What is Torque? (Quick overview)

Torque is a measure of the rotational effect of a force applied to a lever arm. In physics and engineering, torque (commonly denoted by the Greek letter tau, τ) quantifies how much a force causes an object to rotate about an axis or pivot point. Imagine using a wrench: applying force farther from the bolt (increase in distance r) or with greater force F increases the torque and makes the bolt easier to turn.

Units and dimensional analysis

SI unit of torque is the Newton-meter (N·m). In Imperial/US customary units you often see foot-pounds (ft·lb or ft·lbf) or inch-pounds (in·lb). Note: Newton-meter is a unit of torque, not energy — although the unit looks the same as joule (N·m), torque is a vector (rotational) while energy is a scalar. To convert: 1 N·m ≈ 0.737562 ft·lb.

Key formulas

The most common torque formula is:

τ = F × r × sin(θ)

Where:

• τ = torque
• F = force applied
• r = distance from the rotation axis to the point of force application (lever arm)
• θ = angle between force vector and lever arm (use sin(θ) to get perpendicular component)

Rotational power & relationship with RPM

When a shaft rotates, torque and angular velocity produce mechanical power:

P = τ × ω

Where ω is angular velocity in radians per second. If you know RPM (revolutions per minute):

ω = 2π × RPM / 60

So:

P (watts) = τ (N·m) × 2π × RPM / 60

Design & engineering notes

When designing mechanical systems (gearboxes, engines, fasteners), torque is a primary parameter. Fastener torque specs ensure proper clamping force; engine torque curves determine vehicle acceleration; gearbox ratios trade torque for speed. Always keep units consistent — convert inches to meters, pounds to newtons, etc. — to avoid errors.

Step-by-step worked examples

Common mistakes & tips

• Angle matters: If the force is not perpendicular, use sin(θ) to get the effective component.
• Units: Keep SI units or clearly convert between systems before calculations.
• Sign convention: Torque direction (clockwise/anticlockwise) may be important; use a sign convention if solving equilibrium problems.

FAQ

Is torque the same as moment?

Yes — in many engineering contexts, torque and moment are used interchangeably (moment of force). Both refer to rotational effect due to force applied at a distance.

How to convert N·m to ft·lb?

Multiply by 0.737562 to convert N·m → ft·lb. To convert ft·lb → N·m multiply by 1.3558179483314004.

Why torque units look like joules?

Because both have dimensions of force × distance (N·m). Context matters: torque is rotational (vector), energy is scalar. Never confuse the two in calculations.

Advanced: Vector cross product (when forces aren't coplanar)

In 3D, torque is the cross product between position vector r and force F:

τ = r × F

Where τ is a vector perpendicular to the plane formed by r and F. Magnitude = r F sin(θ) as above.

References & Further Reading

• Engineering textbooks on statics and dynamics
• Machine design references for fastener torque specifications

Full calculator examples & practice problems

At the top of this page you can interact with the calculator to verify results from the worked examples. Use the reset button to clear entries.

Conclusion

Understanding torque is essential for mechanics, engineers, DIYers and anyone working with rotating systems. This guide and calculator help compute torque from force and distance, find required force or lever length, and convert torque into rotational power using RPM.

Frequently used conversions quick table