About the Work and Energy Calculator
Energy is one of the most useful ideas in physics because it is conserved: it changes form but the total stays the same. Many problems that are awkward with forces and accelerations become a line or two of algebra once you track work and energy instead.
This calculator handles the four core relationships in any introductory mechanics course: the work done by a constant force, kinetic energy, gravitational potential energy near Earth's surface, and power. Results are in joules and watts, and every formula can be solved for whichever quantity is missing.
What are work and energy?
Work is energy transferred to or from an object by a force acting along a displacement. A force of one newton moving its point of application one metre in the direction of the force does one joule of work. Pushing on a wall that does not move does no work, however tiring it feels.
Energy is the capacity to do work. Kinetic energy is the energy of motion, ½mv², and gravitational potential energy is the energy stored by height, mgh. The work–energy theorem ties them together: the net work done on an object equals its change in kinetic energy.
How to use the Work and Energy Calculator
- Select work, kinetic energy, potential energy or power.
- Enter the known values in SI units (N, m, kg, m/s, s).
- Leave exactly one value empty to make it the unknown.
- For work, add the angle θ if the force is not along the motion.
- Press Calculate and follow the rearrangement and substitution.
Formulas
Work
Kinetic energy
Gravitational potential energy
Power
Work–energy theorem
Worked example: Work: 10 N over 5 m at 60°
A 2 kg ball is dropped from 10 m. Its potential energy at the top is J.
Ignoring air resistance, all of it becomes kinetic energy just before impact, so and m/s. Enter KE = 196.2 and m = 2 in kinetic mode to reproduce this.
The solution below is generated by the same engine that powers the calculator above.
Final answer
work W = 25 J
How we read your problem
Use the work done by a constant force formula, rearranged for the unknown, in SI units.
Step-by-step solution
Formula: work done by a constant force
Substitute the known values
Formulas used
work done by a constant force
Only the component of the force along the displacement does work, hence the cos θ. Work is positive when the force has a component along the motion, negative when it opposes it (θ > 90°), and zero when it is perpendicular.
Verification
- Substituted every value back into the formula: both sides agree ✓
Detailed explanation
Why work has a cos θ
Only the part of the force along the direction of motion transfers energy. If you pull a suitcase with 10 N at 60° above the floor over 5 m, the useful component is 10 cos 60° = 5 N, so the work is 25 J, not 50 J.
When the angle is greater than 90° the cosine is negative and so is the work: the force is taking energy away, as friction or braking does. At exactly 90°, as with the normal force on a level road or the tension in a string whirling a ball in a circle, the work is zero.
Conservation of mechanical energy
Without friction or air resistance, the sum KE + PE stays constant. A roller-coaster car that starts at rest 30 m up has the same speed at every point 30 m lower, regardless of the shape of the track, because only the height difference matters.
When friction acts, mechanical energy is not conserved; some becomes thermal energy. The work done by friction is negative and equals the loss in KE + PE, which is how you can estimate friction from a measured final speed.
Power in everyday units
Power tells you how fast work is done. Climbing stairs that raise your 60 kg body 3 m takes about 1766 J; doing it in 2 seconds needs roughly 883 W, more than one horsepower (about 746 W) for a moment.
Electricity bills use kilowatt-hours, an energy unit: one kWh is 1000 W for 3600 s, or 3.6 million joules. A 1200 W kettle running for 3 minutes uses 216 kJ, which is 0.06 kWh.
Common mistakes
- Forgetting to square the speed in ½mv².
- Using the full force instead of F cos θ when pulling at an angle.
- Measuring height from different zero levels in one problem.
- Mixing up the symbol W for work with W for watts.
- Entering minutes instead of seconds when finding power.
Tips
- Choose a zero level for potential energy and keep it fixed.
- Use energy methods when the path is curved or forces are complicated.
- Check that kinetic energy is never negative.
- Remember that doubling the speed quadruples the kinetic energy.
- Use the force calculator to find F before computing work.
Frequently asked questions
How do I calculate work done?
Multiply the force by the displacement and by the cosine of the angle between them: W = Fd cos θ. With the force along the motion, W = Fd.
How do I find speed from kinetic energy?
Rearrange KE = ½mv² to v = √(2KE/m). For 100 J and 2 kg, v = 10 m/s.
Can work be negative?
Yes. When the force has a component opposite to the motion, such as friction, the work is negative and the object loses energy.
What is the unit of energy?
The joule (J), equal to one newton-metre or one kg·m²/s². Food energy uses kilocalories; 1 kcal ≈ 4184 J.
What is the difference between work and power?
Work is the energy transferred; power is how quickly it is transferred. One watt equals one joule per second.
Does potential energy depend on the path taken?
No. Gravitational potential energy depends only on height, so the change between two points is the same for any route.
What is the work–energy theorem?
It states that the net work done on an object equals the change in its kinetic energy.
Work out energy and power
Select a quantity above, enter the known values and leave the unknown empty.