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Calcimator

Potential Energy Calculator

Calculate gravitational potential energy from mass and height. Use the formula PE = mgh.

About this calculator

Gravitational potential energy is the energy an object has by virtue of its position in a gravitational field, relative to some chosen reference height -- lift a mass higher, and you store more energy in it that can later be released as motion (as when the object falls). The formula PE = mgh multiplies three quantities: mass (how much matter is being lifted), gravitational acceleration (how strongly gravity pulls, 9.81 m/s^2 on Earth), and height (how far above the reference point the object sits). Because all three appear as simple multipliers with no other terms, potential energy scales in direct proportion to each one individually -- doubling the mass doubles the energy, doubling the height doubles the energy, and moving the same object to a body with double the gravitational acceleration (like a hypothetical heavier planet) also doubles it.

This calculator's gravity input defaults to Earth's 9.81 m/s^2 but can be changed to model potential energy on the Moon (about 1.62 m/s^2) or another body. Importantly, potential energy is always measured RELATIVE TO a chosen reference height -- "height" in this calculator is the object's elevation above whatever datum you pick, not an absolute measurement, so consistent results require using the same reference point throughout a calculation.

Inputs

lb
ft

Results

Potential Energy (J)

981 J

Potential Energy (kcal)0.234 kcal
How to Use This Calculator
  1. Enter the object mass (kg) and height above the reference point (m).
  2. Set gravitational acceleration -- 9.81 m/s2 for Earth, 1.62 m/s2 for Moon.
  3. Review potential energy in joules using PE = mgh.
  4. Note: potential energy is relative to the chosen reference height -- choose a consistent datum.

How the result changes with Mass

MassPotential Energy (J)
5490.5 J
7.5735.75 J
151,471.5 J
252,452.5 J

What each input means

Mass
Mass of the object in kilograms.
Height
Height above reference point in meters.
Gravitational Acceleration
Gravitational acceleration (9.81 m/s² on Earth).

How this is calculated

Formula

PE = mgh

Worked example, using the default values

  1. Identify Input Parameters
    Mass = 10, Height = 10, Gravitational Acceleration = 9.81 = 3 input(s) provided
  2. Calculate Potential Energy
    Potential Energy
    981 = 981
  3. Calculate Potential Energy
    Potential Energy
    0.234 = 0.234

Engine last updated . Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does doubling the height double the potential energy?

PE = mgh is a direct product of mass, gravitational acceleration, and height with no other terms involved -- so height is a simple linear multiplier. Doubling height while holding mass and gravity fixed exactly doubles the calculated potential energy, the same way doubling any single factor in a multiplication doubles the product.

How would potential energy change for the same object on the Moon versus Earth?

Since PE = mgh and gravity (g) is a direct multiplier, an object at the same mass and height would have roughly 6 times LESS potential energy on the Moon (g about 1.62 m/s^2) than on Earth (g = 9.81 m/s^2) -- the Moon's much weaker gravity means less energy is stored by lifting the same mass to the same height.

What does 'height' actually mean in this formula if there's no true zero elevation?

Height here is measured relative to whatever reference point (datum) you choose -- the ground, a table top, sea level, or anything else. Potential energy itself is always a relative quantity, not an absolute one, so the calculated value only means something when compared against energy calculated using the SAME reference height.

Why does this calculator also show potential energy in kilocalories?

Joules are the standard SI unit for potential energy, but kilocalories (kcal) are a more familiar energy unit in everyday and nutritional contexts -- the conversion divides the joule value by 4,184 (the number of joules in one kilocalorie), giving the same physical energy expressed in a more relatable unit.

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