Potential Energy Calculator: E = mgh

The energy stored by lifting a mass: energy, mass, gravity or height.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • E_p = m\,g\,h
  • h = \frac{E_p}{m\,g}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the potential energy: potential energy = mass x gravitational field strength x height
  2. Put the values in (every value in its SI unit): potential energy = 10 x 9.80665 x 5
  3. The answer: potential energy: 490.332 J
  4. The same answer in other units: 0.490333 kJ; 0.000136203 kWh; 361.651 ft lbf

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Height; Potential energy (leave it as it is if this is what you are finding) 490.33 J; Mass (leave it as it is if this is what you are finding) 10 kg.

  1. The formula, arranged to find the height: height = (potential energy) / (mass x gravitational field strength)
  2. Put the values in (every value in its SI unit): height = (490.33) / (10 x 9.80665)
  3. The answer: height: 4.99997 m
  4. The same answer in other units: 499.997 cm; 16.4041 feet

Common questions

What is the formula for gravitational potential energy?

Mass times gravity times height. A 10 kg mass lifted 5 m gains 490 J.

What value of g do I use?

9.81 m/s2 on Earth. The calculator starts with 9.80665, the standard value.

Where does the energy go when it falls?

It turns into kinetic energy, so the speed after falling a height h is the square root of 2gh.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any school physics text (gravitational potential energy).

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