50 N over 3 m at 60°
W = F × d × cos(θ)
50 × 3 × 0.5 = 75 J. The force component along the displacement is 25 N.
Energy transferred by a force
Work Calculator
Find the work done by a constant force, or solve for force or displacement. Include the angle to distinguish positive, negative, and zero work.
Calculate work, force, or displacement
Work
Enter the known values and angle, then select Calculate.
- Work in joules
- Force in newtons
- Displacement in meters
- Angle
- cos(θ)
- Force along displacement, F cos(θ)
- Formula
Calculation steps
≈ marks rounding or numerical trigonometry. Calculations run in your browser. Press Enter to calculate. Successful results appear in this tab's Recent calculations.
Three worked examples
−120 J over 4 m at 180°
F = W ÷ [d × cos(θ)]
−120 ÷ (4 × −1) = 30 N. Force magnitude is positive; the angle gives the opposing direction.
1 kJ from 200 N at 0°
d = W ÷ [F × cos(θ)]
1,000 ÷ (200 × 1) = 5 m. Convert the work to joules before applying SI units.
Model, units, and rounding
The model is W = Fd cos(θ) for one force that is constant in magnitude and direction, over a straight displacement. It does not integrate variable forces or combine the work of several forces. Reference: OpenStax — Work.
Conversions use exact definitions: 1 kJ = 1,000 J, 1 MJ = 1,000,000 J, 1 Wh = 3,600 J, 1 kWh = 3,600,000 J, 1 kN = 1,000 N, 1 km = 1,000 m, 1 cm = 0.01 m, 1 ft = 0.3048 m, 1 in = 0.0254 m, and 1 lbf = 4.4482216152605 N. References: NIST conversion factors and NIST exact pound-force definition, note 23.
At exactly 90°, work is zero. Solving for force or displacement then has no unique answer when work is zero, or is inconsistent when work is nonzero. A zero known magnitude creates the same ambiguity. Otherwise, zero work gives a uniquely inferred zero magnitude. Positive work requires an angle below 90°; negative work requires an angle above 90°, when both magnitudes are positive.
Inputs accept at most 64 characters, 15 integer digits, and 10 decimal places. Numeric fields do not accept units, expressions, or scientific notation. Hidden inputs are disabled and ignored. Angles use degrees from 0 through 180; radians are not accepted.
Unit conversions and arithmetic use exact fractions. Cosines of 0°, 60°, 90°, 120°, and 180° are exact here; other angles use a private 120-significant-digit numerical calculation. Only final displays are rounded. Halfway values round away from zero, trailing zeros are omitted, and ≈ marks rounding or numerical trigonometry. A tiny nonzero main result receives a notice that preserves its sign. Changing precision or result units does not add a recent-calculation entry.
Common questions
Why can work be negative?
The sign describes energy transfer by the selected force. If its component opposes displacement, its work is negative. This is different from a negative force magnitude.
Does this give net work or a change in kinetic energy?
It gives the work of the force you enter. Net work requires adding the work of all forces; this calculator does not infer the other forces acting on an object.
Is work the same as torque?
They share dimensions but represent different quantities. Work uses the component along displacement and is expressed in joules. Torque describes a turning effect about a pivot and is conventionally expressed in N·m.
Why is 89.9999999999° different from 90°?
The first angle has a tiny nonzero cosine. Solving for force or displacement can therefore produce a large finite result. At exactly 90°, the tool reports whether the inputs are ambiguous or inconsistent.