What is the formula for gravitational potential energy?

The standard near-surface formula is PE = m × g × h, where m is mass in kg, g is gravitational acceleration in m/s² (9.81 on Earth), and h is the height above the chosen reference level in metres. The result is in joules (J). For large distances from a planet, the more general form is PE = −GMm/r, where G = 6.674 × 10⁻¹¹ N·m²/kg², M is the planet mass, m is the object mass, and r is the centre-to-centre distance.

What value of g should I use?

For everyday Earth problems use g = 9.81 m/s² (the international standard). If you need the precise local value, it varies from about 9.78 m/s² at the equator to 9.83 m/s² at the poles. For other bodies: Moon = 1.62, Mars = 3.72, Jupiter = 24.79, Venus = 8.87 m/s². This calculator ships with eight planet presets plus a Custom field.

What is the reference level for height?

Gravitational PE is always measured relative to a chosen reference level — typically the ground, sea level, or the lowest point in the problem. Only changes in PE matter physically; you can set h = 0 wherever is convenient. The calculator uses whatever height you enter, so pick the reference that makes sense for your scenario.

Can I solve for mass or height instead of energy?

Yes. Rearranging PE = mgh gives m = PE/(g × h) and h = PE/(m × g). Select the variable you want from the "Solve for" drop-down and enter the other three quantities. The calculator shows the rearranged formula and full working for every mode.

How do I convert joules to kilocalories or kWh?

1 kcal = 4,184 J and 1 kWh = 3,600,000 J. The calculator displays the result in the energy unit you choose from the drop-down (J, kJ, MJ, cal, kcal, kWh, eV, or BTU) and also lists conversions into the other units below the main answer.

When does PE = mgh stop being accurate?

The formula assumes g is constant, which is a good approximation within a few tens of kilometres of the surface. At 10 km altitude g falls by about 0.03 m/s² — less than 0.3 % error. For orbital mechanics, satellite trajectories, or any scenario where altitude is comparable to the planet radius, use PE = −GMm/r instead.

Gravitational Potential Energy Calculator

Gravitational potential energy (GPE) is the energy stored in an object because of its position in a gravitational field. Lift a book off the floor, raise a skydiver to jump altitude, or park a satellite in orbit and you have converted kinetic or chemical energy into gravitational potential energy — energy that can be released when the object falls back down.

This calculator implements the near-surface formula PE = m × g × h in full solve-for-any-variable mode. Enter any three of the four quantities and get the fourth, with step-by-step working and automatic unit conversion across eight planet presets.

How it works

The formula follows directly from Newton’s second law and the definition of work:

PE = m × g × h

m — mass of the object (kg, g, lb, or tonne)
g — gravitational acceleration at the surface (m/s²)
h — height above the reference level (m, cm, km, ft, in, mi, yd)
PE — gravitational potential energy (J, kJ, MJ, cal, kcal, kWh, eV, BTU)

When you raise an object by height h against gravity, you do work equal to the gravitational force (mg) multiplied by the displacement (h). That work is stored as potential energy. When the object falls the same distance, all that PE converts back to kinetic energy (ignoring air resistance), which is the basis of the conservation of energy: KE + PE = constant for a closed system.

The calculator rearranges the formula automatically:

Solving for	Formula used
PE	PE = m × g × h
m	m = PE / (g × h)
h	h = PE / (m × g)
g	g = PE / (m × h)

Every intermediate step is shown in the Working panel so you can follow the algebra, copy it into coursework, or verify your own hand calculation.

Worked example

A 70 kg person climbs to the top of a 10-metre building. How much gravitational PE have they gained?

m = 70 kg, g = 9.81 m/s², h = 10 m
PE = 70 × 9.81 × 10
PE = 70 × 98.1
PE = 6,867 J ≈ 6.87 kJ

That 6.87 kJ is exactly the kinetic energy the person would have just before hitting the ground if they fell (in a vacuum). On the Moon (g = 1.62 m/s²) the same climb stores only 70 × 1.62 × 10 = 1,134 J — about six times less.

Constants and planet presets

The calculator ships with eight planet presets, all using the standard mean surface gravitational acceleration:

Body	g (m/s²)
Earth	9.81
Moon	1.62
Mars	3.72
Venus	8.87
Jupiter	24.79
Saturn	10.44
Mercury	3.70
Neptune	11.15

For a custom planetary body or non-standard altitude, choose Custom and type any value in m/s², ft/s², or multiples of g₀ (1 g₀ = 9.80665 m/s²).

The universal gravitational constant used in the footnote is G = 6.674 × 10⁻¹¹ N·m²/kg² (CODATA 2018). This appears in the full formula PE = −GMm/r relevant to orbital mechanics, but is not used in the near-surface approximation PE = mgh that this calculator implements.

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