What is the difference between torque and power?

Torque is the rotational force at any instant. Power is the rate of doing work: P = torque × angular velocity. An engine can have high torque at low RPM (diesel truck) or low torque at high RPM (motorcycle). Power determines top speed; torque determines acceleration.

Why are torque wrenches important?

Over-tightening a bolt can strip threads, crush gaskets, or snap the bolt. Under-tightening can let it loosen. Torque wrenches click or beep at the specified torque, ensuring consistent and safe clamping force.

What are common torque units?

Newton-meters (N·m) is the SI unit. Pound-feet (lb·ft) is common in the US automotive industry. Kilogram-force centimeters (kgf·cm) are used in hobby servos. 1 N·m = 0.7376 lb·ft.

How does lever arm length affect torque?

Torque is directly proportional to lever arm length. A wrench twice as long produces twice the torque with the same force. This is why cheater bars (pipe extensions) on wrenches are so effective and also why they can damage bolts.

What is the relationship between torque and angular acceleration?

tau = I × alpha, where I is the moment of inertia and alpha is angular acceleration. This is the rotational equivalent of F = ma. A larger moment of inertia requires more torque to achieve the same angular acceleration.

Torque Calculator

Calculate torque, force, or moment arm for rotational mechanics problems.

Torque Calculator

Calculate torque (T = F x r)

Torque Calculator

Enter force and distance

Force (N)

Distance (m)

Formula

T = F x r

What Is Torque?

Torque (also called moment of force) is the rotational equivalent of linear force. It measures how much a force tends to rotate an object around a pivot point, or axis. Torque depends on two things: the magnitude of the force applied and the perpendicular distance from the axis of rotation to the line of action of the force — called the moment arm (or lever arm).

Torque is everywhere in mechanical engineering: tightening bolts, designing gears, sizing motors, and analyzing engines. The SI unit of torque is the newton-meter (N·m). In the US, torque is also expressed in foot-pounds (ft·lb) or inch-pounds (in·lb). Understanding torque helps engineers select motors, calculate power transmission, and prevent mechanical failure.

How to Use This Calculator

Select what you want to calculate: Torque (τ), Force (F), or Moment Arm (r).
Enter the two known values — force in newtons (N) and distance in meters (m), or their equivalents.
Click Calculate to see the result instantly.
Use Reset to clear all fields and start over.

Formula & Explanation

τ = F × r × sin(θ)
F = τ / (r × sin(θ))
r = τ / (F × sin(θ))

τ = torque (N·m), F = force (N), r = distance from pivot to force application (m), θ = angle between force vector and moment arm. When force is perpendicular to the arm (θ = 90°), sin(θ) = 1 and τ = F × r (maximum torque).

Worked Examples

Example 1 — Tightening a Bolt

A wrench applies 50 N at 0.25 m from the bolt center, perpendicular to the handle. τ = 50 × 0.25 = 12.5 N·m.

Example 2 — Bicycle Pedal

A cyclist applies 200 N downward on a pedal 0.17 m from the crank center. τ = 200 × 0.17 = 34 N·m of torque on the crankshaft.

Example 3 — Angled Force

A force of 100 N is applied at 30° to a 0.5 m lever arm. τ = 100 × 0.5 × sin(30°) = 100 × 0.5 × 0.5 = 25 N·m.

Frequently Asked Questions

What is the difference between torque and force?▾

Force causes linear acceleration (F = ma). Torque causes angular acceleration (τ = Iα). Force is measured in newtons; torque in newton-meters. A large force applied close to a pivot produces less torque than the same force applied far from the pivot.

How is torque related to power?▾

Power (P) = Torque (τ) × Angular velocity (ω). In consistent units: P (watts) = τ (N·m) × ω (rad/s). An engine producing 300 N·m at 3,000 RPM generates P = 300 × (3000 × 2π/60) ≈ 94 kW = 126 hp.

What is the right-hand rule for torque?▾

Point your right hand's fingers in the direction of the moment arm, then curl them toward the force direction. Your thumb points in the direction of the torque vector. Counterclockwise torque is positive by convention.

What are typical torque values for common fasteners?▾

Torque specs vary by fastener size and material. A typical M8 bolt in steel requires 20–25 N·m; a 3/8-inch SAE bolt requires 25–30 ft·lb. Always consult the manufacturer's specifications for critical fasteners.

How does gear ratio affect torque?▾

A gear system multiplies torque by the gear ratio while reducing speed by the same ratio (ignoring friction). A 5:1 gear reduction takes 10 N·m input and delivers 50 N·m output at 1/5 the speed. This is why low gears in vehicles provide more pulling force.