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Gravitational potential energy calculator

Calculate the energy associated with an object’s height in a uniform gravitational field.

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Fill in three quantities with their units and leave the unknown blank. Measure height from your chosen reference level.

Mass and g must be positive. Finding mass or g at zero height is indeterminate, so the calculator rejects that division. Constant g is an approximation suitable for small changes in altitude near Earth’s surface. This model does not calculate orbits or the elastic energy of a spring.

Results

Potential energy
-
Mass
-
Relative height
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Gravity
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Applied relationship

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    How does this tool work?

    A raised load can release energy as it descends. To quantify that energy, you need its mass, gravity and height measured from a chosen level. This calculator uses a uniform gravitational field model. It can find potential energy, or solve for mass, height or gravity when the other three quantities are known.

    The model uses Ep = mgh. Inputs are converted to SI units before calculation: kilograms, metres and metres per second squared. The physical result does not depend on the input unit: 250 cm is the same height as 2.5 m. Results use your selected units, while the numerical substitution uses SI units.

    Height is relative to a reference such as the ground or a machine platform. Choosing another zero changes the energy assigned to a given position. To compare two positions in the same field, use the change ΔEp = mg(h₂ − h₁). It does not depend on the chosen zero, provided both heights use the same reference.

    The calculation assumes constant g. It suits exercises and movements where changes in gravity are negligible; it does not model an orbit or travel between Earth and the Moon. The initial 9.80665 m/s² is conventional standard gravity, not a measurement at your location. Mass stays positive; the sign of energy follows the sign of relative height.

    How to use this tool

    1. Choose the unknown

      Clear the energy, mass, height or gravity field you want to solve for.

    2. Enter known values

      Fill in the other three fields and check each unit. Mass and gravity must be positive.

    3. Read the applied relation

      Review the calculated value and substitution into Ep = mgh; the quantities in that relation are expressed in SI units.

    Energy and inverse relations

    Calculate energy

    Ep = m × g × h

    The product gives joules when m, g and h are in SI units.

    Find height

    h = Ep / (m × g)

    Mass and g must be strictly positive.

    Find mass

    m = Ep / (g × h)

    Height must be nonzero and the values must yield a positive mass.

    Find gravity

    g = Ep / (m × h)

    Height must be nonzero and the result must be positive.

    Compare two positions

    ΔEp = m × g × (h₂ − h₁)

    To find this change with the tool, enter h₂ − h₁ as the height and leave energy blank.

    m
    Mass, in kilograms (kg).
    g
    Gravitational acceleration, in m/s².
    h
    Height relative to the reference, in metres (m).
    Ep
    Gravitational potential energy, in joules (J).

    Use cases

    Study lifting work

    Estimate the minimum mechanical energy needed to raise a load between two known levels.

    Compare reference levels

    Check that an energy difference stays unchanged when the chosen zero level changes.

    Solve an inverse problem

    Find the height for a given energy when the mass and gravitational acceleration are known.

    Examples

    Height entered in centimetres

    The tool converts 250 cm to 2.5 m, then calculates 2 × 9.80665 × 2.5. Entering 2.5 m directly must give the same result: changing the unit does not change the physical situation.

    Input

    Energy: blank
Mass: 2 kg
Height: 250 cm
Gravity: 9.80665 m/s²

    Result

    Potential energy: 49.03325 J

    Find height from energy

    Divide the energy by the object’s weight: 98.0665 / (2 × 9.80665). Clear the Height field instead of entering zero; zero is a known value, not an unknown.

    Input

    Energy: 98.0665 J
Mass: 2 kg
Height: blank, unit m
Gravity: 9.80665 m/s²

    Result

    Relative height: 5 m

    Descend from 10 m to 4 m

    The height change is 4 − 10 = −6 m. Potential energy decreases by 117.6798 J. In an ideal descent, that decrease can become kinetic energy; the tool does not calculate losses or braking.

    Input

    Energy: blank
Mass: 2 kg
Height: −6 m
Gravity: 9.80665 m/s²

    Result

    Change in potential energy: −117.6798 J

    Tips and best practices

    • For lifting between two levels, use the height difference, not the building’s absolute altitude.
    • The gain in potential energy is ideal mechanical energy. Efficiency, friction and other losses increase the energy a motor must supply.
    • When both height and energy are zero, mass or g cannot be inferred: multiple values satisfy the relation. The calculator rejects this indeterminate case.

    Sources and references

    Frequently asked questions

    Why does the height reference matter?

    The zero of potential energy is a choice. Different references give different energies for the same object, but the energy change between two positions is unchanged when the same g is used.

    Can height be negative?

    Yes, for a position below your chosen reference. This does not imply a negative mass.

    Is this the energy the motor needs?

    No. The result is ideal potential energy; motor efficiency and other losses are not modelled.

    Why does the result change with g?

    Energy is proportional to g. The initial 9.80665 m/s² is a conventional reference; change it if you know gravity at the location being studied.

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