Quick answer
Torque is τ = r × F × sin θ. A 150 N force applied 0.3 m from the pivot at 90° produces 45 N·m (33.19 lbf·ft).
Enter the lever arm, force and angle. The calculator returns the torque in N·m and lbf·ft.
Related tools: Angular Velocity Calculator: Angular velocity from rpm, frequency, or an angle and time. Angular Acceleration Calculator: Angular acceleration from a change in angular velocity.
How to use the Torque Calculator
- Enter lever arm (m) (above 0).
- Enter force (N) (above 0).
- Enter angle between force and lever (°) (between 0 and 180). It starts at 90.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Lever arm | A number, in m | > 0 |
| Force | A number, in N | > 0 |
| Angle between force and lever | A number, in ° | ≥ 0, ≤ 180, starts at 90 |
Formula and method
Formula
τ = r × F × sin θ
IEEE-754 double precision; shown to the decimals indicated.
Maximum torque when the force is perpendicular to the lever.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Lever arm = 0.3; Force = 150; Angle between force and lever = 90.
| Result | Value |
|---|---|
| Torque | 45 N·m |
| In lbf·ft | 33.1903 |
Example 2
Inputs: Lever arm = 0.25; Force = 200; Angle between force and lever = 60.
| Result | Value |
|---|---|
| Torque | 43.30127 N·m |
| In lbf·ft | 31.9374 |
Example 3
Inputs: Lever arm = 2; Force = 10; Angle between force and lever = 30.
| Result | Value |
|---|---|
| Torque | 10 N·m |
| In lbf·ft | 7.3756 |
The first line is the headline result (torque). Below it the torque Calculator lists in lbf·ft, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Worked example
0.3 × 150 × sin 90° = 45 N·m. Pushing at 30° instead gives 22.5 N·m. A longer wrench multiplies torque for the same force.
Angle
Only the force component perpendicular to the lever arm counts. A 0° angle (force along the arm) gives zero torque. Typical car wheel nuts are tightened to about 100 to 140 N·m.
How the result changes with lever arm
Holding every other input at the first worked example, this table changes only lever arm. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Lever arm | Torque | In lbf·ft |
|---|---|---|
| 0.15 | 22.5 N·m | 16.5951 |
| 0.3 | 45 N·m | 33.1903 |
| 0.6 | 90 N·m | 66.3806 |
| 1.2 | 180 N·m | 132.7612 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Lever arm: entering "0" shows "Lever arm must be greater than 0." beside that field and no result.
- Angle between force and lever: entering "200" shows "Angle between force and lever must be at most 180." beside that field and no result.
Choosing between the Torque Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Engine Torque Calculator](/engineering/engine-torque-calculator/) | calculate and engine speed | Torque |
| [Angular Velocity Calculator](/science/angular-velocity-calculator/) | starting from | Angular velocity |
| [Angular Acceleration Calculator](/science/angular-acceleration-calculator/) | initial angular velocity, final angular velocity and time | Angular acceleration |
| [Bolt Torque Calculator](/engineering/bolt-torque-calculator/) | nut factor K, nominal diameter and target preload | Torque |
| [Dew Point Calculator](/science/dew-point/) | air temperature and relative humidity | Dew point |
Background: gravity, rotation and optics
Gravity and rotation calculations use a few core relations: a circular orbit has speed v = √(GM ÷ r), torque equals moment of inertia times angular acceleration (τ = Iα), and a thin lens obeys 1/f = 1/dₒ + 1/dᵢ. The moment of inertia depends on both the shape and the axis of rotation.
Use SI units (metres, kilograms, seconds) and check the sign conventions of the formula before interpreting a negative result.
Assumptions and limitations
- A 0° angle gives zero torque
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for lever arm and angle between force and lever to confirm this.
Frequently asked questions
What is the unit of torque?
Torque is in newton-metres (N·m); 1 N·m is 0.7376 lbf·ft.
How do I double the torque?
Double the arm or the force.
What is torque in lbf·ft?
Multiply N·m by 0.7376.
What does the Torque Calculator calculate?
Torque from force, lever arm and angle. It returns Torque and In lbf·ft.
What formula does the Torque Calculator use?
τ = r × F × sin θ. Maximum torque when the force is perpendicular to the lever.
What do I need to enter in the torque Calculator?
You enter Lever arm (m), Force (N) and Angle between force and lever (°).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. A 0° angle gives zero torque.
What is an example of a torque result?
With lever arm 0.3, force 150 and angle between force and lever 90, the torque is 45 N·m.
Related calculators
- Angular Velocity Calculator — Angular velocity from rpm, frequency, or an angle and time.
- Angular Acceleration Calculator — Angular acceleration from a change in angular velocity.
- Dew Point Calculator — Dew point from temperature and relative humidity.
- Acceleration Calculator — Average acceleration from change in velocity over time.
Sources
- OpenStax, University Physics Volume 1 (Rice University): mechanics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.