How to calculate mechanical work
Enter force, displacement, and the angle between them. The Work Calculator converts the selected values to newtons, meters, and radians, then applies W = F × d × cos(θ). The result includes each conversion and formula step, plus text you can copy or download.
- Enter a value in Force (F) and a value in Displacement (d).
- Enter a value in Angle between force and displacement (θ), or leave it blank to use 0 degrees.
- Choose the matching options in Force unit, Displacement unit, and Angle unit.
- Click Calculate to show the work, converted values, formula, and calculation steps.
- Use Copy result or Download result (.txt) to keep the plain-text result. Click Reset to clear the inputs and restore the default units.
What units can I use in the work calculator?
Under Force unit, choose Newtons (N), Pound-force (lbf), Kilogram-force (kgf), or Dynes (dyn). Under Displacement unit, choose Meters (m), Centimeters (cm), Millimeters (mm), Kilometers (km), Feet (ft), Inches (in), or Miles (mi). Under Angle unit, choose Degrees (°) or Radians (rad).
The result reports joules, kilojoules, foot-pounds, calories, and ergs. With force and displacement aligned, the calculation looks like this:
Force (F): 10 N
Displacement (d): 5 m
Angle between force and displacement (θ): 0°
Work: 50 JHow does the work formula use the angle?
The calculator converts the selected angle to radians, finds cos(θ), and multiplies that value by the converted force and displacement. At 0 degrees, the cosine is 1, so the full converted force contributes. At 90 degrees, the cosine is 0 and the calculated work is zero. An angle greater than 90 degrees can produce a negative result.
What does the work calculator reject?
Force (F) and Displacement (d) are required, must be valid numbers, and cannot be negative. They can be zero. Angle between force and displacement (θ) accepts negative, positive, and zero values; a blank angle becomes 0 degrees. The calculator rejects any force, displacement, or angle whose absolute value is above 1e12, and it stops if the calculated work is not finite.
The formula covers a constant force over a straight-line displacement. The calculator does not integrate a changing force along a path or model curved motion. The calculation values are processed locally in the browser.
What the calculation steps let you check
- Enter 10 N, 5 m, and 0 degrees to check the 50 J example and its displayed unit conversions.
- Select a force or displacement unit other than the default, then check its conversion in the step list.
- Enter an angle above 90 degrees to inspect a negative work result when the cosine is negative.
When to use another science calculator
Browse Science Calculators when the unknown is outside this force, displacement, and angle calculation. Use the Force Calculator for force from mass and acceleration. Use the Power Calculator for work or energy over time. Use the Kinetic Energy Calculator for mass and speed.
Frequently asked questions
How do you calculate mechanical work?
Use W = F × d × cos(θ). The calculator converts the entered units, applies the formula, and displays the intermediate values.
What units can I enter in the work calculator?
Enter force in newtons, pound-force, kilogram-force, or dynes; displacement in meters, centimeters, millimeters, kilometers, feet, inches, or miles; and angle in degrees or radians.
Why does the angle change the work result?
The cosine of the angle scales the converted force in the formula. At 0 degrees the full force contributes, while at 90 degrees the calculated work is zero.
Can the work calculator show negative work?
Yes. An angle greater than 90 degrees makes the cosine negative, so the calculated work is negative.
Does the work calculator handle a changing force or curved path?
The calculator applies the constant-force formula to a straight-line displacement. It does not integrate a changing force or model curved motion.