Torque Calculator (τ = r F sin θ, N·m and lb·ft)
Torque from force, lever arm and angle in N·m, lb·ft and kgf·m, with the effective lever arm and the working.
Inputs
- Working
- τ = r × F × sin θ = 0.3 m × 50 N × sin(90°) = 0.3 × 50 × 1 = 15 N·m
- In lb·ft and kgf·m
- 11.0634 lb·ft = 1.5296 kgf·m
- Effective lever arm r sin θ
- 0.3 m
- Same torque at 90°
- 15 N·m — the most this force and arm can give
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What each Torque input means
- Force
- The push or pull in newtons. A kilogram's weight is about 9.81 N; a pound-force is 4.448 N.
- Lever arm
- The distance in metres from the pivot (the bolt, the hinge) to where the force is applied — where your hand is, not the end of the tool.
- Angle
- The angle between the force and the lever, in degrees. 90° is a push at right angles, which gives the most torque.
Torque formula
τ = r × F × sin θ · at 90° (force at right angles to the lever) τ = r × F · 1 N·m = 0.7376 lb·ft = 0.10197 kgf·m
Torque is the turning effect of a force: the force times the perpendicular distance from the pivot to its line of action. Pushing at right angles to a spanner uses the whole arm length, and the torque is simply force × length; pushing at an angle only counts the perpendicular part, r sin θ, and pushing straight along the spanner turns nothing at all. The page multiplies force, lever arm and sin θ, shows the effective lever arm, converts to the pound-feet on a torque wrench and the kgf·m in older manuals, and states what the same force and arm would give at 90° — the most they can. Torque is what tightens bolts, turns engines and balances see-saws; equilibrium, the section's subject, is when the torques about any pivot cancel.
Torque worked example
50 N applied at right angles 0.3 m from the pivot: 0.3 × 50 × sin 90° = 15 N·m, which is 11.1 lb·ft or 1.53 kgf·m. Push the same 50 N at 30° to the spanner and the effective arm falls to 0.3 × 0.5 = 0.15 m, halving the torque to 7.5 N·m. To tighten a wheel nut to 110 N·m with a 0.5 m bar takes 220 N of push at right angles.
More Torque examples
200 N (about the weight of 20 kg) at right angles on a 0.45 m breaker bar: 0.45 × 200 = 90 N·m, or 66.4 lb·ft — a typical wheel-nut setting.
Where the Torque calculator can give the wrong answer
- θ is the angle between the force and the lever arm, so 90° is the full-torque case and 0° or 180° is none. Some texts measure from the perpendicular instead; if your angle is small for a near-perpendicular push, use 90° minus it.
- r is measured from the pivot to the point where the force acts, not to the end of the lever. Holding a spanner halfway along halves the torque.
- Torque wrenches read lb·ft or N·m; lb·in is 12 times smaller, and a conversion mix-up over-tightens by a factor of 12.
- Torque and energy share the unit newton-metre but are different quantities; a torque of 15 N·m is not 15 J of energy — the joule is reserved for energy to keep them apart.
- The page gives the magnitude. Direction (clockwise or anticlockwise, the sign in equilibrium sums) is yours to assign.
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Torque reference table
| N·m | lb·ft | lb·in |
|---|---|---|
| 1 | 0.74 | 8.9 |
| 5 | 3.69 | 44.3 |
| 10 | 7.38 | 88.5 |
| 25 | 18.44 | 221.3 |
| 50 | 36.88 | 442.5 |
| 100 | 73.76 | 885.1 |
| 200 | 147.51 | 1,770.1 |
Torque FAQ
- Multiply the force by the perpendicular distance from the pivot to where it acts — force × lever arm × sin of the angle between them. 100 N at right angles on a 0.25 m spanner is 25 N·m. The page shows the three-way multiplication.
- Divide the torque by the lever arm: F = τ ÷ (r sin θ). 90 N·m on a 0.45 m wrench, pushing at right angles, needs 200 N — about 20 kg of push. A longer bar means less force.
- Multiply by 0.7376: 100 N·m is 73.8 lb·ft. For lb·in, multiply N·m by 8.851. Going the other way, lb·ft × 1.3558 = N·m. The page prints lb·ft and kgf·m under every result.
- Force pushes or pulls in a straight line (newtons); torque turns things about a pivot (newton-metres) and depends on where and at what angle the force is applied as much as on how big it is. The same 50 N is a large torque on a long wrench and a small one on a short screwdriver.
- Torque is force × lever arm, so doubling the arm halves the force needed for the same torque: 90 N·m needs 300 N on a 0.3 m wrench but only 150 N on a 0.6 m bar.