Torque calculator
Torque magnitude from force, application-point distance and angle.
Fill in the fields and the result will appear here automatically.
Finds the magnitude of one force’s torque about a chosen reference point: τ = Fr sin θ. r is the distance to the force’s application point; the actual moment arm d is the perpendicular distance to its line of action. They coincide only at 90°. These inputs do not determine clockwise or counterclockwise direction; adding torques requires their individual signs.
How it works
Formula and logic
The magnitude of r × F is Fr sin θ. The effective moment arm is d = r sin θ, so τ = Fd. At fixed F and r, torque is greatest at 90°. Exactly 0° and 180° give zero arm and torque; nearby angles retain their small non-zero values.
Example
50 N, r = 0.3 m and 90° give d = 0.3 m and τ = 15 N·m. At 30°, d = 0.15 m and τ = 7.5 N·m. At 180°, torque is 0, not −15 N·m: this page displays magnitude.
Fields and units
- Force — N
- Distance to force application point — m
- Angle between r and force — °
How to use
- — Enter a non-negative force magnitude in N.
- — Enter r in metres, measured to the force’s application point, rather than an already known perpendicular moment arm.
- — Use 0–180° between the r vector and the force.
- — Read torque in N·m and effective arm d = r sin θ in m; if d is already known, enter r = d and 90°.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: torque magnitude and perpendicular moment arm
- Limitation
- Magnitude of one force’s torque about a chosen point; direction, net torque and mechanism strength are not calculated.
FAQ
How is this different from the torque converter?
A converter changes the units of known torque. This tool uses force and geometry to calculate it; N·m denotes torque and does not by itself establish work done in J.
Why is torque zero at both 0° and 180°?
The force’s line of action passes through the reference point, giving zero perpendicular moment arm. Exact endpoint angles do not retain a numerical sine residue.
What is the moment arm, and how does it differ from r?
d is the shortest distance to the force’s line of action; r reaches its application point. d = r sin θ, so at 30° it is half of r.
At what angle is torque magnitude greatest?
At 90° for fixed F and r. Increasing distance or force increases torque; this form does not assess tool strength.
Can this result determine the direction of rotation?
No. Magnitude does not specify the spatial orientation of r × F. Assign consistent signs on the chosen axis before summing torques instead of adding all magnitudes.