Work & Energy Calculator (Work, Kinetic Energy & Potential Energy)

Switch between three formulas to calculate work (W=Fd), kinetic energy (KE=1/2mv²), and potential energy (PE=mgh).

Usage Tips

  • Use the buttons at the top to switch between the three formulas for work, kinetic energy, and potential energy. Select the value you want to solve for, and the other two input fields will appear.
  • The work formula (W=Fd) applies when the force is applied in the same direction as the object's motion. If the force and motion directions differ, you need to use the component of force in the direction of motion (F×cosθ) instead.
  • Kinetic energy (KE=1/2mv²) is proportional to the square of an object's speed, so doubling the velocity quadruples the energy. This relationship is also important when calculating a car's braking distance.
  • Potential energy (PE=mgh) is a relative quantity that depends on where you set the reference height (h=0). This tool uses the standard convention of taking ground level as the reference (h=0).

Frequently Asked Questions

In physics, work is different from its everyday meaning — it measures the amount of effort a force exerts when it moves an object, expressed as W = F × d (force × distance). Its unit is the joule (J). If a force is applied but the object doesn't move, the work done is zero.

Kinetic energy is the energy an object has because it is moving, and depends on velocity (KE=1/2mv²). Potential energy is the energy an object has because of its position, and depends on height (PE=mgh). Lifting an object increases its potential energy, and as it falls, that potential energy converts into kinetic energy.

In a closed system with no external forces, energy can change form, but its total amount stays the same. For example, when an object falls, the potential energy it loses is converted into kinetic energy (plus a small amount of heat from air resistance), so the total mechanical energy (kinetic + potential) remains roughly constant, ignoring air resistance and similar effects.

This is because the kinetic energy formula KE=1/2mv² includes the square of velocity. When velocity doubles (2v), the v² term becomes (2v)²=4v², so kinetic energy increases fourfold. This relationship is one of the physical reasons why car accidents at higher speeds tend to be far more severe.
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Side Note — When Did the Concept of "Energy" Emerge?

The unified concept of "energy" that we now take for granted didn't actually become firmly established in science until the 19th century. Before that, in the era of Newtonian mechanics, "force" and "motion" were discussed extensively, but it took a long time before kinetic and potential energy were treated as a shared quantity called "energy," with a clearly formulated law of conservation.

In the mid-19th century, James Prescott Joule — the physicist after whom the unit of energy, the joule, is named — demonstrated through precise experiments that mechanical work and heat are mutually convertible, making a major contribution to establishing the law of conservation of energy (the first law of thermodynamics). His experiments were painstaking: he used the work of falling weights to stir water and carefully measured the tiny resulting rise in temperature.

The idea that seemingly different phenomena — kinetic energy, potential energy, heat, electrical energy, chemical energy — can all be converted into and conserved as a common quantity called "energy" became the foundation for nearly every field of physics, chemistry, and engineering that followed. Modern power plants (potential energy → kinetic energy → electrical energy) and car engines (chemical energy → heat → kinetic energy) are all built on this same principle of energy conversion.

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