This torque calculator solves τ = r × F × sinθ — the rotational twist produced by a force applied at a distance. Find torque, force or lever arm, accounting for the angle of application.
What Is Torque?
Torque is the rotational equivalent of force — the twist that makes things spin, loosen, tighten and turn. It depends on three things: how hard you push (F), where you push it (the lever arm r from the pivot), and the angle between them. That is why door handles sit far from hinges and why a longer wrench loosens stubborn bolts: torque rewards leverage. This calculator is part of our Physics Calculators collection; the straight-line force behind it is covered by our Force Calculator.
The Torque Formula
τ = r × F × sinθ
Worked example (verified): a 100 N push at the end of a 0.5 m wrench, applied perpendicular (θ = 90°, sin θ = 1): τ = 0.5 × 100 × 1 = 50 N·m (36.9 lb·ft). Push at 60° instead and the same effort yields only 43.3 N·m — the sin θ term quietly taxes every angled push, which is why mechanics instinctively push at right angles to their wrenches.
Torque in Real Life
- Car engines: rated in N·m or lb·ft — torque is the twisting force at the wheels that you actually feel as pull; horsepower is torque × rpm in disguise.
- Tightening specs: wheel lug nuts (~110–140 N·m), cylinder-head bolts and bike pedals all have torque specs because “tight enough” is a number, not a feeling — over-torque strips threads, under-torque loosens under vibration.
- See-saws and balance: equilibrium means torques cancel — a 30 kg child at 2 m balances a 60 kg adult at 1 m (both ≈ 588 N·m with gravity as F).
- Opening doors: pushing near the hinge needs enormous force for the same torque — push at the handle.
Torque Units
The SI unit is the newton-meter (N·m); US practice uses pound-feet (lb·ft): 1 N·m ≈ 0.738 lb·ft, 1 lb·ft ≈ 1.356 N·m. Despite sharing dimensions with energy, torque is not energy — a torque held statically does no work, which is why engineers keep N·m for torque and joules for energy conceptually separate.
Related Tools
- Force Calculator — the F in τ = rF sinθ
- Momentum Calculator — linear counterpart concepts
- Physics Calculators — the full collection
Frequently Asked Questions
How do I calculate torque?
τ = r × F × sinθ: lever-arm distance times force times the sine of the angle between them. Perpendicular force (90°) gives sinθ = 1, the maximum.
Why does angle matter?
Only the component of force perpendicular to the lever arm twists the pivot. Pushing along the wrench (θ = 0°) produces no torque at all — you are just compressing the bolt.
What is the difference between torque and force?
Force pushes or pulls in a line; torque twists around an axis. Same newton shows up in both, but torque multiplies force by the lever distance.
How do I convert N·m to lb·ft?
Multiply by 0.738 (or divide lb·ft by 0.738 to go back). 100 N·m ≈ 73.8 lb·ft.
Why do wrenches come in different lengths?
Because torque = force × distance: a longer wrench gives more torque for the same hand force. It is also why “cheater bars” work — and why they sometimes snap bolts.
Is this torque calculator free?
Yes — free, instant, no sign-up.