Work-Energy Calculator
Work, kinetic energy, and power from force and displacement.
About this calculator
This calculator applies the definition of mechanical work, W = Fd·cos(θ), where θ is the angle between the applied force and the direction of motion — cos(0°) gives full credit for a force pushing straight along the displacement, while a 90° angle (force perpendicular to motion) contributes zero work regardless of how hard you push. From that work value, it invokes the work-energy theorem to back out a final velocity assuming the object starts from rest: v = √(2W/m), then recomputes kinetic energy from that velocity as a consistency check — it should match the work done. Power is simply the work divided by the time you specify, also reported in horsepower.
The calculator additionally converts work into kilojoules, calories, and BTU, and — if the angle implies vertical motion — computes the height gained and the gravitational potential energy of lifting the mass, which is useful when the "force at an angle" represents something like pulling a load up a ramp. Key limitation: the final-velocity and kinetic-energy figures assume the object starts at rest and that all the work goes into speeding it up, with no friction losses, so they don't apply if the object was already moving or if some work is dissipated as heat. If the force direction opposes motion (angle beyond 90°), work comes out negative or zero and the velocity calculation is skipped rather than returning an imaginary result.
Inputs
Results
Work (J)
500
Final Velocity (m/s)
10
How to Use This Calculator
- Enter force (N), distance (m) over which it is applied, and angle (degrees) between force and displacement.
- Enter mass (kg) of the object and time (s) over which work is done.
- Read work done (J) and its equivalents in kJ and calories.
- Review final velocity (m/s) from rest via the work-energy theorem and kinetic energy (J).
- Check power (W and HP) — the rate of doing work over the given time.
How the result changes with Force (N)
| Force (N) | Work (J) | Final Velocity (m/s) |
|---|---|---|
| 50 | 250 | 7.07 |
| 75 | 375 | 8.66 |
| 150 | 750 | 12.25 |
| 250 | 1,250 | 15.81 |
What each input means
- Force (N)
- Applied force in newtons.
- Distance (m)
- Displacement over which force is applied.
- Angle (°)
- Angle between force and displacement. 0° = same direction.
- Mass (kg)
- Mass of the object (for velocity calculation).
- Time (s)
- Time over which work is done (for power).
What each result means
- Work (J)
- W = Fd·cos(θ). Work in joules.
- Work (kJ)
- Work in kilojoules.
- Work (cal)
- Work in calories.
- Final Velocity (m/s)
- v = √(2W/m) from rest via work-energy theorem.
- Kinetic Energy (J)
- KE = ½mv². Should equal net work.
- Power (W)
- P = W/t. Rate of doing work.
- Power (HP)
- Power in horsepower.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersForce (N) = 100, Distance (m) = 5, Angle (°) = 0, Mass (kg) = 10 = 5 input(s) provided
- Calculate Work500 = 500
- Calculate Final Velocity10 = 10
- Calculate WorkWork = work / 10000.5 = 0.5
- Calculate WorkWork = work / 4.184119.5 = 119.5
Engine last updated . Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does the angle input top out at 180° instead of allowing any value?
The calculator clamps the angle between 0° and 180°, which covers the full physical range from a force pushing entirely along the direction of motion (0°) to one pushing entirely against it (180°). Cosine is symmetric beyond that range anyway, so any angle you'd want to describe — including sideways or opposing pushes — is already representable within 0–180° without needing negative or larger values.
Why is my final velocity showing as 0 even though I entered a nonzero force?
The engine only computes a final velocity when work comes out positive (`work > 0`) — if your angle is 90° or greater, cos(θ) drives the work to zero or negative, and the calculator returns 0 for final velocity instead of an invalid or imaginary result. A force applied perpendicular to or against the direction of travel doesn't add kinetic energy under this model, so there's no speed increase to solve for.
Why do I get a gravitational potential energy value even though I didn't say anything about lifting?
The calculator treats any nonzero angle as implying some vertical component of motion, computing height gained as distance times sin(θ) and gravitational PE from that height and your mass. If your scenario is purely horizontal, enter an angle of 0° so sin(θ) is zero and the gravitational PE output comes out as zero as well.
Kinetic energy and work are both shown — shouldn't they always be identical?
They should match closely, since kinetic energy is recomputed from the final velocity that was itself derived from the work value via the work-energy theorem — it's included as a consistency check rather than an independent measurement. Small differences you might see come only from the rounding applied to each output individually, not from any physical difference between the two quantities.
Related Calculators
The questions that sit next to this one — chosen by subject, including calculators filed under a different category.
Kinetic Energy Calculator
Calculate kinetic energy from mass and velocity. Use the formula KE = ½mv².
PhysicsElastic Collision Calculator
Final velocities and energy transfer in 1D elastic collisions.
Science & EngineeringPower Calculator
Calculate power from work and time, or force and velocity. Use formulas P = W/t or P = Fv.
Science & EngineeringPhysics Essentials Calculator
Complete classical mechanics calculator — force, velocity, acceleration, kinetic/potential energy, momentum, power, and projectile motion calculations.
BallisticsMuzzle Energy Calculator
Calculate muzzle energy in foot-pounds and joules from bullet weight and muzzle velocity. Also computes power factor and momentum.
More in Science & Physics.