Torque Calculator
Torque from force, lever arm, and angle with unit conversions.
About this calculator
Torque is the rotational analog of force — it measures how effectively a push or pull twists something around a pivot, rather than how hard it pushes in a straight line. The formula, τ = r·F·sin(θ), captures three things that all matter: how much force is applied, how far from the pivot it's applied (the lever arm), and the angle between the force and the arm. That sine term is why torque wrench technique matters in practice — pulling straight along the wrench handle's length (θ near 0°) contributes almost nothing, while pulling perpendicular to it (θ = 90°) delivers the full force as torque, which is why proper technique always applies force perpendicular to the lever arm.
This calculator also reports rotational power, P = τ·ω, which combines torque with angular velocity (converted here from RPM) to show how much mechanical power a rotating shaft is delivering — the same torque produces far more power at higher RPM, which is why low-torque, high-RPM electric motors can still move heavy loads through a gear reduction. Torque is reported in newton-meters alongside the pound-foot, pound-inch, and kilogram-centimeter conversions used across different engineering and automotive contexts.
Inputs
Results
Torque (N·m)
15
Power (W)
1,570.8
How to Use This Calculator
- Enter applied force (N) and lever arm length (m) from the pivot to the force application point.
- Enter the angle (degrees) between the force vector and the lever arm — 90 degrees gives maximum torque.
- Enter RPM for power calculation.
- Read torque (N·m) and its equivalents in lb·ft, lb·in, and kg·cm.
- Review power (W and HP) produced at the given RPM.
How the result changes with Force (N)
| Force (N) | Torque (N·m) | Power (W) |
|---|---|---|
| 25 | 7.5 | 785.4 |
| 38 | 11.4 | 1,193.81 |
| 75 | 22.5 | 2,356.19 |
| 125 | 37.5 | 3,926.99 |
What each input means
- Force (N)
- Applied force in newtons.
- Lever Arm (m)
- Distance from pivot to point of force application.
- Angle (°)
- Angle between force vector and lever arm. 90° = maximum torque.
- RPM (for power)
- Rotational speed for power calculation.
What each result means
- Torque (N·m)
- τ = rF·sin(θ).
- Torque (lb·ft)
- Torque in pound-feet.
- Torque (lb·in)
- Torque in pound-inches.
- Torque (kg·cm)
- Torque in kilogram-centimeters.
- Power (W)
- P = τω. Rotational power in watts.
- Power (HP)
- Rotational power in horsepower.
- Angular Velocity (rad/s)
- ω = RPM × 2π/60.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersForce (N) = 50, Lever Arm (m) = 0.3, Angle (°) = 90, RPM (for power) = 1000 = 4 input(s) provided
- Calculate Torque15 = 15
- Calculate PowerPower = torque * omegaRadS1570.8 = 1570.8
- Calculate TorqueTorque = torque * 0.737611.064 = 11.064
- Calculate TorqueTorque = torque * 8.8507132.761 = 132.761
Engine last updated . Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does the angle between force and lever arm matter so much?
Only the component of force that is perpendicular to the lever arm actually contributes to rotation — force applied straight along the arm's length just pulls or compresses it without twisting anything. That's why the formula multiplies by sine of the angle, which peaks at 1 when the force is fully perpendicular (90°) and drops to 0 when it's applied straight along the arm (0° or 180°).
Why does the same torque produce different power at different RPM?
Power is torque multiplied by angular velocity, so at a fixed torque, spinning faster delivers proportionally more power per unit time — the shaft is doing the same twisting work more often each second. This is why a small, high-RPM electric motor can output serious power despite modest torque, while a slow-turning diesel engine needs much higher torque to match it.
How do I convert torque between newton-meters and pound-feet?
One newton-meter equals approximately 0.7376 pound-feet, so multiplying a newton-meter value by that factor converts it directly. This calculator does that conversion automatically alongside pound-inch and kilogram-centimeter equivalents, since different fields and regions default to different torque units on their tools and specifications.
Does a longer lever arm always mean more torque for the same force?
Yes, assuming the angle between force and arm stays the same — torque scales directly and proportionally with lever arm length, which is the entire principle behind using a breaker bar or cheater pipe to loosen a stuck bolt. Doubling the effective arm length doubles the torque delivered by the same applied force.
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