What This Tool Does
Use this calculator to find mechanical work from force, displacement, and the angle between them. It applies W = F × d × cos(θ), converts the inputs to SI units, and shows the formula with intermediate steps. Results are displayed in J, kJ, ft·lb, cal, and erg.
Inputs & Supported Units
- Force unit: newtons (N), pound-force (lbf), kilogram-force (kgf), or dynes (dyn). Force must be zero or a positive number.
- Displacement unit: meters (m), centimeters (cm), millimeters (mm), kilometers (km), feet (ft), inches (in), or miles (mi). Displacement must be zero or a positive number.
- Angle unit: degrees (°) or radians (rad). Angle may be positive, negative, or zero; a blank angle defaults to 0°.
- Result units: the calculated work is reported in joules (J), kilojoules (kJ), foot-pounds (ft·lb), calories (cal), and ergs.
Input Validation and Calculation Limits
Force and displacement reject blank, non-numeric, negative, or non-finite values. Angle accepts negative, positive, and zero values; a blank angle is treated as 0. Each numeric input is rejected when its absolute value exceeds 1e12, and a non-finite calculated result is rejected.
How to Use the Work Calculator
- Enter force, displacement, and angle values.
- Choose values in Force unit, Displacement unit, and Angle unit.
- Click Calculate to display the work and intermediate steps.
- Use Copy result to copy the plain-text output, or Download result (.txt) to download
work-calculator-result.txt. - Click Reset to clear the three inputs, restore the default units, hide the result, and clear errors.
Formula, Results, and Limitations
The calculator converts force to newtons, displacement to meters, and angle to radians before applying W = F × d × cos(θ). It represents a constant force acting over a straight-line displacement. Angles greater than 90° can produce negative work.
It does not integrate a varying force over a path or model curved motion. The output is not presented as certified engineering, physics coursework, or professional advice.
Calculation Data Handling
The calculation code processes the values you enter locally in the browser and does not fetch external data to calculate the result. This applies to the calculation code, not to every network request made by the page.
Frequently Asked Questions
What is the formula for mechanical work?
Mechanical work equals force times displacement times the cosine of the angle between them: W = F × d × cos(θ). This gives the work done by a constant force acting on an object as it moves through a displacement.
What units does this calculator support?
Force can be entered in newtons, pound-force, kilogram-force, or dynes. Displacement can be entered in meters, centimeters, millimeters, kilometers, feet, inches, or miles. Angle can be entered in degrees or radians. The result is shown in joules, kilojoules, foot-pounds, calories, and ergs.
Why does the angle matter in the work formula?
Work only counts the component of force that acts along the direction of displacement. The cosine of the angle between the force and displacement vectors scales the result: at 0° the force fully contributes (cos 0° = 1), and at 90° a force perpendicular to the displacement does zero work (cos 90° = 0).
Can work be negative?
Yes. When the angle between force and displacement is greater than 90°, cos(θ) is negative, so the calculated work is negative. This represents a force acting opposite to the direction of motion, such as friction or braking.
Does this calculator handle non-constant forces or curved paths?
No. This calculator applies W = F × d × cos(θ) for a constant force acting over a straight-line displacement. It does not integrate a varying force over a path or model curved motion.