Newton Meter Calculator

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Table of contents

• How to use
• Common mistakes
• Definitions
• Methodology
• Limitations & assumptions
• Sources

Torque: A turning effect around a pivot or rotation axis. This calculator reports its magnitude, not clockwise or counterclockwise direction.

Newton-meter (N*m): The SI unit of torque. One N*m is produced by a one-newton force applied one meter from a pivot at a right angle.

lb-ft: Pound-force feet, a torque unit used in many US vehicle and tool specifications. It may also be written ft-lb or lbf*ft.

Lever arm: The distance from the pivot to the point where the force is applied.

Perpendicular force: The part of a force acting at a right angle to the lever arm. This is the part that creates torque.

Angle between force and lever arm: The smaller angle between the lever arm and the force direction. A 90-degree angle gives the greatest torque for the same force and length.

Pound-force (lbf): A unit of force, not mass. One lbf equals about 4.44822 N.

Mistake: Entering a wrench setting in N*m while "Torque unit" is set to lb-ft.
Fix: Choose the unit printed beside the source number before calculating. Changing the unit changes what the entered number means.

Mistake: Treating lb-ft as pounds of mass.
Fix: Use lb-ft for torque and lbf for force. Pounds of mass are not a force value.

Mistake: Measuring from the end of a handle instead of from the pivot.
Fix: Measure from the rotation axis to the exact point where the force is applied.

Mistake: Leaving the angle at 90 degrees when the force is pushed along the handle.
Fix: Enter the smaller angle between the force direction and lever arm. An angled force produces less torque than a perpendicular force.

Mistake: Typing a comma as a decimal mark, such as 1,5.
Fix: Use a decimal point for fractions, such as 1.5. Use commas only as thousands separators, such as 1,000.

• The calculator uses torque magnitude only. It does not calculate clockwise or counterclockwise direction, vector components, or net torque from multiple forces.
• The entered angle must be greater than 0 and less than 180 degrees. At 0 or 180 degrees, the perpendicular force component is zero.
• Use the pivot-to-force distance, not the full handle length unless the force is applied exactly at the handle end.
• Friction, bending, flexing, off-center loading, and tool calibration can make real applied torque differ from this ideal calculation.
• N*m has the same physical dimensions as a joule, but this calculator uses N*m as torque, not energy.
• Displayed values are rounded to the selected decimal places while calculations use unrounded values.

Calculation method

The calculator converts torque to N*m, force to newtons, and lever-arm length to meters before solving. It then uses the part of the force that is perpendicular to the lever arm.

τ (torque in N*m) = F (force in N) * r (lever-arm length in m) * sin(θ)

θ is the angle between the force direction and lever arm. At 90 degrees, sin(θ) is 1, so the full force contributes to torque. [1]

Finding force or length

For "Find required force" and "Find lever arm", the calculator rearranges the same equation. A zero force or zero lever arm cannot be used in the matching inverse calculation because it would require division by zero.

F (force in N) = τ / (r * sin(θ))

r (lever-arm length in m) = τ / (F * sin(θ))

Unit conversions

The torque conversions use 1 lb-ft = 1.3558179483314004 N*m and 1 lb-in = 0.1129848290276167 N*m. The force and length conversions include 1 lbf = 4.4482216152605 N and 1 in = 0.0254 m.

lb-ft = N*m / 1.3558179483314004

Worked example

A 100 N force applied 0.5 m from a pivot at 90 degrees produces 50 N*m. That converts to about 36.878 lb-ft and 442.537 lb-in when three decimal places are selected.

τ = 100 * 0.5 * sin(90 degrees) = 50 N*m