Torque Calculator

Three calculation modes: force × arm, power/speed, or gear stage output.

Mode A — Torque from Force

Force F (N)

Moment Arm r (m)

Angle θ between force and arm (degrees)

τ = F · r · sin(θ). Default 90° = perpendicular force.

Output torque unit

Torque (τ)60.000 N·m

Also60.000 N·m = 44.254 ft·lb

Effective moment arm0.3000 m

What This Calculator Does

Torque is the rotational equivalent of force. This calculator provides three modes: basic torque from force and moment arm (including angle correction), torque derived from power and shaft speed, and output torque through a gear reduction stage accounting for mechanical efficiency losses.

It combines Force, Lever Arm to estimate Torque, Also.

Formula & Method

Basic torque (Mode A):

\tau = F \cdot r \cdot \sin(\theta)

where

\theta

is the angle between the force vector and the moment arm. Torque from power (Mode B):

\tau = \frac{P}{2\pi n/60} = \frac{9549 \cdot P_{kW}}{n_{RPM}}

Gear stage output torque (Mode C):

\tau_{out} = \tau_{in} \times GR \times \eta

where

GR

is gear ratio and

\eta

is mechanical efficiency.

Notation used in the formulas: $R$ = Torque; $x_{1}$ = Force; $x_{2}$ = Lever Arm.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Worked Examples

Mode A — Wrench at 45°

Applying F = 80 N at r = 0.25 m with θ = 45°: τ = 80 × 0.25 × sin(45°) = 80 × 0.25 × 0.707 = 14.14 N·m = 10.43 ft·lb

Mode B — Electric motor at 1450 RPM, 3 kW

τ = 9549 × 3 / 1450 = 19.76 N·m = 14.59 ft·lb

Mode C — Gear reduction 4:1, η = 95%

Input torque 20 N·m, gear ratio 4:1, η = 95%: τ_out = 20 × 4 × 0.95 = 76 N·m

Reference Book

Engineering Mechanics: Statics & Dynamics

Russell C. Hibbeler · Pearson

A standard mechanics reference for torque, pulleys, equilibrium, load balance, and rigid-body reasoning.

View Book

Inputs Used

Force: Used directly in the calculation.
Lever Arm: Used directly in the calculation.

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