of Height gained
| Height gained (m) | Potential energy gained (kJ) |
|---|---|
| 1 | 0.7845 |
| 2.175 | 1.706 |
| 4.729 | 3.71 |
| 10.28 | 8.067 |
| 22.36 | 17.54 |
| 48.62 | 38.15 |
| 105.7 | 82.95 |
| 229.9 | 180.4 |
| 500 | 392.3 |
Sweep one variable
Potential energy gained (kJ)Hover, touch, or use the arrow keys on the chart
Variables and how each one contributes
ΔEp
Potential energy gained
What the equation gives you. Everything else feeds it.
m
Mass
Mass lifted. Directly proportional.
Δh
Height gained
Vertical rise. Directly proportional.
Worked example with the values above
- Weight: mg = 80 × 9.80665 = 784.5 N.
- Multiply by height: 784.5 × 25 = 19,610 J.
- ΔEp = 19.61 kJ.
Assumptions and limits
- Uniform gravitational field.
- Height measured vertically.
Common mistakes
- Using the length of a slope instead of its vertical height.
- Using weight instead of mass.
Statistics and uncertainty
Height is usually the larger uncertainty: a 0.5 m error on a 25 m rise is 2% on the energy.
Where it is used
- Lifting and hoisting energy.
- Energy stored in elevated water or masses.
Maths you need
- Weight: W = mg
- Energy: joules