What is the torque formula?

Torque (τ) equals force (F) multiplied by lever arm length (r) and the sine of the angle (θ) between the force and the arm: τ = F × r × sin θ. When the force is applied at 90° (perpendicular), sin θ = 1 and the formula simplifies to τ = F × r.

What happens when the angle is 0° or 180°?

At 0° or 180° the force is parallel to the lever arm and produces zero torque (sin 0° = 0, sin 180° = 0). Maximum torque is generated at exactly 90°.

How do I convert N·m to ft·lbf?

1 N·m ≈ 0.7376 ft·lbf. To convert, multiply the Newton-meter value by 0.7376. Equivalently, 1 ft·lbf ≈ 1.3558 N·m. This calculator performs all conversions automatically.

What units are commonly used for torque in automotive work?

Automotive specs in the United States use foot-pounds (ft·lbf) for large fasteners such as lug nuts and cylinder head bolts, and inch-pounds (in·lbf) for smaller fasteners. European and modern specifications often use Newton-meters (N·m).

What is the difference between torque and force?

Force is a linear push or pull measured in Newtons or pound-force. Torque is the rotational effect of a force applied at a distance from a pivot; it is measured in N·m or ft·lbf. A larger lever arm amplifies the same force into greater torque.

Can I solve for force or lever arm instead of torque?

Yes. Select "Solve for Force" or "Solve for Lever Arm" from the dropdown, enter the other two known values, and the calculator will derive the missing quantity.

Torque Calculator

Name: Torque Calculator
Availability: InStock
Author: Nham Vu

Solve for torque, force, or lever arm length using τ = F × r × sin θ, with full unit support for N·m, ft·lbf, and in·lbf.

Input Parameters

Solve for

Force (F)

Lever Arm (r)

Angle θ between force and lever arm

degrees

Set to 90° for perpendicular force (maximum torque).

Results

Enter values and click Calculate

Common Torque Conversion Reference

N·m	ft·lbf	in·lbf	Common Use
1	0.738	8.851	Base unit (SI)
10	7.376	88.51	Small fasteners
100	73.76	885.1	Lug nuts (typical)
200	147.5	1770	Cylinder head bolts

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Summary

Solve for torque, force, or lever arm length using τ = F × r × sin θ, with full unit support for N·m, ft·lbf, and in·lbf.

How it works

Select what you want to solve for: Torque, Force, or Lever Arm.
Enter the two known values with their units.
Set the angle θ between the force vector and the lever arm (default 90°).
Click Calculate — the result appears instantly in N·m, ft·lbf, and in·lbf.
Use the Reset button to start a new calculation.

Use cases

Calculating the torque produced by a wrench when tightening a bolt.
Finding the force required to generate a target torque at a given radius.
Determining the lever arm length needed to achieve a desired rotational moment.
Converting torque values between SI (N·m) and imperial (ft·lbf, in·lbf) units.
Analyzing angled force application in mechanical linkages and levers.
Verifying motor, actuator, and drive torque specifications.
Teaching rotational mechanics and moment of force in physics courses.
Sizing robotic joint actuators based on required output torque.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu