Answer first
What this calculator tells you
Calculate the potential energy of a mass raised to a height. See how much energy a lifted load stores and releases if it falls. Formula: Gravitational potential energy = m × g × h. At the worked-example inputs, the potential energy (j) is 490.5. Holding every other input steady, moving mass (kg) from 8 to 12 moves the result from 392.4 to 588.6.
Transparent method
The formula
See how much energy a lifted load stores and releases if it falls.
Worked example
Example inputs
How to interpret the result
Lifting a mass stores energy equal to its weight times the height. Ten kilograms raised 5 meters under standard gravity holds 490.5 joules, which is what it would release if it fell. In kilowatt-hours that is a tiny 0.00014, which is why gravity storage needs enormous masses or heights to matter.
At the worked-example inputs the potential energy (j) is 490.5. It rises with mass (kg), height (m) and gravity (m/s²).
These are textbook formulas for ideal conditions: no air resistance, no friction, gravity of 9.81 meters per second squared and gases that behave ideally. Real results differ, so treat them as first estimates and use the units the formulas expect (meters, kilograms, seconds).
Before you rely on it
What to check
Measure the height as the vertical drop, not the path taken. A ramp changes the effort but not the stored energy.
The common error
Where people go wrong with gravitational potential energy calculator
Using the mass in pounds. The formula wants kilograms, and pounds without conversion overstate the energy by more than double.
Sensitivity evidence
How mass (kg) changes the potential energy (j)
Holding every other input at the worked-example value, moving mass (kg) from 8 to 12 moves the potential energy (j) from 392.4 to 588.6: a spread of 196.2, or 40% of the worked-example result.
| Mass (kg) | Potential energy (J) | Potential energy (kWh) |
|---|---|---|
| 8 | 392.4 | 0.00011 |
| 9 | 441.5 | 0.00012 |
| 10worked example | 490.5 | 0.00014 |
| 11 | 539.6 | 0.00015 |
| 12 | 588.6 | 0.00016 |
Every input, tested
Which input moves the potential energy (j) most
Of the 3 inputs, mass (kg) moves the potential energy (j) most (98.1 across the range tested) and gravity (m/s²) moves it least (100).
| Input | Tested from | To | Potential energy (J) at each end | Swing |
|---|---|---|---|---|
| Mass (kg) | 9 | 11 | 441.5 to 539.6 | 98.1 (20%) |
| Height (m) | 4.5 | 5.5 | 441.5 to 539.6 | 98.1 (20%) |
| Gravity (m/s²) | 9 | 11 | 450 to 550 | 100 (20%) |
Two variables at once
Potential energy (J) by mass (kg) and gravity (m/s²)
Across the grid the potential energy (j) runs from 320 to 720. Moving mass (kg) from 8 to 12 shifts it by 200 at the middle column, and moving gravity (m/s²) from 8 to 12 shifts it by 200 at the middle row, so neither is the bigger lever here.
| Mass (kg) \ Gravity (m/s²) | 8 | 10 | 12 |
|---|---|---|---|
| 8 | 320 | 400 | 480 |
| 9 | 360 | 450 | 540 |
| 10 | 400 | 500 | 600 |
| 11 | 440 | 550 | 660 |
| 12 | 480 | 600 | 720 |
The highlighted cell is the worked example.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Mass (kg) | 10 | Enter the mass (kg) used in this calculation. |
| Gravity (m/s²) | 9.8 | 9.81 on Earth. About 1.62 on the Moon. |
| Height (m) | 5 | Enter the height (m) used in this calculation. |
| Potential energy (J) | 490.5 | |
| Potential energy (kWh) | 0.00014 | |
Inputs, definitions and assumptions
Mass (kg)
Enter the mass (kg) used in this calculation. The prefilled worked-example value is 10.
Gravity (m/s²)
9.81 on Earth. About 1.62 on the Moon. The prefilled worked-example value is 9.8.
Height (m)
Enter the height (m) used in this calculation. The prefilled worked-example value is 5.
How to use this calculator
- 1Verify the inputs. Gather mass (kg), gravity (m/s²) and height (m) from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the potential energy (j) at 490.5. Store your own version of it as Scenario A.
- 3Test one change. Start with mass (kg), the input with the biggest effect here: moving mass (kg) from 9 to 11 takes the potential energy (j) from 441.5 to 539.6, a swing of 20% of the worked-example figure.
- 4Check the extremes. At half the example mass (kg) (5) the potential energy (j) is 245.3; at double (20) it is 981.
People also ask
Frequently asked questions
How do you calculate gravitational potential energy?
Gravitational potential energy = m × g × h. At the worked-example inputs the potential energy (j) is 490.5.
What does the gravitational potential energy result mean?
See how much energy a lifted load stores and releases if it falls. At the worked-example inputs the potential energy (j) is 490.5. It rises with mass (kg), height (m) and gravity (m/s²).
How much does mass (kg) change the potential energy (j)?
Holding every other input at the worked-example value, moving mass (kg) from 8 to 12 moves the potential energy (j) from 392.4 to 588.6, a spread of 196.2.
What are the limits of this gravitational potential energy calculator?
These are textbook formulas for ideal conditions: no air resistance, no friction, gravity of 9.81 meters per second squared and gases that behave ideally. Real results differ, so treat them as first estimates and use the units the formulas expect (meters, kilograms, seconds). The tables on this page test mass (kg) only from 8 to 12; a value outside that range is not tabulated here.
Which input moves the potential energy (j) most in the gravitational potential energy calculator?
Ranked by how far each moves the potential energy (j) across the range tested: mass (kg) (98.1, 20%), height (m) (98.1, 20%) and gravity (m/s²) (100, 20%).
If I double mass (kg) in the gravitational potential energy calculator, does the potential energy (j) double?
Doubling it from 10 to 20 takes the potential energy (j) from 490.5 to 981, which is 2.00 times the worked-example figure. So the result scales almost exactly in proportion. Halving it to 5 gives 245.3.
How much does gravity (m/s²) matter in the gravitational potential energy calculator?
The worked example uses 9.8. Holding every other input at its worked-example value, moving gravity (m/s²) from 9 to 11 takes the potential energy (j) from 450 to 550, a swing of 20% of the worked-example figure.
How much does height (m) matter in the gravitational potential energy calculator?
The worked example uses 5. With the other inputs left at the worked example, moving height (m) from 4.5 to 5.5 takes the potential energy (j) from 441.5 to 539.6, a swing of 20% of the worked-example figure.
Which inputs change the potential energy (kwh) in the gravitational potential energy calculator?
At the worked-example inputs it is 0.00014. Mass (kg) takes it from 0.00012 to 0.00015, gravity (m/s²) takes it from 0.00013 to 0.00015 and height (m) takes it from 0.00012 to 0.00015.
Is the ideal gas law accurate for real gases?
It works well for gases at moderate pressure and well above their condensing temperature. Near condensation or at high pressure, real gases depart from it, and a more detailed model is needed.
Sources and evidence
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