Torque Calculator
Torque depends on force, the distance from the pivot, and the angle at which the force is applied — pushing straight down on a wrench close to the nut does far less than pushing perpendicular to it further out.
Inputs
Result
60 N·m
How it works
τ = F × r × sin θ
How the torque calculator works
τ = F × r × sin θ, where θ is the angle between the applied force and the lever arm.
Torque is maximised when the force is applied perpendicular to the lever (θ = 90°, sin θ = 1) and drops to zero when the force is applied directly along the lever's length (θ = 0°).
Worked example: 150 N applied at 0.4 m, 90°
- τ = 150 × 0.4 × sin(90°) = 150 × 0.4 × 1 = 60 N·m.
- The same force and distance at a 30° angle instead gives 150 × 0.4 × sin(30°) = 150 × 0.4 × 0.5 = 30 N·m — exactly half, from the angle alone.
Common mistakes to avoid
Ignoring the angle and assuming τ = F × r always
That formula only holds when the force is applied exactly perpendicular to the lever. At any other angle, the effective torque is reduced by the sine of that angle, sometimes substantially.
Confusing torque (N·m) with energy or work, which share the same unit
Torque and work/energy are dimensionally the same (N·m or joules) but conceptually different — torque is a rotational force, not energy transferred, even though the units look identical.
Frequently asked questions
Why does pushing at 90° to the lever give the most torque?
sin(90°) = 1, the maximum value the sine function reaches — any other angle reduces the effective perpendicular component of the applied force.
What happens to torque if the force is applied exactly along the lever's length?
It produces zero torque — sin(0°) = 0, meaning no rotational effect at all, since the force does nothing but pull or push along the arm rather than rotate it.
How does torque relate to power in a rotating system?
Power = torque × angular velocity — a motor's torque combined with how fast it's spinning determines its power output.
Is this the same calculation used for wrench and bolt tightening specs?
Yes, exactly — bolt torque specifications assume a perpendicular force applied at a specified lever-arm distance, which is precisely what this formula models.
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