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Potential Energy Calculator

Computes the gravitational potential energy of a mass raised to a height near a planet's surface with PE = m·g·h (standard gravity by default), and the speed the mass would reach if it fell that height freely.

When to use

You need the energy stored by lifting a mass to a height, the minimum work to lift it, or the energy released when it falls (lifted loads, pumped hydro, dropped objects).

Do not use when: Heights are a significant fraction of the planet's radius (g is not constant; use gravitational-force), or you need elastic energy (use hookes-law) or energy of motion (use kinetic-energy).

Formula

PE = mass_kg × gravity_m_s2 × height_m; fall_speed_m_s = √(2 × gravity_m_s2 × height_m)

Valid where g can be treated as constant (heights small compared with the planet's radius, i.e. within a few tens of kilometres of Earth's surface).

Inputs

ParameterTypeUnitRequiredDescription
mass_kgnumberkgyesMass of the object in kilograms. Range: > 0
height_mnumbermyesHeight above the reference level (ground) in metres. Range: ≥ 0
gravity_m_s2numberm/s²default 9.80665Local gravitational acceleration. Default is standard gravity g_n = 9.80665 m/s² (Moon ≈ 1.62, Mars ≈ 3.72, Jupiter ≈ 24.8). Range: > 0, ≤ 10000

Outputs

OutputTypeUnitDescription
potential_energy_jnumberJPE = m × g × h.
potential_energy_kjnumberkJPotential energy in kilojoules.
potential_energy_kwhnumberkWhPotential energy in kilowatt-hours (J ÷ 3,600,000).
fall_speed_m_snumberm/s√(2·g·h): speed reached if all the potential energy became kinetic energy (no air resistance).

Example

70 kg lifted 10 m: {"mass_kg":70,"height_m":10} → {"potential_energy_j":6864.655,"potential_energy_kj":6.864655,"potential_energy_kwh":0.001907,"fall_speed_m_s":14.0047}

2 kg at 1.5 m with g = 9.81: {"mass_kg":2,"height_m":1.5,"gravity_m_s2":9.81} → {"potential_energy_j":29.43,"fall_speed_m_s":5.4249}

GET https://tttkmbb.com/api/v1/calculate/potential-energy?mass_kg=70&height_m=10

Machine access

Sources

FAQ

Which reference level should I use?

Any level you choose; only differences in potential energy matter. Height is measured from that reference, and objects below it have negative potential energy.

Should I use 9.81 or 9.80665?

9.80665 m/s² is the defined standard gravity; the actual value varies from about 9.78 at the equator to 9.83 at the poles. The difference is under 0.3 %.

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