How can I calculate torque from a perpendicular force and its lever arm?

For a perpendicular force, multiply the force by the perpendicular lever arm: |τ| = F × r⊥. The lever arm is measured from the pivot to the force’s line of action, at right angles to that line—not necessarily the length of the object. Torque is defined about a specified pivot, so identify that point before choosing the distance. The SI unit is the newton-metre (N·m). [S1]

For example, assume a force of 12 N acts perpendicular to a bar, and its line of action is 0.25 m from the pivot. Then |τ| = 12 × 0.25 = 3 N·m. This is a worked example using assumed values, not a measurement.

Here is a simplified top-down sketch. Assume the handle is horizontal and the force points straight down on the page, so it is perpendicular to the handle:

                    ↓ F = 12 N
P (pivot) ●─────────● end of handle
          <─ r⊥ = 0.25 m ─>

The pivot is P. The handle runs from P to the point where the force is applied. In this particular perpendicular setup, the distance along the handle from P to the force’s line of action is also the perpendicular lever arm, 0.25 m. Substituting the labels gives |τ| = (12 N)(0.25 m) = 3 N·m. The diagram shows magnitude calculation; it does not assign a clockwise/counterclockwise sign.

Convert before multiplying so the force and lever arm use consistent units. To report N·m, express the force in newtons and the distance in metres. For example, with stated values of 500 N and 0.40 m, the magnitude is 500 × 0.40 = 200 N·m. These are illustrative values.

The formula here gives magnitude, which is nonnegative. A plus or minus sign depends on the axis and sign convention chosen for the problem. If none is specified, report the magnitude and state that direction/sign has not been assigned; do not guess a convention. [S1]

Use this template:

Pivot: [point]
Force magnitude: [value] N
Force line of action: [direction or sketch]
Perpendicular distance from pivot to that line: [value] m
Calculation: |τ| = F × r⊥ = [value] N × [value] m = [answer] N·m
Direction/sign convention: [given convention, or not assigned]

On your sketch, mark the pivot, draw or extend the force’s line of action, and label the shortest perpendicular distance from the pivot to that line. For the specific perpendicular-force case, that distance may match the distance along a straight handle, as in the diagram. If your force is not perpendicular, this guide’s shortened calculation does not apply as written; the general magnitude relationship is |τ| = rF sin θ. [S1] The source does not establish a sign convention for your particular problem, so use the convention supplied with the exercise or label your result as magnitude only.