Torque Calculator

Torque: The twisting effect of a force around a pivot or axis. It depends on force, distance from the pivot, and the angle of the force.

Lever arm distance: The distance from the pivot to where the force is applied. This is the length used before angle adjustment [1].

Force angle from lever arm (degrees): The angle between the lever arm and the force direction. Only the perpendicular part of the force creates torque.

Perpendicular-force factor: The value of sin(angle). It tells you what fraction of the total force actually contributes to torque.

Perpendicular force component: The effective part of the force that acts at 90 degrees to the lever arm, found from force times sin(angle).

Signed torque: A torque value with a plus or minus sign. In this calculator's signed mode, positive means counterclockwise and negative means clockwise.

Newton-meter (N m): A common torque unit made from force times distance [3].

Mistake: Entering a value in Torque (selected unit) while Solve for is set to Torque and expecting that number to affect the answer.
Fix: When solving for torque, fill in Force (selected unit) and Lever arm distance (selected unit) . The hidden or unused torque input is ignored.

Mistake: Treating Force angle from lever arm (degrees) as the angle from vertical or horizontal instead of the angle between the force and the lever arm.
Fix: Enter the angle between the lever arm and the force direction. If the force is straight across the lever arm, use 90 degrees.

Mistake: Typing a negative number for Lever arm distance (selected unit) .
Fix: Distance is a length, so enter 0 or a positive value only. Use Applied rotation direction for clockwise or counterclockwise meaning, not a negative distance.

Mistake: Mixing units, such as entering force in pounds while Force unit is still set to Newton (N).
Fix: Make Force unit , Distance unit , and Torque unit match the numbers you entered before you calculate.

Mistake: Trying to solve for Force (selected unit) or Lever arm distance (selected unit) when Force angle from lever arm (degrees) is 0 degrees or 180 degrees and torque is not zero.
Fix: Change the angle or the setup. At those angles, the perpendicular part of the force is zero, so no finite force or distance can create nonzero torque.

Mistake: Seeing a negative Calculated result in signed mode and thinking it is an error.
Fix: Check Direction convention and Direction note . In signed counterclockwise-positive mode, a negative torque means clockwise rotation.

• The calculator uses the standard single-force relation for torque magnitude: force times lever arm distance times sin(angle).
• The angle must be the angle between the lever arm and the force, not the angle from the floor, wall, or vertical unless those are the same in your setup.
• Lever arm distance (selected unit) is treated as a nonnegative length. Use signed mode for direction, not a negative distance.
• When solving for force or distance, the calculator cannot give one unique nonzero answer if sin(angle) = 0. If torque is also 0 in that case, there are infinitely many possible solutions.
• Very small angles near 0 degrees or 180 degrees make the result highly sensitive. Tiny changes in angle can cause very large changes in solved force or distance.
• This tool handles one applied force and one lever arm. It does not add multiple forces or calculate net torque from several objects.
• Unit conversions are built into the math, but real systems may differ if friction, bending, changing geometry, or three-dimensional effects matter.

Core idea

Torque is the twisting effect caused by a force acting some distance from a pivot. Only the part of the force that is perpendicular to the lever arm produces torque [1][3].

Formulas used

T = F * r

This is the basic torque magnitude formula when the force is perpendicular to the lever arm.

T = F * r * sin(θ)

Use this when the force is at an angle. Here, θ means the angle between the lever arm and the force.

F = T / (r * sin(θ))

This rearranged formula is used when solving for force.

r = T / (F * sin(θ))

This rearranged formula is used when solving for lever arm distance.

F_perp = F * sin(θ)

The calculator shows this as Perpendicular force component so you can see how much of the input force is actually creating torque.

T_signed = s * |T|

In signed mode, s = +1 for counterclockwise and s = -1 for clockwise.

How the calculator computes results

First, the calculator converts the entered values into base units: newtons for force, meters for distance, and newton-meters for torque. It then computes sin(angle) from Force angle from lever arm (degrees), finds the perpendicular force component, solves for the requested quantity, and converts the final result back to your selected output unit.

For signed torque, the calculator first finds the torque magnitude and then applies the sign from Applied rotation direction using the selected convention.

Worked mini-example

Suppose Force (selected unit) = 20 N, Lever arm distance (selected unit) = 2 m, and Force angle from lever arm (degrees) = 30.

sin(30 deg) = 0.5

F_perp = 20 * 0.5 = 10 N

T = 20 * 2 * 0.5 = 20 N m

So the Calculated result is 20 N m, and the Perpendicular-force factor is 0.5.

Conversions used

The calculator uses these constants for unit conversion:

1 kgf = 9.80665 N, 1 ft = 0.3048 m, 1 in = 0.0254 m, 1 lbf = 4.4482216152605 N, 1 N m = 0.737562149277 ft lb, and 1 N m = 8.850745791327 in lb.

Error conditions and boundary handling

If you solve for force or distance when sin(angle) = 0 and torque is nonzero, the calculator shows an error because no finite answer exists. If torque is also zero in that setup, it shows that there is no unique single answer. Negative lever arm distance is blocked as an error.

Assumptions behind the math

This method assumes a single force, a fixed pivot, and a lever arm measured from the pivot to the point of force application. It does not include multiple torques, friction, deforming parts, or full 3D vector analysis, so real measurements can differ when those effects matter.