Torque Calculator
Torque from a force and a lever arm at any angle, τ = rF sin θ, or the force or arm length needed for a torque, in newton metres or pound-feet.
Result
Torque: 75 lbf·ft
One force at one point. This is not a tightening specification: use the maker’s torque figure for a fastener.
- Force
- 50 lbf (222.4 N)
- Lever arm
- 1.5 ft
- Force across the arm, F sin θ
- 50 lbf (222.4 N)
- Perpendicular lever arm, r sin θ
- 1.5 ft
https://calcgallery.com/physics/torque-calculator/
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How to use the Torque Calculator
- Choose whether to find the torque, the force needed or the lever arm needed.
- Enter the lever arm, measured from the pivot to where the force acts, and the force or the torque.
- Enter the angle between the arm and the force, 90° if you push straight across it, and read the torque in pound-feet or newton metres.
The formulas
τ = r × F × sin θF = τ ÷ (r × sin θ)r = τ ÷ (F × sin θ)r is the distance from the pivot to where the force acts, F the force and θ the angle between the arm and the force. F sin θ is the part of the force that turns, and r sin θ the perpendicular distance from the pivot to the line of the force; either product gives the same torque.
Limits
One force at one point, in magnitude only: the page does not add torques from several forces or keep track of which way they turn. A force along the arm, at 0° or 180°, gives no torque, so no force or arm can be found from a torque at that angle.
With your numbers
- τ = r × F × sin θ = 1.5 ft × 50 lbf × sin 90 ° = 75 lbf·ft
Quick reference
One force at one point. This is not a tightening specification: use the maker’s torque figure for a fastener.
| Example | Result |
|---|---|
| 50 lbf on a 1.5 ft wrench | Torque: 75 lbf·ft |
| 200 N on a 0.3 m wrench | Torque: 60 N·m |
| 30 N at 53°, 5 m from the pivot | Torque: 119.8 N·m |
| Force for 100 lbf·ft on a 1.5 ft arm | Force: 66.67 lbf |
| Force for 50 N·m on a 0.3 m arm | Force: 166.7 N |
| Arm for 50 N·m with 200 N at 60° | Lever arm: 0.2887 m |
Common questions about the Torque Calculator
- How do I calculate torque?
- Multiply the force by the lever arm and by the sine of the angle between them: τ = rF sin θ. Pushing straight across a 1.5 ft wrench with 50 lbf gives 75 lbf·ft, about 101.7 N·m. At 90° the sine is 1, so torque is simply force times distance.
- Why does the angle matter?
- Only the part of the force across the arm turns it. Pull along the arm and nothing rotates, however hard you pull. OpenStax University Physics example 10.14 has 30 N acting 5 m from the pivot at 53°, giving (5)(30) sin 53° ≈ 120 N·m instead of the 150 N·m a square push would give.
- How much force do I need for a given torque?
- Divide the torque by the arm length, and by sin θ if the push is not square: F = τ ÷ (r sin θ). 100 lbf·ft on a 1.5 ft arm needs about 66.7 lbf; a longer handle needs proportionally less. The page also finds the arm length for a force you can apply.
- What is the difference between N·m and lbf·ft?
- Both are a force times a distance. One pound-force foot is about 1.356 N·m, and one pound-force inch a twelfth of that. Torque has the same units as energy but is a different quantity, which is why it is written N·m rather than joules.
- Does this give bolt tightening torques?
- No. It turns a force and an arm into a torque and back. The torque a particular fastener should be tightened to comes from its maker or the equipment’s service data, and depends on the thread, the material and the lubrication.