What is the torque formula?

Torque (τ) equals force (F) multiplied by the lever arm length (r) and the sine of the angle (θ) between the force vector and the arm: τ = F × r × sin θ. When θ = 90° (force perpendicular to the arm) sin θ = 1, so torque is simply τ = F × r at its maximum.

What does the angle θ represent?

θ is the angle between the direction of the applied force and the lever arm (the line from pivot to point of application). At 90° the force is perpendicular and produces maximum torque. At 0° or 180° the force is parallel and produces zero torque.

What happens at 0° or 180°?

sin(0°) = sin(180°) = 0, so τ = 0. A force directed straight along the lever arm cannot rotate it around the pivot — it only pushes the pivot itself. Maximum torque occurs 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. This calculator performs all unit conversions automatically.

What is the difference between torque and force?

Force is a linear push or pull, measured in Newtons. Torque is the rotational effect of a force applied at a distance from a pivot, measured in N·m. A longer lever arm amplifies the same force into greater torque.

Does gravity affect torque direction?

Yes — torque is a vector. Its direction (clockwise or counterclockwise) depends on the direction of the force relative to the arm. This calculator computes the magnitude only; direction depends on your physical setup.

Torque From Force Calculator

Enter force, lever arm length, and the angle between them to instantly compute torque in N·m, ft·lbf, and in·lbf.

Input Values

Force (F)

Lever Arm Length (r)

Angle θ between Force and Lever Arm 90°

deg

90° produces maximum torque; 0° or 180° produces zero torque.

Results

Enter values and click Calculate

Angle Diagram

Blue = lever arm | Red arrow = force | Arc = angle θ

sin θ Quick Reference

θ (°)	sin θ	Torque efficiency
0°	0.000	None (parallel force)
30°	0.500	50%
45°	0.707	70.7%
60°	0.866	86.6%
90°	1.000	100% (perpendicular)
120°	0.866	86.6%
180°	0.000	None (anti-parallel)

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Summary

Enter force, lever arm length, and the angle between them to instantly compute torque in N·m, ft·lbf, and in·lbf.

How it works

Enter the force magnitude and choose its unit (N, lbf, or kgf).
Enter the lever arm length and choose its unit (m, cm, ft, or in).
Set the angle θ between the force vector and the lever arm (0–180°). Use the slider for quick adjustments.
Click Calculate to compute τ = F × r × sin θ.
Read the torque result in N·m, ft·lbf, and in·lbf simultaneously.
Use Reset to clear all inputs and start a new calculation.

Use cases

Determining the torque a wrench exerts on a fastener at a given push angle.
Calculating the moment produced by a structural load on a beam or bracket.
Analyzing angled cable forces on a rotating joint in robotics or machinery.
Finding the rotational effect of a muscle force in biomechanics problems.
Verifying actuator or motor output torque against a design requirement.
Teaching the relationship between force, lever arm, and angle in physics courses.
Quick unit conversion between N·m, ft·lbf, and in·lbf for engineering specs.
Checking the torque produced when a force is not applied perpendicularly.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu