acalculator

What is the torque from this force?

Type the force, the lever arm and the angle between them. The torque calculator shows the torque in N·m, lb·ft and lb·in, or finds the force or lever arm for the torque you need.

Your numbers

Units
Find
Torque unit
Answer
50

The torque is 50 lb·ft.

Answer unit
lb·ft
Answer is
torque
Torque (N·m)
67.790897
Torque (lb·ft)
50
Torque (lb·in)
600
Force (N)
222.41108
Force (lbf)
50
Lever arm (m)
0.3048
Lever arm (ft)
1
Perpendicular lever arm r⊥ (m)
0.3048

Answer: 50. The torque is 50 lb·ft.

How to calculate

Computes torque from a force, the lever arm and the angle between them (τ = rF sin θ), or the force or lever arm for a torque, in N·m, lb·ft and lb·in.

Example with the default inputs (Find Torque, Force (F) 50 lbf, Lever arm (r) 12 in, Torque unit lb·ft, Angle (θ, degrees) 90): The torque is 50 lb·ft.

Method: τ = r × F × sin θ; F = τ ÷ (r sin θ); r = τ ÷ (F sin θ).

  • θ is the angle between the lever arm (from the axis to where the force acts) and the force, from 0° to 180°.
  • The answer is the size of the torque; its direction (clockwise or counterclockwise) is not shown.
  • 1 lb·ft = 1 lbf × 1 ft = 0.3048 × 4.4482216152605 N·m (NIST SP 811).

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Find Torque, Force (F) 8.992 lbf, Lever arm (r) 157.5 in, Angle (θ, degrees) 90, Torque unit N·m gives Answer 160, Torque (N·m) 160.Source: OpenStax, University Physics Volume 1, §10.6 Torque (|τ| = r⊥F = rF sin θ). https://openstax.org/books/university-physics-volume-1/pages/10-6-torque, Example 10.14 (40 N at 4 m and 90° gives 160 N·m)
  2. Find Torque, Force (F) 4.496 lbf, Lever arm (r) 19.69 in, Angle (θ, degrees) 150, Torque unit N·m gives Answer 5, Perpendicular lever arm r⊥ (m) 0.25.Source: OpenStax, University Physics Volume 1, §10.6 Torque (|τ| = r⊥F = rF sin θ). https://openstax.org/books/university-physics-volume-1/pages/10-6-torque, Example 10.15 (20 N at r = 0.5 m and 150° gives 5.0 N·m)
  3. Find Torque, Force (F) 10 lbf, Lever arm (r) 24 in, Angle (θ, degrees) 90, Torque unit lb·ft gives Answer 20, Torque (lb·ft) 20, Torque (lb·in) 240, Torque (N·m) 27.116359.Source: NIST SP 811 (2008), Appendix B.8 (1 lbf = 4.4482216152605 N; 1 ft = 0.3048 m). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8
  4. Find Force, Torque (τ) 80, Lever arm (r) 18 in, Angle (θ, degrees) 90, Torque unit lb·ft gives Answer 53.333333, Force (lbf) 53.333333.Source: OpenStax, University Physics Volume 1, §10.6 Torque (|τ| = r⊥F = rF sin θ). https://openstax.org/books/university-physics-volume-1/pages/10-6-torque
  5. Find Lever arm, Torque (τ) 120, Force (F) 89.92 lbf, Angle (θ, degrees) 30, Torque unit N·m gives Answer 0.6, Lever arm (m) 0.6.Source: OpenStax, University Physics Volume 1, §10.6 Torque (|τ| = r⊥F = rF sin θ). https://openstax.org/books/university-physics-volume-1/pages/10-6-torque

How it works

  • Torque: τ = r × F × sin θ, where r is the lever arm, F the force and θ the angle between them (0° to 180°). τ = r⊥ × F with r⊥ = r sin θ, the perpendicular lever arm.
  • Force: F = τ ÷ (r sin θ).
  • Lever arm: r = τ ÷ (F sin θ).
  • When you find the force or the lever arm, θ = 0° or 180° (sin θ = 0) has no answer.
  • Units: 1 lb·ft = 1 lbf × 1 ft = 4.4482216152605 × 0.3048 N·m; 1 lb·in = 1 lbf × 1 in = 4.4482216152605 × 0.0254 N·m. The answer is in the torque unit you pick. A force you find is in N when the torque unit is N·m and in lbf otherwise; a lever arm you find is in m (N·m), ft (lb·ft) or in (lb·in). Every value is also listed in N·m, lb·ft, lb·in, N, lbf, m and ft.

Exact arithmetic. Each force and length is read as the exact decimal you typed, in the unit you typed it in (2 ft is exactly 0.6096 m). When you type a size, the page stores it in newtons or metres and reads it back as the decimal with the fewest significant digits, in one of the box's units (force: N, lbf, kN, kgf; length: m, cm, mm, ft, in), that gives the same stored number; on a tie the first unit in that list wins. When none does, the stored number's own shortest decimal is used. sin θ is exact at 0° and 180° (0), 30° and 150° (1/2) and 90° (1); at other angles it is the double-precision sine of θ × π ÷ 180. With an exact sine, every step is an exact fraction, so 10 lbf on a 2 ft wrench is exactly 20 lb·ft.

Output format. Every value shows to 8 significant figures, rounded half up. An answer of 10³⁰⁰ or more has no answer.

Assumptions

  • The force acts in one plane with the lever arm; the page gives the size of the torque, not its direction.
  • Force and lever arm are more than 0 and at most 10⁹ in base units (N, m); the torque you type is more than 0 and at most 10¹²; the angle is from 0° to 180°.

Worked examples by hand

40 N at 4 m, 90° (OpenStax Example 10.14). τ = 4 × 40 × 1 = 160 N·m.

20 N at 0.5 m, 150° (OpenStax Example 10.15). sin 150° = 0.5, so r⊥ = 0.25 m and τ = 0.5 × 20 × 0.5 = 5 N·m.

10 lbf on a 2 ft wrench, 90°. τ = 2 × 10 = 20 lb·ft = 20 × 12 = 240 lb·in = 20 × 1.3558179483314 = 27.116 N·m.

The push for 80 lb·ft on an 18 in bar, 90°. r = 1.5 ft; F = 80 ÷ 1.5 = 53.333 lbf.

The lever arm for 120 N·m with 400 N at 30°. r = 120 ÷ (400 × 0.5) = 0.6 m.

Other questions people ask

How do I calculate torque?

Multiply the lever arm by the force and by the sine of the angle between them: τ = rF sin θ. Pushing 40 N square to a 4 m arm gives 4 × 40 × sin 90° = 160 N·m.

What is the lever arm?

The lever arm r is the distance from the axis of turning (the bolt or hinge) to the point where the force pushes. The part of it square to the force, r sin θ, is the perpendicular lever arm r⊥, and τ = r⊥F.

Why does the angle matter?

Only the part of the force square to the arm turns it. At 90° all of it counts (sin 90° = 1); at 30° half of it counts (sin 30° = 0.5); at 0° or 180° the force points along the arm and makes no torque.

How much force do I need on a wrench?

Divide the torque by the lever arm: F = τ ÷ (r sin θ). For 80 lb·ft on an 18 in (1.5 ft) bar pushed square to it, you need 80 ÷ 1.5 = 53.3 lbf.

How do I convert lb·ft to N·m?

One pound-foot is 1 lbf × 1 ft = 4.4482216152605 N × 0.3048 m = 1.3558 N·m. So 20 lb·ft is 27.12 N·m, and 20 lb·ft is 240 lb·in.

Is torque the same as work?

Both can be written in N·m, but they are different. Work is a force times a distance moved along it; torque is a force times a lever arm square to it, and it turns things.