Enter values
How to use this calculator
- Enter the constant force magnitude and choose its unit.
- Enter displacement (distance moved) and choose its unit.
- Provide the angle between force direction and motion.
- Press Calculate Work to view results above.
- Use CSV/PDF buttons to save the computed summary.
Formula used
For a constant force and straight-line displacement, the work done is: W = F · d · cos(θ).
- F is the force magnitude.
- d is the displacement magnitude.
- θ is the angle between force and displacement.
- If θ > 90°, work becomes negative.
Example data table
| Force (N) | Displacement (m) | Angle (deg) | Work (J) | Interpretation |
|---|---|---|---|---|
| 10 | 5 | 0 | 50 | Fully aligned with motion |
| 20 | 3 | 60 | 30 | Partial alignment |
| 15 | 4 | 90 | 0 | Perpendicular force does no work |
| 12 | 2 | 120 | -12 | Opposes motion (negative work) |
Tip: If your angle is uncertain, test a range to see sensitivity.
Article
1) Meaning of work in mechanics
Mechanical work quantifies energy transferred when a force causes displacement. In SI units, one joule equals one newton‑meter. For example, pushing with 50 N through 2 m along the motion delivers 100 J. This calculator reports joules and also converts to kilojoules, megajoules, and watt‑hours for practical reporting.
2) When “constant force” is a good model
Many lab and field problems approximate a constant force: steady towing, uniform tension in a rope, or a fixed magnetic/electric actuator over a small travel. If the force changes significantly with position, you would typically integrate F(x) over distance instead of using a single value.
3) Direction matters: the dot product
Only the component of force parallel to motion contributes to work. The dot product form W = F · d · cos(θ) captures this direction effect. When θ is 0°, all force is effective. When θ is 60°, only half of the force contributes because cos(60°)=0.5.
4) Key angle cases and expected outcomes
Three angles are especially useful for quick checks. At 0°, work is maximized: W = Fd. At 90°, cos(90°)=0 and the work is zero, even with large force (like a centripetal force). Beyond 90°, work becomes negative because the force opposes the displacement.
5) Positive, negative, and zero work in data
Positive work increases the object’s mechanical energy, often increasing speed. Negative work removes mechanical energy, like braking or friction acting opposite motion. Zero work means no net energy transfer through that force along the path, common for perpendicular forces or when displacement is zero.
6) Unit handling and real‑world scales
Forces appear in newtons, kilonewtons, or pounds‑force, while displacement may be entered in meters, centimeters, feet, or inches. Conversions are applied before computing work. As scale guidance: 1 lbf ≈ 4.448 N, and 1 Wh equals 3600 J, useful for comparing mechanical work to battery energy ratings.
7) Measurement tips for better accuracy
Use consistent reference directions: measure θ between the force direction and the displacement direction, not between components. If the motion is not straight, use the displacement along the path segment where the force is approximately constant. For experimental data, report uncertainty in force and distance to bound the work estimate.
8) Common applications and checks
This calculator supports quick engineering and classroom tasks: estimating winch effort, evaluating pulling angles, comparing work for different handle orientations, and sanity‑checking energy transfer in a setup. A practical check is dimensional: newtons times meters must yield joules. If the sign surprises you, recheck θ and motion direction.
FAQs
1) Does the displacement have to be straight?
The formula applies directly to straight‑line displacement with a constant force direction. For curved paths or changing directions, compute work over small segments or use an integral approach.
2) Why is work zero at 90°?
At 90°, the force is perpendicular to displacement, so the parallel component is zero. Since only the parallel component does work, the dot product gives W = 0.
3) What does negative work mean physically?
Negative work means the force removes mechanical energy from the object along the motion, such as braking, drag, or friction opposing displacement.
4) Which angle should I enter?
Enter the angle between the force vector and the displacement direction. If you know the pulling angle relative to the motion axis, that is typically the correct θ.
5) Can I include friction in the force value?
Yes, if you want work done by a specific net force component, use the appropriate force magnitude and direction. For work by friction, use its magnitude with θ = 180° when it directly opposes motion.
6) Should force or displacement ever be negative?
This tool treats force and displacement as magnitudes and uses θ for direction. If you have signed quantities, convert them into a magnitude plus the correct θ that represents the relative direction.
7) How is work related to power?
Power is the rate of doing work. If work W occurs over time t, the average power is P = W/t. This helps connect mechanical results to electrical energy in watt‑hours.