torque formulas and interpretation
Torque measures the turning effect of a force about an axis.
The perpendicular component of force determines torque, so the force angle is essential.
How to use the torque calculator
- Choose a model: Select the physical relationship that matches the known values.
- Choose the unknown: Select the quantity you need to calculate.
- Enter values and units: Provide every requested measurement using consistent units.
- Calculate: Check the formula, converted result, sign, and units.
Formula and variables
Torque equals radius times force times the sine of their included angle.
τ = rF sin(θ)- τ — Torque
- Moment of force (N·m)
- r — Lever arm
- Distance from axis to force point (m)
- F — Force
- Applied force magnitude (N)
- θ — Angle
- Angle between radius and force (degrees)
Wrench example
A 100 N force acts perpendicular to a 0.25 m wrench.
- Force
- 100 N
- Radius
- 0.25 m
- Angle
- 90°
- τ = 0.25 × 100 × sin(90°)
- τ = 25 N·m
Result: Torque is 25 N·m.
The perpendicular force produces a 25 N·m turning effect.
Understanding your results
Interpreting the result
Torque is greatest at 90 degrees and zero when the force points along the lever arm.
A sign indicates direction only when a consistent rotational sign convention is used.
Assumptions
- Rotation is evaluated about a specified axis.
- Inputs are converted through coherent SI units.
- The selected formula adequately represents the physical system.
Limitations
- The calculator does not simulate time-varying inputs.
- Vector directions and multiple axes must be resolved separately.
- Losses such as friction are not added unless represented in the entered net value.
Common mistakes
- Mixing RPM with radians per second.
- Using diameter instead of radius.
- Entering a zero divisor.
- Ignoring the direction represented by a negative value.
Practical use cases
Physics and education
Check rotational kinematics and dynamics exercises.
Machines and mechanisms
Estimate quantities for wheels, shafts, rotors, and rotating equipment.
Frequently asked questions
Why are radians used in rotational formulas?
Radians make angular and linear relationships dimensionally coherent without an extra conversion factor.
Can the result be negative?
Yes. A negative value means the quantity points opposite the direction chosen as positive.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.