Torque Calculator

Torque is evaluated from Force, Lever Arm and Angle. The calculation reports Torque, Torque and Force.

Results

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About the Torque Calculator

Torque is treated here as a quantitative relation between Force, Lever Arm, Angle and Torque - to convert and Torque, Torque, Force and Lever Arm.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
τ = r x F x sin(θ)
τ = torque (N·m)
r = lever arm distance (m)
F = applied force (N)
θ = angle between force vector and lever arm (degrees)
At θ = 90 deg: sin(90 deg) = 1, so τ = r x F (maximum torque)
Conversion: 1 ft·lbf = 1.35582 N·m

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

τ = r x F x sin(θ)
τ = torque (N·m)
r = lever arm distance (m)
F = applied force (N)
θ = angle between force vector and lever arm (degrees)
At θ = 90 deg: sin(90 deg) = 1, so τ = r x F (maximum torque)
Conversion: 1 ft·lbf = 1.35582 N·m

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Tightening Lug Nuts

Inputs

force: 667 lever_arm: 0.3 angle: 90
Torque: 200.1 N·m. Torque: 147.586 ft·lbf

With Force = 667, Lever Arm = 0.3 and Angle = 90 as the stated inputs, the result is Torque = 200.1 N·m and Torque = 147.586 ft·lbf. Each value corresponds to the declared output fields.

Example 2: Engine Torque Conversion

Inputs

torque_nm: 542
Torque: 542 N·m. Torque: 399.759 ft·lbf

With Torque - to convert = 542 as the stated inputs, the result is Torque = 542 N·m and Torque = 399.759 ft·lbf. Each value corresponds to the declared output fields.

Example 3: Wrench Force at an Angle

Inputs

force: 200 lever_arm: 0.25 angle: 60
Torque: 43.301 N·m. Torque: 31.937 ft·lbf

With Force = 200, Lever Arm = 0.25 and Angle = 60 as the stated inputs, the result is Torque = 43.301 N·m and Torque = 31.937 ft·lbf. Each value corresponds to the declared output fields.

Example 4: Door Hinge — Opening Force

Inputs

lever_arm: 0.9144 angle: 90 torque_nm: 10
Torque: 10 N·m. Torque: 7.376 ft·lbf. Force: 10.936 N

With Lever Arm = 0.9144, Angle = 90 and Torque - to convert = 10 as the stated inputs, the result is Torque = 10 N·m, Torque = 7.376 ft·lbf and Force = 10.936 N. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate tightening torque for a bolt
  • Find force needed to turn a wrench at a given arm length
  • Convert engine torque between ft-lbf and N-m