Torque Calculator (τ = Fr sin θ)
Torque Calculator (τ = Fr sin θ)
Torque measures a force's tendency to rotate an object around an axis, depending on the force, the distance from the axis (the lever arm), and the angle at which the force is applied. Choose which quantity you want to solve for, enter the other two known values, and this calculator computes the missing one.
- The core formula is τ = F × r × sin(θ), so a 50 N force applied perpendicular (θ = 90°) at a 0.3 m radius gives τ = 50 × 0.3 × 1 = 15 N·m.
- Torque is maximized when the force is perpendicular to the lever arm (θ = 90°) - this is why wrenches and door handles are most effective when pushed straight-on rather than at an angle.
- A longer lever arm needs less force for the same torque - this is the entire principle behind using a longer wrench for a stubborn bolt.
How do I calculate torque?
Multiply the force by the radius (distance from the pivot) and by the sine of the angle between them: τ = F × r × sin(θ).
What is the torque from a 50 N force applied perpendicular at a 0.3 m radius?
τ = 50 × 0.3 × sin(90°) = 15 N·m.
Torque Calculator (τ = Fr sin θ)
Torque measures a force's tendency to rotate an object around an axis, depending on the force, the distance from the axis (the lever arm), and the angle at which the force is applied. Choose which quantity you want to solve for, enter the other two known values, and this calculator computes the missing one.
- The core formula is τ = F × r × sin(θ), so a 50 N force applied perpendicular (θ = 90°) at a 0.3 m radius gives τ = 50 × 0.3 × 1 = 15 N·m.
- Torque is maximized when the force is perpendicular to the lever arm (θ = 90°) - this is why wrenches and door handles are most effective when pushed straight-on rather than at an angle.
- A longer lever arm needs less force for the same torque - this is the entire principle behind using a longer wrench for a stubborn bolt.
How do I calculate torque?
Multiply the force by the radius (distance from the pivot) and by the sine of the angle between them: τ = F × r × sin(θ).
What is the torque from a 50 N force applied perpendicular at a 0.3 m radius?
τ = 50 × 0.3 × sin(90°) = 15 N·m.