Torque with a Lever Arm (τ = rF sin θ)
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
Learning zone
Only the component of force perpendicular to the lever actually turns it — hence the sin θ. Push straight along a wrench handle (θ = 0) and nothing rotates; push at right angles (θ = 90°) and every newton counts. That is why a longer wrench loosens a stuck bolt with the same effort: doubling r doubles τ. A 200 N push at the end of a 30 cm wrench, applied perpendicular, delivers 60 N·m.
Torque with a Lever Arm (τ = rF sin θ)
Where
- = Torque
- = Lever arm length
- = Force
- = Angle
Missing one of these? Work it out first, then come back
- Torque — Torque, Rotational Power (P = τω)
- Lever arm length — Torque, Mechanical Advantage of a Lever
- Force — Newton's Second Law, Work (W = Fd cos θ)
- Angle — Angular Velocity (ω = θ/t), Projectile Range on Level Ground