Force, Work, Energy and Power Calculator
Newton's second law, work and power, kinetic and potential energy, and rotating shaft power, with every step shown.
Engineering student calculators
Free textbook calculators with every step shown, so you can check your own working. Pick one, type in your numbers and see the formulas worked out. Or switch to Ask a question for an explained answer. No account needed.
Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.
How this calculator works
A net force on a mass gives it an acceleration, F equals m a. Moving a force through a distance does work, W equals F d cosine of the angle between them, and the rate of doing work is power. A moving mass has kinetic energy half m v squared, and a raised mass has potential energy m g h.
For a rotating shaft the matching quantities are the torque, the angular speed and the power, which is torque times angular speed. A mass on a rotating arm needs an inward centripetal force m omega squared r to hold it on its circle, which grows with the square of the speed.
Formulas used
- F = m a
- W = F d \cos\theta
- P = T \omega
- E_k = \tfrac12 m v^2,\;\; E_p = m g h
- F_c = m \omega^2 r
Worked example
With the default numbers in the calculator above:
- Acceleration: 5 m/s²
- Weight of the mass: 981 N
- Momentum at the given speed: 1000 kg m/s
- Time to reach that speed from rest: 2 s
- Distance covered in that time: 10 m
- Impulse (force times time): 1000 N s
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
What is the difference between mass and weight?
Mass is the amount of matter, in kilograms. Weight is the force of gravity on it, m g, in newtons: about 9.81 N for each kilogram on Earth.
Why is the work zero when the force is at 90 degrees?
Only the part of the force along the movement does work. A force at right angles to the movement, such as the weight of a box pushed along a level floor, does no work on it.
What is a horsepower?
The mechanical horsepower is 745.7 watts. The metric horsepower is about 735.5 watts.
Is energy always conserved?
Total energy is. Mechanical energy is only conserved when nothing is lost to friction, drag or heat, so in real machines the useful energy at the output is less than the energy put in.
Related calculators
Further reading: Meriam and Kraige, Engineering Mechanics: Dynamics; Hibbeler, Engineering Mechanics: Dynamics; Rao, Mechanical Vibrations.
Need a calculator we do not have?
Embed this calculator on your own page
Copy this code into your page. The calculator runs inside the frame and links back to Drafting Central.
Need this drawn, designed or checked?
Drafting Central is a mechanical engineering and drafting business in Burleigh Waters on the Gold Coast. A calculator gives you the numbers; we can turn them into drawings and designs.
Need help with a real project?
Talk to Drafting Central →