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Torque Calculator

Torque τ = F·r·sinθ with the effective lever arm drawn as a perpendicular, torque against angle, and angular acceleration from τ = Iα.

τ = F · r · sinθ — force times the perpendicular distance from the pivot to the line the force acts along.

Force F (N)Radius / lever length r (m)

Angle between the lever and the force90°100% effective

0° — along the lever, no torque at all90° — maximum180° — none again

Moment of inertia I (kg·m²)Give it a moment of inertia to watch it turn.

87.50 N·m

torque

Effective lever arm

350.00 mm

r · sinθ

If pulled square on

87.50 N·m

100% of it now

In pound-feet

64.54 lb·ft

Angular acceleration

—

needs a moment of inertia

τ = F · r · sinθ = 250 × 0.35 × 1 = 87.50 N·m

Torque lost to the angle0.00 nN·m

Force needed for the same torque square on250.00 N

Other units774.4 lb·in · 892.3 kg·cm

Instant insight

87.50 N·m of torque
τ = F · r · sinθ = 250.00 N × 350.00 mm × sin(90°). Equivalently, force times the *lever arm* — the perpendicular distance from the pivot to the line the force acts along, which here is 350.00 mm.
At 90° the lever arm is the full radius — this is the maximum
Every other angle gives less. The curve beside the wrench is a sine: it is flat near the top, so being a few degrees off costs almost nothing, and steep near zero, so the last stretch towards a straight pull is where the torque vanishes fastest.
Length beats force, for the same effort
Doubling the spanner length doubles the torque exactly as doubling the force does — but your arm can only pull so hard, and it costs nothing to reach further. At 350.00 mm you need 250.00 N; at twice that you would need half. This is the entire reason breaker bars exist.
Torque is not work, even though both are newton-metres
A newton-metre of torque and a joule of energy have identical units and are different quantities. Torque is a force applied at a distance perpendicular to it; work is a force applied through a distance along it. Holding a heavy spanner still applies torque indefinitely and does no work at all, which is why torque is written N·m and never J.
What the model leaves out
A single force on a rigid lever about a fixed pivot, with the force in the plane of rotation. Real fasteners add friction between the threads and under the head — often most of the applied torque never reaches the clamping force at all, which is why critical joints are tightened by angle or by bolt stretch rather than by a torque wrench alone.

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Everyday Uses

Tightening fasteners

Convert a torque spec between N·m and lb-ft before setting a torque wrench.

Leverage problems

Find the force needed at a given distance, or how much a longer lever helps.

When the force is not perpendicular

Work with the angle term rather than assuming a perpendicular force.

Motor and drive sizing

Relate torque, speed and power when specifying a motor.

Bicycle gears

A low gear converts the same leg force into far more turning effort at the rear wheel, trading speed for the torque needed to climb.

Handles, taps and spanners

Every lever you use is a torque argument: the further from the pivot you push, the less force it takes. It is why a stiff valve opens with a longer handle.

Frequently Asked Questions

What is torque?

The turning effect of a force — force times the perpendicular distance from the pivot, measured in newton metres. Applying 20 N at 0.5 m from a bolt gives 10 N·m. The distance matters as much as the force, which is why a longer spanner loosens a stubborn bolt that a short one cannot: you are not stronger, you have more leverage.

Why does the angle matter?

Only the component of force perpendicular to the lever arm produces rotation, so torque is F × r × sin θ. Push straight along the spanner, at 0°, and you generate no torque at all — just a force trying to slide the tool off. Push at 90° and every newton counts. At 45° you lose about 30% of the effect, which is why awkward angles make jobs feel disproportionately hard.

What is the difference between torque and power?

Torque is turning force; power is the rate of doing work, equal to torque times rotational speed. An engine can produce high torque at low revs — good for pulling away and towing — while peak power arrives higher up the rev range. It is why a tractor and a sports car have very different characters despite comparable power figures.

Why are bolts tightened to a specified torque?

Because torque is a proxy for the clamping force stretching the bolt. Too little and the joint loosens under vibration; too much and the bolt yields or the thread strips. Published torque specs assume a particular lubrication state — a lubricated thread reaches the same tension at noticeably lower torque than a dry one, so applying a dry spec to an oiled bolt over-tightens it.

How do I convert between torque units?

One newton metre is about 0.738 pound-feet, and one pound-foot is 1.356 N·m. Also common is the kilogram-force metre, roughly 9.81 N·m. Watch for pound-feet versus foot-pounds — dimensionally identical and often used interchangeably, though strictly foot-pounds denotes energy and pound-feet denotes torque. Both appear on tools, so read the tool rather than the convention.

What is the relationship between torque and angular acceleration?

Torque equals moment of inertia times angular acceleration — the rotational counterpart of F = ma. Moment of inertia depends not just on mass but on how far that mass sits from the axis, which is why a flywheel with its mass at the rim resists speed changes far more than a solid disc of the same weight.