Torque Calculator

About the Torque Calculator

This calculator finds the torque produced by a force applied at a distance from a pivot point, accounting for the angle between the force and the lever arm. It's a straightforward tool for mechanics, engineering students, and anyone working with wrenches, levers, or rotating machinery who needs to know how much rotational effect a given force actually produces.

How It Works

You enter the applied force in newtons, the distance from the pivot point to where the force is applied in meters, and the angle between the force direction and the lever arm in degrees. The calculator multiplies force by distance by the sine of that angle, since only the component of force perpendicular to the lever arm contributes to rotation.

Torque = F x r x sin(theta), where F is the applied force, r is the distance from the pivot, and theta is the angle between the force vector and the lever arm.

Formula & Methodology

By hand, convert the angle to radians if working outside a calculator with a built-in degree mode, then take its sine. Multiply that sine value by the force and by the distance from the pivot, in either order, to arrive at torque in newton-meters.

Examples

Wrench applied perpendicular to a bolt

A 50 N force applied 0.3 m from a bolt, perfectly perpendicular to the wrench handle at 90 degrees, produces a torque of 50 x 0.3 x sin(90) = 15 N times m.

Same wrench pulled at a shallow angle

Using the same 50 N force and 0.3 m distance but pulling at only 30 degrees from the handle instead of straight on, torque drops to 50 x 0.3 x sin(30) = 7.5 N times m, half the torque for the same physical effort, because the angled pull wastes half its force along the handle instead of turning it.

Advantages

Accounts for the angle between force and lever arm directly, instead of assuming a perpendicular, maximum-torque application by default.
Gives an immediate side-by-side sense of how much torque is lost when force isn't applied perpendicular to the lever, easy to underestimate intuitively.
Works for any consistent set of force and distance units as long as they're entered in newtons and meters, returning a standard newton-meter torque result.

Common Mistakes

Assuming force and torque are the same thing, when torque also depends on both the distance from the pivot and the angle of application.
Applying the formula with the angle measured from the wrong reference line, such as from the perpendicular instead of from the lever arm itself, which inverts the sine relationship.
Overlooking that pulling at a shallow angle can waste a large fraction of applied force, since sin(theta) drops off quickly for angles well below 90 degrees.

Edge Cases to Watch For

At an angle of exactly 0 or 180 degrees, sin(theta) equals zero, so the calculated torque is zero regardless of how large the force is, since the force is acting entirely along the lever arm with no rotational component.
At 90 degrees, sin(theta) equals 1, so torque is simply force multiplied by distance, the maximum possible torque for a given force and distance combination.
The calculator does not validate that force and distance are positive, so negative inputs will still compute a signed result rather than being flagged as an error.

Common Use Cases

Mechanics and DIYers estimating how much force is needed on a wrench or lever to achieve a target torque.
Engineering students working through statics or dynamics problems involving rotational force.
Anyone designing or analyzing simple mechanical systems, like levers, hinges, or hand tools, where the angle of applied force matters.

Frequently asked questions

Why does angle matter for torque?

Only the component of force perpendicular to the lever arm actually contributes to rotation - a force applied straight along the lever arm (0° or 180°) produces zero torque no matter how strong it is, which is why torque = F × r × sin(θ) rather than a simple F × r.