Mechanics
Torque
Torque causes angular acceleration. τ = r × F.
Variables
τN·m
Torque
Rotational force
In SI units: kg·m²/s²
rm
Lever arm
Distance from pivot
Allowed values: 0 or more
FN
Force
Applied force
In SI units: kg·m/s²
θ°
Angle
Angle between r and F
In SI units: rad
Derivation
Cross product magnitude: |τ| = rF sin θ.
Your notes
0/5000
Check value
Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.
- r = 2 m (Lever arm)
- F = 3 N (Force)
- θ = 4 ° (Angle)
Result: τ = 0.41853884 N·m
Other mechanics formulas with the same quantities
Where this formula is listed
- Mechanics formulas, under Rotational Motion, alongside Angular Velocity, Angular Acceleration, Linear-Angular Velocity Relation, Centripetal Acceleration and Centripetal Force.
- In the mechanics list it comes after Centripetal Force and before Moment of Inertia (Point Mass).
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Torque formula?
Torque is written τ = rF sin θ. Torque causes angular acceleration. τ = r × F. It belongs to Mechanics, under Rotational Motion.
What are the units in τ = rF sin θ?
In SI units, τ is torque, measured in kg·m²/s²; r is lever arm, measured in m; F is force, measured in kg·m/s²; θ is angle, measured in rad.
How is the Torque formula derived?
Cross product magnitude: |τ| = rF sin θ. The result is τ = rF sin θ.