Torque Calculator
A 100 newton force on a 0.5 meter lever arm pushed at a right angle produces 50 newton-meters of torque. This torque calculator turns three simple inputs, the applied force in newtons, the lever arm length in meters, and the angle between them, into the twisting force that rotates an object around a pivot. It uses the standard physics relationship tau equals force times lever arm times the sine of the angle, so a push straight across the arm gives the most torque and a push aimed along the arm gives none. Enter your numbers and the tool returns the torque in newton-meters as the primary answer, converts that figure to pound-feet for anyone working in imperial units, and shows both the angle you used and the effective lever arm, which is the part of the arm length that actually contributes to rotation once the angle is taken into account. Whether you are checking a wrench setting, a physics homework problem, or a simple machine design, the calculator keeps the arithmetic exact and rounds the display to four decimal places.
Quick answer
Torque measures how much a force tends to rotate an object around a pivot point or axis.
What this tells you
- •Torque measures how much a force tends to rotate an object around a pivot point or axis.
- •The formula is tau = F times r times sin(theta), where F is force, r is the lever arm, and theta is the angle between them.
- •A force applied at 90 degrees to the lever arm gives the maximum torque because sin(90) equals 1.
- •A force aimed straight along the lever arm produces zero torque because sin(0) equals 0.
- •The result is measured in newton-meters, which is one newton of force applied one meter from the pivot at a right angle.
- •Multiply newton-meters by 0.737562 to convert the answer into pound-feet, the common imperial torque unit.
How to Use
- 11. Enter the force in newtons in the Force field. This is how hard you push or pull on the lever, wrench, or arm.
- 22. Enter the lever arm length in meters in the Lever Arm field. This is the straight-line distance from the pivot to the point where the force is applied.
- 33. Enter the angle in degrees between the force and the lever arm. Leave it at 90 for a force applied straight across the arm, which is the most common case.
- 44. Read the primary result as the torque in newton-meters and check the pound-feet figure below if you need imperial units.
- 55. Review the effective lever arm value to see how much of your arm length actually contributes to rotation once the angle reduces it.
How It Works
Formula
tau = F * r * sin(theta)Torque, written with the Greek letter tau, equals the applied force F multiplied by the lever arm length r multiplied by the sine of the angle theta between the force and the arm. The angle is entered in degrees and converted to radians before the sine is taken. When theta is 90 degrees the sine is 1, so all of the force turns into torque and the effective lever arm equals the full arm length. As the angle drops toward 0, less of the force acts to rotate the object, and at 0 degrees the torque is zero because the force points straight along the arm. Force and lever arm must both be zero or greater. A lever arm of zero correctly gives zero torque, since a force applied right at the pivot cannot make anything spin. The tool rounds displayed values to four decimal places while keeping full precision internally.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
A wrench turned at a right angle
A 100 newton force on a 0.5 meter wrench pushed straight across gives 100 times 0.5 times sin(90). Since sin(90) is 1, the torque is 50 newton-meters, which converts to roughly 36.88 pound-feet.
Force applied at a slant
At 30 degrees the sine is 0.5, so only half the force acts to rotate. 200 times 0.4 times 0.5 gives 40 newton-meters, and the effective lever arm shrinks from 0.4 meters to 0.2 meters.
A push straight along the arm
When the angle is 0 degrees the force points directly along the lever arm, so sin(0) is 0 and the torque is zero. No matter how hard you push, a force aimed at the pivot cannot create rotation.
A large industrial bolt
A 500 newton force on a 1.2 meter breaker bar at a right angle gives 500 times 1.2 times 1, which is 600 newton-meters. That converts to about 442.54 pound-feet, a value typical of heavy machinery fasteners.
Torque Quick Reference
Common force, lever arm, and angle combinations and the torque each produces.
| Force (N) | Lever Arm (m) | Angle | Torque (N*m) | Torque (lb-ft) |
|---|---|---|---|---|
| 50 | 0.3 | 90 | 15.00 | 11.06 |
| 100 | 0.5 | 90 | 50.00 | 36.88 |
| 200 | 0.4 | 30 | 40.00 | 29.50 |
| 300 | 1.0 | 45 | 212.13 | 156.46 |
| 500 | 1.2 | 90 | 600.00 | 442.54 |
| 100 | 1.0 | 0 | 0.00 | 0.00 |
Pound-feet values use the conversion factor of 0.737562 newton-meters per pound-foot and are rounded for display.
Why the angle changes torque so much
Torque is not just about how hard you push and how long the lever is. The direction of the push matters just as much. Only the part of the force that acts across the lever arm, at a right angle to it, produces rotation. Any part of the force that points along the arm toward or away from the pivot does nothing to spin the object, it only tries to stretch or compress the arm.
This is why the sine of the angle appears in the formula. The sine function measures exactly how much of the force acts perpendicular to the arm. At 90 degrees the entire force is perpendicular and sine equals 1, giving full torque. At 45 degrees sine is about 0.707, so you lose almost 30 percent of your turning power compared to a straight push. At 0 degrees none of the force is perpendicular and the torque vanishes.
In everyday terms, this is why you instinctively pull a wrench at a right angle rather than at an awkward slant, and why a door is hardest to open when you push near the hinge or push at a shallow angle. The effective lever arm the calculator reports, r times sin(theta), captures this in a single number, telling you how long a right-angle lever would need to be to produce the same torque as your actual angled push.
Common mistakes
- Measuring the lever arm from the wrong point. The arm length is the distance from the pivot or axis of rotation to where the force is applied, not the total length of the tool.
- Forgetting to account for the angle. If the force is not applied at 90 degrees, using the full lever arm overstates the real torque, sometimes by a wide margin.
- Mixing up units. This tool expects force in newtons and lever arm in meters. Entering centimeters or pounds without converting first gives a wrong answer.
- Confusing torque with force. Torque depends on both the force and the distance from the pivot, so a small force on a long arm can beat a large force on a short arm.
- Assuming a lever arm of zero is an error. A force applied right at the pivot legitimately produces zero torque, which the calculator reports correctly rather than rejecting.
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