Engineering Mechanics

How to Calculate Torque

Torque is the rotational equivalent of linear force. Where force causes straight-line acceleration, torque causes rotation about a pivot. The formula is simple - force multiplied by the perpendicular lever arm distance - but the most common mistakes happen in the unit conversions and in handling forces that are not applied at a right angle.

Final answer from the example

Torque

80 N·m

200 N force on a 0.4 m wrench handle

In US units

59.0 lb·ft

Converted at 1 N·m = 0.7376 lb·ft

Lever arm

0.4 m

Perpendicular distance from pivot to force

Key formulas

Torque (perpendicular force)

T = F × r

Use this when the force is already perpendicular to the lever arm - the most common textbook and tool scenario.

Torque (force at an angle)

T = F × r × sin θ

Use this when the force is applied at angle θ to the lever arm. Only the perpendicular component (F sin θ) produces torque. At θ = 90°, sin 90° = 1 and the formula reduces to T = F × r.

Unit conversion

1 N·m = 0.7376 lb·ft | 1 lb·ft = 1.3558 N·m

Torque specifications on fasteners and motors are often in lb·ft or lb·in in the US and N·m in metric standards.

Variables and units

Symbol	Meaning	Typical units
T	Torque (rotational moment)	N·m, lb·ft, lb·in
F	Applied force	N, kN, lbf
r	Perpendicular lever arm length (pivot to force line)	mm, cm, m, in, ft
θ	Angle between force direction and lever arm	degrees or radians

Quick reference conversions

1 N·m

0.7376 lb·ft

Standard conversion for torque between SI and US customary.

1 lb·ft

1.3558 N·m

Reverse conversion - useful when reading US fastener specs.

1 lb·ft

12 lb·in

Bolt specs for small fasteners are often in lb·in rather than lb·ft.

Typical M8 bolt (8.8)

22–25 N·m

General reference only - always use manufacturer torque specs.

Typical M10 bolt (8.8)

45–55 N·m

General reference only - varies with lubrication and thread condition.

Typical M12 bolt (8.8)

75–90 N·m

General reference only - always verify against the specific fastener spec.

Step-by-step solved example

Example problem

A mechanic applies 200 N of force to the end of a 0.4 m (400 mm) torque wrench. The force is perpendicular to the wrench handle. Calculate the torque applied to the bolt.

1. Confirm the force is perpendicular

The problem states the force is perpendicular to the handle (θ = 90°). This means sin 90° = 1 and the full formula T = F × r × sin θ reduces to T = F × r. No angle correction is needed.

2. Confirm both values are in consistent units

F = 200 N (SI). r = 0.4 m (already in metres). Both are in SI base units, so no conversion is needed. If r were in mm, divide by 1,000 first.

3. Substitute into T = F × r

T = 200 N × 0.4 m.

4. Calculate the torque

T = 80 N·m. The bolt receives 80 newton-metres of tightening torque.

5. Convert to lb·ft if needed and compare to a spec

T = 80 N·m × 0.7376 = 59.0 lb·ft. A typical M12 Grade 8.8 bolt torque spec is around 75–90 N·m depending on lubrication - this result of 80 N·m sits within that range and would be verified against the fastener or equipment manufacturer's specification.

Practical field notes

The lever arm is the perpendicular distance, not the wrench length

If you apply force at the very end of a wrench handle and the force is perpendicular to the handle, the lever arm equals the wrench handle length. If your grip is not at the end, or your force is not perpendicular, the effective lever arm is shorter. Use r = wrench length × sin θ to find the actual perpendicular lever arm.

Torque and moment are the same physical quantity

In mechanical engineering and machine design, 'torque' is used for rotating shafts, fasteners, and motors. In structural and civil engineering, the same rotational effect is called a 'bending moment' or simply 'moment'. The formula is the same: T = F × r.

Always match torque to the fastener or equipment specification

The torque you calculate is the torque applied to the fastener or shaft. Compare it to the manufacturer's torque specification - not a generic table - because the correct value depends on bolt grade, thread pitch, lubrication, and the joined material.

Motor torque is related to power and speed

For rotating machinery, torque, power, and angular speed are linked: P = T × ω, where ω is angular velocity in rad/s. A motor rated at 10 kW spinning at 1,500 RPM produces T = P / ω = 10,000 / (1,500 × 2π / 60) ≈ 63.7 N·m. This is a separate calculation from the static T = F × r formula.

Common mistakes to avoid

Using the wrench length in mm without converting to metres, producing a result 1,000× too large.
Applying T = F × r when the force is at an angle - use T = F × r × sin θ unless the force is truly perpendicular.
Confusing lb·ft with lb·in - divide lb·in by 12 to get lb·ft, or multiply lb·ft by 12 to get lb·in.
Using a generic bolt torque table instead of the fastener manufacturer's actual specification.
Treating T = F × r as a shaft-power formula - power requires angular speed and uses P = T × ω, not T = F × r.

When to use the calculator instead

Use the calculator when you need to switch between N·m, lb·ft, and lb·in, work with forces in N or lbf and lever arms in m, ft, or in without hand-converting, or verify a torque value for a bolt, lever, or mechanism.

Calculation FAQs

What is torque?

Torque is a rotational force - the tendency of a force to cause rotation about a pivot. It equals the applied force multiplied by the perpendicular distance from the pivot to the line of action of the force: T = F × r.

What is the difference between torque and moment?

They describe the same physical quantity. 'Torque' is standard in mechanical engineering and machine design (shafts, motors, fasteners). 'Moment' or 'bending moment' is standard in structural engineering. The formula is identical: T = F × r.

What if the force is not perpendicular to the lever arm?

Only the perpendicular component of force produces torque. Use T = F × r × sin θ, where θ is the angle between the force direction and the lever arm. At θ = 90° (perpendicular), sin θ = 1 and the formula becomes T = F × r.

How do I convert N·m to lb·ft?

Multiply by 0.7376. For example, 80 N·m × 0.7376 = 59.0 lb·ft. To convert lb·ft to N·m, multiply by 1.3558.

How is torque related to power?

For a rotating shaft, power equals torque multiplied by angular velocity: P = T × ω. Angular velocity in rad/s equals RPM × 2π / 60. This is a separate calculation from the static T = F × r formula used to find torque from a force and lever arm.

References

Torque - Definition and Formulas
Engineering ToolBox
Explains torque as force × perpendicular distance, with unit conversions and examples including wrenches and shafts.
Rotational Motion and Torque
OpenStax University Physics
Defines torque as the cross product τ = r × F, explains the moment arm, and connects to angular acceleration.
Fastener Torque Guidelines
Bolt Science
Explains how tightening torque relates to bolt preload and why the correct torque depends on friction, lubrication, and grade.

Open Torque Calculator →Back to examples →