What is joint torque?

Joint torque (also called joint moment) is the turning effect of a force around a joint axis. For a force applied a distance r from the axis, it is τ = F × r × sin(θ) and is measured in Newton-meters (N·m).

What is a moment arm?

The true moment arm d is the perpendicular distance from the joint axis to the force line of action. This calculator asks for the radius r to the force application point and computes d = r × sin(θ). If you already know the perpendicular moment arm, torque is simply τ = F × d.

Why does the angle matter?

Torque is maximized when force is applied at 90 degrees (perpendicular) to the segment, because sin(90°) = 1. At 0° or 180° the force acts along the segment and produces no torque.

Force is entered in Newtons (N), radius r in meters (m), and the resulting torque is in Newton-meters (N·m). You can convert pounds-force to Newtons by multiplying by 4.448, and centimeters to meters by dividing by 100.

Can I use pounds and inches instead?

This calculator uses SI units. Convert: 1 lb = 4.448 N, 1 inch = 0.0254 m, 1 cm = 0.01 m. Multiply them and the torque result will be in N·m.

Is this suitable for clinical use?

This tool is for educational and estimation purposes. Clinical decisions should always involve a licensed healthcare professional using validated measurement instruments.

Biomechanics Joint Torque Calculator

Enter force, radius from the joint axis, and force angle to calculate signed joint torque for biomechanics or physical therapy analysis.

Inputs

Enter the three values that define the torque scenario.

Applied Force (N)

1 lb ≈ 4.448 N

Radius to Force Point, r (m)

Straight-line distance from the joint axis; 1 cm = 0.01 m

Force Angle (°)

Angle between force vector and body segment (0–360°)

Adjust Angle

Joint Torque

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Newton-meters (N·m)

Formula

τ = F × r × sin(θ)

τ = Torque (N·m)

F = Applied Force (N)

r = Distance from joint axis to force point (m)

θ = Angle between force and segment (°)

Torque vs. Angle (current F & r)

Torque peaks at 90° where sin(θ) = 1

Summary

Joint torque is the turning effect of a force about a joint axis. This calculator uses τ = F × r × sin(θ), where r is the straight-line distance from the joint axis to the force application point. The true perpendicular moment arm is d = r × sin(θ), so torque can also be written τ = F × d. The signed result in Newton-meters (N·m) indicates rotational direction under the stated angle convention.

How it works

Enter the applied force in Newtons (N).
Enter r in meters (m) — the straight-line distance from the joint axis to the point where the force is applied.
Enter the angle (degrees) between the force vector and the segment.
Click Calculate to get the torque in Newton-meters (N·m).
Review the formula breakdown and adjust inputs for different scenarios.

Use cases

Analyze shoulder, elbow, or knee joint loading during rehabilitation exercises.
Compare torque demands across different exercise positions or joint angles.
Estimate muscle torque requirements for a given external load.
Teach biomechanics concepts in physical therapy or kinesiology courses.
Assess joint stress in occupational ergonomics assessments.
Optimize sporting technique by minimizing harmful joint torques.
Plan progressive loading in post-surgical rehabilitation protocols.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu