Calculate gravitational potential energy from mass, height and gravity
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Faiq Ur Rahman is a web designer, digital product developer, and founder of Toolraxy, a growing platform of web-based calculators and utility tools. He specializes in building structured, user-friendly tools focused on health, finance, productivity, and everyday problem-solving.
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Lift something up and you give it stored energy. A 2 kg book moved from the floor to a shelf 1.8 m up gains about 35 J. That energy sits there until the book falls or gets pushed off. This potential energy calculator works out that number from three inputs: mass, height, and gravity. The gravity dropdown covers Earth, the Moon, Mars, Jupiter, and a custom value, so you can compare how the same lift stores different energy on different worlds. A 10 kg weight raised 2 m holds 196 J on Earth and 32.4 J on the Moon. Six times less. Same mass, same height, different planet.
Pick a preset from the dropdown, or leave it on Custom / manual input.
Enter the mass. Units include kg, g, lb, oz, and metric tons.
Type the height above your reference point. Units include m, cm, km, ft, and in.
Choose a gravity value from the dropdown. Earth standard is the default at 9.807 m/s².
Select Custom gravity to type your own value in m/s².
Watch the hero number update as you type.
Read the four tiles for kilojoules, foot-pounds, calories, and drop-impact speed.
Compare your result against the scale table and the reference table.
Gravitational potential energy equals mass times gravity times height. That’s the whole formula for an object near a planet’s surface, and it gives the energy in joules.
Formula: PE = m × g × h
Formula: v = √(2 × g × h)
PE is potential energy in joules. m is mass in kilograms. g is gravitational acceleration in m/s². h is height above the reference point in meters. The second formula returns the impact speed if the object were dropped from that height.
The calculator converts every mass unit to kilograms and every height unit to meters before multiplying. Gravity comes from the dropdown: Earth standard (9.80665 m/s²), Earth equator (9.780), Earth poles (9.832), Moon (1.62), Mars (3.71), Venus (8.87), Jupiter (24.79), and a Sun option, plus custom. Pick the one that matches your scenario, or type your own.
If mass or height is negative, the tool shows dashes and a warning. Zero is allowed and returns zero energy. Gravity must be positive; if the custom field holds something invalid, the tool falls back to Earth standard. The impact speed formula assumes no air resistance, so it’s an upper bound for real falls.
Load the crane load preset. The mass is 2,000 kg. The height is 30 m. Gravity is Earth standard, 9.80665 m/s².
Step 1: Multiply mass by gravity. 2,000 × 9.80665 = 19,613.3.
Step 2: Multiply by height. 19,613.3 × 30 = 588,399 J.
The calculator reports about 588 kJ. In foot-pounds, that’s roughly 434,000 ft-lbs. In calories, about 140,600 cal. Impact speed if dropped is √(2 × 9.80665 × 30) = 24.26 m/s.
That’s the energy a crane stores when it lifts a two-tonne load to the top of a ten-storey building. If the cable snapped, the load would hit the ground at 24 m/s, or about 87 km/h. That’s why crane safety standards and load charts exist.
The formula stays the same. Only the value of g changes. The Moon’s surface gravity is 1.62 m/s², Mars is 3.71, Venus is 8.87, and Jupiter is 24.79. Plug in whichever value matches the world you’re calculating for, and the rest of the math is identical.
| Gravity source | g (m/s²) | PE for 10 kg at 2 m |
|---|---|---|
| Earth standard | 9.80665 | 196.1 J |
| Moon | 1.62 | 32.4 J |
| Mars | 3.71 | 74.2 J |
| Venus | 8.87 | 177.4 J |
| Jupiter | 24.79 | 495.8 J |
That table shows why gravity matters. The same 10 kg mass raised 2 m stores 15 times more energy on Jupiter than on the Moon. If you’re running a physics problem set on a fictional planet, use the custom gravity field and type in whatever value the problem gives you.
Potential energy is the energy stored in an object because of its position. For an object lifted above a surface, it equals mass times gravity times height. The unit is the joule.
Multiply mass in kilograms by gravity in m/s² by height in meters. A 5 kg object at 10 m on Earth gives 5 × 9.80665 × 10 = 490.3 J. No squaring, no division by two.
Because the formula multiplies by g. On the Moon, g is 1.62 m/s², so the same lift stores about one-sixth the energy as on Earth. On Jupiter, g is 24.79 m/s², so the same lift stores about 2.5 times more.
At any height h, potential energy is mgh. As the object falls, that energy converts to kinetic energy. At the moment of impact, all of it has become kinetic (assuming no air resistance).
A cubic meter of water at 100 m above a turbine holds 981 kJ. A typical dam releases hundreds of cubic meters per second, which translates to hundreds of megawatts of power.
Mass supports kg, g, lb, oz, and metric tons. Height supports m, cm, km, ft, and in. Gravity supports eight preset values plus a custom option. Output is in joules, kilojoules, foot-pounds, and calories.
Yes. The gravity dropdown includes the Moon, Mars, Venus, Jupiter, and a Sun option, plus a custom field for anything else. Pick the world, enter mass and height, and the calculator handles the rest.
Potential energy is stored energy based on position. Kinetic energy is energy of motion. A ball at the top of a ramp has potential energy; when it rolls, that energy becomes kinetic. The two convert back and forth.
Compute the energy in joules first, then divide by 1.3558. A 500 J result equals about 369 ft-lbs. The calculator does this automatically.
Textbooks often round gravity to 9.8 m/s² or even 10 m/s². This calculator uses 9.80665. The difference is small, usually under 1%, but it shows up in the last digit.
Yes. Height is measured from wherever you define zero. The floor, sea level, or a tabletop all work. The absolute PE changes if you change the reference, but the difference in PE between two heights does not.
Impact speed is √(2gh). It depends only on gravity and height, not on mass. A 1 kg and a 100 kg object dropped from the same height hit the ground at the same speed (ignoring air resistance).
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