Potential Energy Calculator

Related Calculators

Potential energy: Stored energy due to position or shape. In this calculator, that means energy from height in gravity or from stretching/compressing a spring.[3]

Gravitational potential energy: Energy change connected to height relative to a reference level. Near Earth, it is commonly measured in joules.[1][3]

Spring potential energy: Energy stored in an ideal spring when it is stretched or compressed from its relaxed length.

Reference height: The zero level you choose for height. Only the height difference matters, not the absolute label of zero.[3]

Height change used (delta h): The vertical change the calculator actually uses. If you enter start and end heights, it uses end minus start.

Converted SI values used: The mass, length, gravity, or spring values after conversion into standard SI units such as kilograms, meters, newtons per meter, and joules.

Output energy unit: The unit used for the main energy result, such as J, kJ, cal, kcal, eV, or ft lbf.

Mistake: Entering a lower final position as a positive Height change from reference (m) in gravitational mode.
Fix: Use a negative value for Height change from reference (m) , or switch Height entry mode to start/end so the calculator computes the sign for you.

Mistake: Typing feet or inches into Height change from reference (m) or Spring stretch or compression magnitude (m) while the calculator is still using SI inputs.
Fix: Change Input unit system or Spring displacement unit before calculating, then check Converted SI values used .

Mistake: Using a negative value for Spring stretch or compression magnitude (m) even though the spring formula here uses magnitude only.
Fix: Enter the size of the stretch or compression as a positive distance in Spring stretch or compression magnitude (m) .

Mistake: Leaving Potential energy, PE (J) blank when Solve for is set to mass, height, gravity, spring constant, or spring displacement.
Fix: Enter the known energy in Potential energy, PE (J) because the calculator needs it to rearrange the formula.

Mistake: Trying to find Mass (kg) or Gravitational acceleration (m/s^2) when the height change is zero.
Fix: Use a nonzero Height change from reference (m) or a nonzero start-to-end difference so the denominator is not zero.

Mistake: Mixing spring inputs by entering Spring constant (N/m) in N/cm or lbf/ft without changing Spring constant unit .
Fix: Set Spring constant unit to match what you typed, then confirm the converted stiffness in Converted SI values used .

• Gravitational mode uses the near-Earth constant-g model, so it is best for ordinary height changes where gravitational acceleration can be treated as constant.
• Results in gravitational mode are changes relative to a chosen reference level. Changing the reference changes the reported value, but not the physical difference between two points.
• Two-height entry assumes Start height (m, or ft if US units) and End height (m, or ft if US units) use the same reference zero.
• Spring mode assumes an ideal linear spring, so it does not model nonlinear springs, friction, damping, or energy losses.
• When solving for Spring stretch or compression magnitude (m), the calculator requires nonnegative energy and a positive spring constant.
• When solving for Mass (kg), Height change from reference (m), or Gravitational acceleration (m/s^2) in gravitational mode, the needed denominator cannot be zero.
• Displayed values are rounded for readability. Internal math should be more precise than the shown output, so tiny differences from a textbook answer can come from rounding or unit choices.

Core formulas

The calculator uses one of two standard potential-energy models, depending on Energy type.

PE = m x g x delta_h

This is the near-Earth gravitational potential-energy change. The result is in joules when mass is in kilograms, gravitational acceleration is in meters per second squared, and height change is in meters.[1]

PE = (1/2) x k x x^2

This is the ideal spring potential-energy formula. Because displacement is squared, equal stretch and compression magnitudes store the same energy.

Solve-for rearrangements

When you choose a missing variable in Solve for, the calculator rearranges the same formulas.

m = PE / (g x delta_h)

delta_h = PE / (m x g)

g = PE / (m x delta_h)

k = 2 x PE / x^2

x = sqrt(2 x PE / k)

If a required denominator is 0, the requested value is undefined, so the calculator should return an error instead of a fake number.

Height handling

If you use two-height entry, the calculator first finds the change in height from the same reference level.

delta_h = h_end - h_start

A positive delta h means the final position is higher. A negative delta h means it is lower. Britannica notes that gravitational potential energy near Earth's surface is computed relative to a reference point, so the chosen zero level matters.[3]

Unit conversions used internally

The calculator converts all inputs to SI units before doing the math, then converts the final energy to your selected Output energy unit.

1 lbm = 0.45359237 kg

1 ft = 0.3048 m

1 in = 0.0254 m

1 lbf = 4.4482216152605 N

1 cal = 4.184 J

1 eV = 1.602176634 x 10^-19 J

1 ft lbf = 1.3558179483314004 J

Mini-example

Example 1, gravitational: if Mass (kg) = 2, Gravitational acceleration (m/s^2) = 9.80665, and Height change from reference (m) = -3, then:

PE = 2 x 9.80665 x (-3) = -58.8399 J

The negative sign means the object's gravitational potential energy decreased because the final position is lower than the reference.

Example 2, spring: if Spring constant (N/m) = 200 and Spring stretch or compression magnitude (m) = 0.10, then:

PE = 0.5 x 200 x 0.10^2 = 1 J

Assumptions behind the results

These formulas are simplified models. Gravitational mode assumes a nearly constant value of g over the height change, and spring mode assumes an ideal linear spring. Potential energy is a way to describe stored energy due to position or configuration, which matches the standard introductory idea of the topic.[2]