Torque Calculator
Torque is the twisting effect a force produces about a pivot, and it governs everything from tightening a bolt to spinning an engine. This calculator applies the standard definition: torque equals force times the lever-arm length times the sine of the angle between them. Enter the applied force in newtons, the lever-arm length in metres, and the angle in degrees, and it returns the torque in newton-metres and the equivalent in pound-feet. Because the formula is a physical definition, the result is exact for your inputs with no assumed constant.
Torque formula
Torque = force * lever arm * sin(angle)
Perpendicular force = force * sin(angle)
Max torque at this arm = force * lever arm (angle 90 degrees)
Pound-feet = newton-metres * 0.7375621
This is the textbook definition of torque about a pivot. Only the perpendicular component of force, isolated by the sine term, produces rotation. The pound-feet conversion is the exact SI to US customary factor.
Torque in practice
- Maximum torque occurs when the force is perpendicular to the lever arm.
- A longer wrench multiplies the same force into more torque.
- Pushing along the arm direction produces zero torque, since sine of zero is zero.
- Bolt makers specify a target torque; under or over tightening can fail the joint.
- Newton-metres and joules share dimensions but torque and energy are different quantities.
Torque: frequently asked questions
What is the torque formula?
Torque equals force multiplied by the lever-arm distance multiplied by the sine of the angle between the force and the lever arm: tau equals F times r times sin theta. When the force is applied perpendicular to the arm, the angle is 90 degrees and sine is one, giving the maximum torque of F times r.
Why does the angle matter?
Only the component of force perpendicular to the lever arm produces rotation. The sine of the angle extracts that perpendicular component. A force applied straight along the arm, at zero degrees, produces no torque because sine of zero is zero.
What units does torque use?
In SI units torque is newton-metres, the product of force in newtons and distance in metres. In US customary units it is pound-feet. This calculator takes newtons and metres and also shows the equivalent in pound-feet using the standard conversion of 1 N times m equals 0.7375621 lb times ft.
Is torque the same as energy?
No, although both can be expressed as force times distance. Torque is a twisting effect about an axis, a vector quantity, measured in newton-metres. Energy is a scalar measured in joules. They are not interchangeable even though the unit dimensions match.
How do I use this for tightening a bolt?
Enter the force you apply to the wrench, the length of the wrench from the bolt centre to where you push, and the angle of your push. The perpendicular case, 90 degrees, gives the torque you deliver. Compare it to the manufacturer's specified tightening torque.
Official sources
- National Institute of Standards and Technology: SI units, the newton and the metre.
- NIST: unit conversion reference (force and torque).
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.