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).

Last updated: 2026-09-20

Calculating work and energy

Work, in physics, is the amount of energy a force transfers to an object while moving it. The formula is W = Fd, which holds **when the force acts along the direction of motion.** Standing still holding a heavy bag tires your arms, yet nothing moves, so physically no work is being done at all. That gap with everyday intuition is where the subject usually first catches people out.

Energy comes in a form due to motion — kinetic energy, KE = ½mv² — and a form due to position — potential energy, PE = mgh. That **kinetic energy goes with the square of the speed** matters a great deal: double the speed and the energy quadruples. It is why stopping distance grows with the square of speed. This tool switches between the three formulas and lets you choose which quantity to solve for, so you can obtain the unknown without rearranging anything by hand.

How to calculate

Choose the formula Select work, kinetic energy or potential energy.
Choose what to solve for You can work in either direction — recovering the speed from a kinetic energy, for instance.
Enter the known values Mass in kilograms, distance and height in metres, speed in metres per second, force in newtons.
Read the result Both energy and work are reported in joules.

Tips for getting more out of it

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).

Where this helps

Physics homework and exam practice

Put in the values and check that you have not rearranged the formula incorrectly.

Estimating the danger of a fall

Work out roughly how much energy an object dropped from a height carries, from that height and its mass.

Understanding speed against impact

Comparing kinetic energies at different speeds makes the square relationship tangible in numbers.

Finding the work needed to lift something

Establish the minimum energy required to raise a load to a given height.

Mechanics terms explained

Work (W): The energy a force transfers to an object. **When the force is perpendicular to the motion, the work is zero.**
Kinetic energy (KE): The energy a moving object carries, given by ½mv². **It is proportional to the square of the speed.**
Potential energy (PE): The energy stored by virtue of height, given by mgh. The value depends on where you place the reference height.
Joule (J): The unit of energy and of work. One joule is the work done moving something one metre against one newton.
Gravitational acceleration (g): About 9.8 metres per second squared at the Earth's surface, used in the potential energy calculation.
Conservation of mechanical energy: The principle that, absent friction and the like, the sum of kinetic and potential energy stays constant.

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.

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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