Work, Energy & Power Calculator
Find mechanical work, kinetic and potential energy, or power output — switch modes below for each.
Calculator verified • Last updated: August 2026
Not sure which mode? Click here.
- Work — you know the force applied, the distance moved, and the angle between them, and want the mechanical work done.
- Energy — you know an object's mass, speed, and height, and want its kinetic, potential, and total mechanical energy.
- Power — you know how much work was done and how long it took, and want the rate of energy transfer.
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Work, Energy & Power Explained
Work, energy, and power are closely related but distinct quantities describing how forces move objects and how quickly that motion happens.
Work:
W: work done, in joules (J).
F: applied force, in newtons (N).
d: displacement, in meters (m).
θ: the angle between the force and the direction of motion.
Kinetic energy:
KE: kinetic energy, in joules (J).
m: mass, in kilograms (kg).
v: velocity, in meters per second (m/s).
Gravitational potential energy:
PE: gravitational potential energy, in joules (J).
m: mass, in kilograms (kg).
g: gravitational acceleration, ≈ 9.81 m/s².
h: height above the reference point, in meters (m).
Power:
P: power, in watts (W).
W: work done, in joules (J).
t: time taken, in seconds (s).
Work is measured in joules (J), the same unit as energy — because work is literally a transfer of energy. Power is measured in watts (W), one joule per second, and describes the rate of that transfer.
Worked Example: Energy of a Thrown Ball
Using the calculator's default energy-mode values — a 5 kg object moving at 8 m/s, held 12 m above the ground — kinetic energy works out to J, and potential energy to J, for a total mechanical energy of about 748.6 J. As the object falls (ignoring air resistance), that 748.6 J stays constant — potential energy converts into kinetic energy as height decreases and speed increases.
How Work, Energy, and Power Connect
The work-energy theorem ties these ideas together: the net work done on an object equals its change in kinetic energy. Push something and speed it up, and you've done positive work equal to the kinetic energy gained. Power then describes how quickly that work happens — lifting a box slowly and lifting it quickly to the same height takes the same work, but very different power.
A Brief History of Energy Conservation
The formal concept of energy conservation emerged gradually through the 1840s, with James Prescott Joule's careful experiments relating mechanical work to heat playing a central role — work that eventually gave the SI unit of energy his name. Gustave Coriolis had earlier introduced the modern factor-of-½ definition of kinetic energy in 1829, refining an idea about "living force" that dated back to Gottfried Leibniz in the late 17th century, and by the mid-19th century the principle of energy conservation was recognized as one of physics' most fundamental laws.
Common Work, Energy & Power Mistakes
Forgetting the cosθ term in the work formula is the most common error — if the force isn't applied exactly along the direction of motion, multiplying force by distance alone overstates the work done. Mixing up kinetic energy's v² dependence with a simple linear relationship is another frequent slip, leading people to underestimate how much more damage a faster-moving object can do. Confusing energy (joules) with power (watts) — treating them as interchangeable — is a third common mistake, especially in everyday language like "using less energy" when "using less power" is meant.
Work, Energy & Power Terms You Should Know
Joule (J) — the SI unit of work and energy; one joule is one newton of force over one meter.
Watt (W) — the SI unit of power; one watt is one joule per second.
Work-Energy Theorem — the principle that net work done on an object equals its change in kinetic energy.
Mechanical Energy — the sum of an object's kinetic and potential energy in a system.
These formulas assume no energy losses to friction or air resistance; real systems lose some mechanical energy as heat.
Frequently Asked Questions
Why is no work done if you push against a wall that doesn't move?
In physics, work requires displacement — force applied with zero distance moved produces zero work, no matter how hard you push or how tired you get. This is why W = Fd cosθ gives exactly zero when d = 0: you might feel like you're working hard, but no energy is being transferred to the wall.
What's the difference between energy and power?
Energy is the total capacity to do work, measured in joules, while power is how fast that energy is delivered or used, measured in watts (joules per second). Two machines can do the exact same amount of work, but the one that finishes faster has a higher power output — a sports car and a truck can both move a load the same distance, but the sports car does it with more power.
Why does kinetic energy depend on velocity squared, not just velocity?
Kinetic energy's v² dependence comes directly from integrating force over distance for an accelerating object, and it has a very real consequence: doubling an object's speed doesn't double its kinetic energy, it quadruples it. This is why crash severity increases so dramatically with speed — a car going twice as fast carries four times the energy that needs to be absorbed in a collision.