Torque Calculator — Rotational Force Calculator
Calculate torque, force, or lever arm distance using the torque equation τ = F × r × sin(θ). Essential for mechanical engineering, physics, and rotational mechanics analysis. See also our Moment of Inertia Calculator and Angular Acceleration Calculator.
How to Calculate Torque
- Select what you want to calculate from the dropdown menu.
- Enter the known values in the input fields.
- Enter the angle between force and lever arm (90° for perpendicular).
- Click Calculate to solve for the unknown variable.
Torque Formula
Torque Formula:
τ = F × r × sin(θ)
Where:
τ = Torque (N⋅m)
F = Applied force (N)
r = Distance from axis of rotation (m)
θ = Angle between force and lever arm (degrees)
Special cases:
θ = 90° (perpendicular): τ = F × r (maximum torque)
θ = 0° (parallel): τ = 0 (no torque)
Newton's second law for rotation:
τ = I × α
Where: I = moment of inertia, α = angular acceleration
Power relationship:
P = τ × ω
Where: P = power (W), ω = angular velocity (rad/s)Example Calculation
Problem: A 100 N force is applied perpendicular to a 0.5 m wrench. Find the torque.
Given: F = 100 N, r = 0.5 m, θ = 90°
Solution: τ = 100 × 0.5 × sin(90°) = 100 × 0.5 × 1 = 50 N⋅m
Answer: The torque is 50 N⋅m or 36.9 ft⋅lb.
Common Torque Values Reference
| Application | Torque (N⋅m) | Torque (ft⋅lb) |
|---|---|---|
| Bicycle pedal | 20-40 | 15-30 |
| Car lug nuts | 80-120 | 60-90 |
| Motorcycle engine | 50-150 | 37-111 |
| Car engine (small) | 150-250 | 111-184 |
| Car engine (V8) | 400-600 | 295-443 |
| Truck engine | 1000-2000 | 738-1475 |
| Industrial motor | 100-10000 | 74-7376 |
| Wind turbine | 1000000+ | 737600+ |
Technical Details
Torque is the rotational equivalent of force, causing angular acceleration about an axis. It depends on the magnitude of applied force, the distance from the rotation axis (lever arm), and the angle between force and lever arm. Maximum torque occurs when force is perpendicular to the lever arm (θ = 90°). Torque is a vector quantity with direction determined by the right-hand rule. In mechanical systems, torque is transmitted through shafts, gears, and couplings. The relationship τ = Iα connects torque to rotational motion, where higher torque produces greater angular acceleration for a given moment of inertia.
Frequently Asked Questions
What is torque?
Torque is a measure of rotational force that causes an object to rotate about an axis. It's the product of force, distance from the axis, and the sine of the angle between them.
How does angle affect torque?
Torque is maximum when force is perpendicular to the lever arm (90°) and zero when force is parallel (0°). The sine function determines the effective component of force.
What's the difference between torque and power?
Torque is rotational force (N⋅m), while power is the rate of doing work (W). They're related by P = τ × ω, where ω is angular velocity. High torque at low speed can equal low torque at high speed in power.
How do you increase torque?
Increase torque by: applying more force, using a longer lever arm, or positioning force perpendicular to the lever arm. Gear systems can multiply torque at the expense of speed.
Why is torque important in engines?
Engine torque determines acceleration capability and pulling power. Higher torque provides better performance for towing, climbing hills, and accelerating from rest, especially at low RPM.