Work by a constant force
W = Fd cosθ
F is force, d is straight-line displacement, and θ is the angle between them. Assumes constant force.
Work, Power and Energy Calculator
Choose a calculation
A blank angle defaults to 0° (parallel). Standard angle inputs accept 0–180°. Signed displacement is supported in work mode; negative displacement reverses the chosen displacement direction.
Presets switch modes, populate the required fields, and calculate immediately. Press Ctrl/Cmd + Enter to calculate manually.
Results
Enter the known values and select Calculate.
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Formula reference
Average power
Pavg = W/t
W is work transferred during time interval t. This is an interval average.
Power from force and velocity
P = Fv cosθ
v is instantaneous velocity. This dot product gives instantaneous power at the stated moment.
Energy transferred
E = W
Mechanical work is an energy transfer. Both work and energy use joules.
Lifting work
ΔPE = mgh
m is mass, g is gravitational acceleration (9.80665 m/s² here), and h is vertical height change.
Work–energy theorem
Wnet = ΔKE = ½m(vf² − vi²)
Net work by all forces equals the change in kinetic energy, not necessarily work by one force.
Efficiency
η = Eout/Ein × 100%
Useful output and input must use consistent system boundaries and signs.
Unit identities: 1 J = 1 N·m, 1 W = 1 J/s, 1 Wh = 3600 J, and 1 mechanical hp = 745.6998716 W.
Worked examples
Angled pull: W = Fd cosθ
A 50 N pull moves a crate 8 m at 30°. The parallel component is 50 cos30° = 43.3 N. Therefore W = 43.3 × 8 = 346 J. Positive work adds energy to the crate.
Motor: P = W/t
A motor transfers 12 kJ in 15 s. Convert 12 kJ = 12,000 J, then P = 12,000/15 = 800 W or 0.800 kW. This is average power over 15 s.
Lift and efficiency
Lifting 20 kg by 3 m requires mgh = 20 × 9.80665 × 3 = 588 J. If the motor draws 800 J, η = 588/800 × 100% = 73.5%.
How to choose the right calculation
Work is done when a force has a component along an object’s displacement. Cosine matters because it projects the force onto that direction: at 0° the full force contributes, at 90° work is zero, and above 90° work is negative. Negative work removes mechanical energy, as braking or friction often does.
Work and energy share units because work describes energy transferred. Power answers a different question—how quickly that transfer occurs. W/t is average power over an interval; Fv cosθ is instantaneous power for the stated force and velocity.
Be clear whether you need work by one force or net work by all forces. Only net work equals ΔKE. The simple Fd cosθ formula assumes a constant force and straight-line displacement. For a force that changes with position or a curved path, use W = ∫F·dr; this calculator does not evaluate that integral.
Frequently asked questions
What is the difference between work, energy, and power?
Work is energy transferred by a force through a displacement, energy is the capacity to cause change, and power is the rate of transferring energy or doing work.
Do work and energy use the same units?
Yes. Work and energy are both measured in joules (J) in SI; one joule equals one newton metre.
Why does the work formula use cosine?
Cosine selects the component of force parallel to the displacement. Only that parallel component transfers energy along the stated motion.
What angle should I enter?
Enter the angle from the displacement direction to the force vector, from 0 to 180 degrees. A blank angle defaults to 0 degrees where angle is used.
When is work zero or negative?
Work is zero at 90 degrees because no force component acts along the displacement. It is negative for angles greater than 90 degrees because the force opposes the motion.
How do I calculate power from force and speed?
Use P = Fv cosθ, where θ is the angle between force and velocity. This is instantaneous power for the stated force and velocity.
Can efficiency exceed 100 percent?
Not for an ordinary passive energy conversion with consistently defined inputs and outputs. A result above 100 percent indicates mismatched boundaries, signs, units, or measurements.
Which units does the calculator accept?
Force: N and kN; length: m, cm, ft, and in; time: s, min, and h; energy: J, kJ, Wh, and ft·lbf; power: W, kW, and hp. Velocity and mass modes also provide common metric and US units.
Methodology, review, and assumptions
Author and reviewer: Starlight Tools Science Editorial Team. Formula application, conversions, edge cases, and browser behavior were reviewed for this release; no individual professional credential is claimed.
Reviewed: 14 July 2026 · Last updated: 14 July 2026
- Values convert to SI before calculation. Constants include 1 ft = 0.3048 m, 1 in = 0.0254 m, 1 ft·lbf = 1.3558179483314004 J, and standard gravity g = 9.80665 m/s².
- Display rounding uses the selected 2–8 significant figures; calculations retain JavaScript floating-point precision. Values within 10⁻¹² of zero are displayed as zero.
- Inputs and results remain in your browser. Nothing entered into this calculator is uploaded by its calculation code.
- Limitations: constant force and straight displacement for Fd cosθ; constant stated velocity for Fv cosθ; no losses in mgh; no rotational energy, relativistic effects, or variable-force integrals.
References: OpenStax University Physics: Work, OpenStax University Physics: Power, and the NIST Guide to SI derived units.