Work Done by a Force

How it is calculated

The tool calculates W = F × d × cos(θ). F is the force in newtons, d the displacement in metres, and θ the angle in degrees between the force and the direction of movement. The angle is converted to radians internally, and the work W is shown in joules (J) with two decimals.

The result can be negative: an angle between 90° and 270° means the force points partly against the motion (friction or braking), so it removes energy. At exactly 90° the work is 0.00 J. The tool does not reject any numbers, so a negative force or distance simply flips the sign. Use consistent SI units; if you type pounds-force or feet, the result will not be in joules.

Common mistakes

• Taking the angle from the wrong reference: θ is measured between the force and the direction of motion, not between the force and the vertical.
• Typing the angle in radians; the tool expects degrees, so 0.52 is read as about half a degree and the work comes out almost equal to F × d.
• Entering the distance travelled by the object when the force acted for only part of it; only the displacement during which the force was applied counts.
• Ignoring the sign: a friction force opposite to the motion has θ = 180° and gives negative work, not a positive amount.
• Confusing work with power; work is energy in joules, and the time taken does not appear in this formula.