Torque Calculator

Torque is the rotational equivalent of force. It’s what tightens a bolt, spins a wheel, and turns a steering wheel. The full vector form is τ = r × F, but for most practical calculations the scalar magnitude is what you want:

τ = r × F × sin(θ)

Where r is the distance from the axis of rotation to where the force is applied (the “moment arm”), F is the applied force, and θ is the angle between the force vector and the moment arm. When θ = 90° (force perpendicular to the arm), sin(θ) = 1 and you get the maximum possible torque from that force at that distance. Push at any other angle and the effective torque drops.

Quick intuition: why a longer wrench works

A typical hex bolt might need 100 N·m of torque. With a 0.25 m wrench, you’d need to apply F = 100 / 0.25 = 400 N (about 90 lb of force). Switch to a 0.5 m breaker bar and the same 100 N·m requires only 200 N (45 lb). That’s why mechanics keep multiple wrench lengths — the longer arm trades distance for the same torque at lower applied force.

Maximum torque is at θ = 90°

If you pull a wrench at an angle (force vector not perpendicular to the wrench), you waste some of the force on compressing or pulling apart the wrench rather than rotating the bolt. The torque drops by the factor sin(θ):

Pulling at 45° loses you 29% of the torque. Mechanics under a car often have to work at awkward angles, which is one reason ratchets and swivel sockets exist.

Worked examples

Tightening a wheel lug nut

Wheel lug nuts on a passenger car typically need 100 to 120 N·m. With a standard 0.4 m lug wrench: F = 100 / 0.4 = 250 N ≈ 56 lb of pull, perpendicular.

That’s why standing-on-the-wrench works when a nut is stuck: 80 kg of body weight on the end of a 0.5 m arm gives 80 × 9.81 × 0.5 = 392 N·m, far above any reasonable wheel-nut spec. (Don’t stand on lug wrenches you can’t afford to bend.)

An engine producing 300 N·m at the crankshaft

A typical 2.0L gasoline engine produces about 300 N·m of torque at 3,500 RPM. The relationship between torque, angular velocity, and power:

Power (W) = Torque (N·m) × Angular velocity (rad/s)

At 3,500 RPM = 367 rad/s: Power = 300 × 367 = 110,000 W = 110 kW = 147 hp

That matches the rated output of cars in that engine class. Diesel engines tend to produce peak torque at low RPM (e.g., 350 N·m at 1,800 RPM), while gasoline engines peak higher (e.g., 250 N·m at 4,500 RPM). The hp number ends up similar because torque × angular velocity is what determines power.

Newton’s second law for rotation: τ = Iα

The rotational analogue of F = ma. Torque causes angular acceleration α in proportion to the moment of inertia I (which depends on mass and how it’s distributed around the axis). A heavier flywheel has more I and needs more torque to spin up to the same RPM in the same time.

Torque units: N·m, NOT joules

Both torque and energy have the same dimensions (force × distance), but they are conceptually distinct. Torque is a vector quantity describing rotational tendency; energy is a scalar describing the capacity to do work. Engineering specs use N·m or lb·ft for torque, never joules, even though the unit math is identical. The convention exists for clarity.

Unit conversions

• 1 N·m = 0.738 lb·ft
• 1 lb·ft = 1.356 N·m
• 1 kg·m (older but still seen) = 9.81 N·m

For typical fastener specs, US shop manuals use lb·ft (or in·lb for small bolts) while ISO and most non-US manuals use N·m. Always check the unit on the spec sheet — using lb·ft as if it were N·m undertightens by 25% (too loose); the reverse overtightens by 35% (snapped bolt territory).

Where this calculator helps

• Sizing wrenches and breaker bars for fastener specs
• Designing levers, cranks, and rotating mechanisms
• Estimating engine output from force at the crank
• Pre-checking dynamometer setups and load cells
• Teaching rotational mechanics