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Enter your values, then click Calculate result.How this calculator helps
This work calculator uses the dot product of a constant force and a straight displacement. It also divides the supplied work by time to show average power. Use it when an exercise explicitly provides the magnitude and angle of the relevant force. The result belongs to that force; it becomes net work only after all other forces are accounted for. A separate kinetic energy worksheet answers a state-energy question, whereas this page answers an energy transfer over displacement.
How to use it
- 1
Choose the unknown or identify the quantity required by your problem before entering measurements.
- 2
Convert each supplied measurement to the SI units printed beside its field. Keep the directional sign convention consistent throughout the problem.
- 3
Read the method and worked example, then click Calculate result. The saved result remains visible while you edit inputs.
- 4
Check the units, limiting case and reconstructed equation before copying the answer into a report or worksheet.
Formula and methodology
W = F d cos θ; average power = W/Δt. θ is the angle between the force and displacement vectors.
The calculator applies the displayed arithmetic to the values entered on this device. It does not silently load a local tax rate, currency conversion or commercial assumption.
Worked calculation example
A 50 N force acting over 4 m at 60 degrees to displacement does 100 J of work because cos 60° = 0.5. If that motion takes 5 s, the average power of the supplied work is 20 W. At 90 degrees, the same force and displacement give zero work. At 180 degrees, the work is −200 J. The sign depends on alignment with displacement, not on whether the force itself is described as large.
How to interpret your result
The output reports signed work, average power and the force component along displacement. Use the component result to understand why an angled force contributes less than an aligned force of the same magnitude. If comparing with a change in kinetic energy, make sure all force contributions and the same system boundary are represented. A time input affects average power but cannot change the computed work.
For different inputs or formulas, use Kinetic Energy Calculator; Hookes Law Calculator; Gravitational Potential Energy Calculator.
Related questions this calculator covers
- work calculator physics
- work energy calculator
- average power calculator
Scenario comparison
| Scenario | What it shows |
|---|---|
| Aligned pull | zero angle gives the full Fd product. |
| Perpendicular force | a right angle contributes zero work. |
| Opposing force | 180 degrees produces negative work. |
Common mistakes to avoid
- Using a diagram angle that is not between force and displacement.
- Equating one force’s work with net work automatically.
- Treating average mechanical power as measured electrical consumption.
Compute the example as 50 × 4 × 0.5 = 100 J and divide by 5 to obtain 20 W. Check zero and 180 degrees as limiting cases. Double elapsed time while keeping force, distance and angle fixed: work stays the same and average power halves. Units N·m must equal joules, and J/s must equal watts.
Authoritative reference. Method reference checked for this worksheet. The calculation and examples are independently implemented; read the specific scope and units above.What can affect the result?
Angle means angle between vectors
The input is in degrees and ranges from zero to 180. Zero means force aligns with displacement; 90 means perpendicular; 180 means opposite. It is not automatically an angle measured from the ground, a slope angle or the angle of a cable shown elsewhere in a diagram. Identify both vectors before transferring a geometric angle into this field.
Constant force is a model assumption
The formula Fd cos θ assumes the supplied force and its alignment remain constant over the displacement. For a varying force, work is an integral of force along the path. A spring force changes with extension, so multiplying its final force by full extension overstates the ideal elastic energy. Use the Hooke’s law worksheet for linear spring storage rather than this constant-force approximation.
Work by one force versus net work
Gravity, friction, a motor and a normal reaction can each contribute differently. Net work is the sum of work by all relevant forces and equals the change in translational kinetic energy under the appropriate particle model. This page does not infer unentered forces. Label a result “work by the applied force” when only that force has been supplied.
Negative work is physically meaningful
An opposing force removes kinetic energy from the described motion when considered in the net work balance. Friction often does negative work on a sliding object; gravity can do positive work during a downward displacement. A negative result is not an input error. Average power computed from that signed work also carries a sign, indicating the direction of the modeled energy transfer.
Average power requires elapsed time
Power in watts is joules per second. The calculation gives an interval average and cannot determine an instantaneous value without a force and velocity history. Halving time for the same work doubles average power. Convert minutes to seconds before entering the interval. A zero or negative time cannot serve as an elapsed duration and is rejected.
Keep energy and efficiency separate
Mechanical work here is not automatically electrical consumption. A motor’s input energy can exceed useful mechanical work because of efficiency and auxiliary loads. Converting joules to watt-hours requires division by 3,600, but a utility bill additionally depends on the electrical energy actually used. The battery runtime worksheet models load energy and conversion efficiency with its own explicit assumptions.
Privacy and browser processing
Values entered on this page are processed in the current browser session. SolvePilot does not require an account and does not receive the values entered into the calculator. Refreshing or closing the page clears the working values unless the browser itself restores a previous session. Avoid entering identifying or account information because the calculation needs summary values only.
Accuracy and verification
Accuracy depends first on input quality. Confirm definitions, scales, dates and source information before entering a value. Keep an independent record of any result used for planning because this page does not create an official statement or retain a calculation history.
Limits of this estimate
Use only the disclosed input domains and model. Using a diagram angle that is not between force and displacement. Review the method-specific boundaries above and the linked source before interpreting a result. Calculations use browser floating-point arithmetic; displayed digits are not a measure of real-world certainty. Your entries stay on this device and are not submitted to a calculation server.
Sources and review information
Frequently asked questions
Why is work zero at 90 degrees?＋
A perpendicular force has no component along the displacement.
Can the result be negative?＋
Yes. A force opposing displacement produces negative work.
Is this net work?＋
Only if the entered force is the appropriate net constant force, or other work contributions have been included separately.
Can it calculate a spring’s work from its final force?＋
Not accurately with this constant-force model. Use the spring energy expression for a linear spring.
Does average power equal instantaneous power?＋
Not necessarily. The output is work divided by the supplied elapsed time.