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Torque Calculator

Enter force and distance to calculate torque.

Input Information

Result

Enter force and distance, then press Calculate.

Torque Calculator is a physics tool that accurately measures the tendency of a force to rotate an object about a specific axis. Unlike a simple linear push or pull, torque is a core physical quantity of rotational motion whose effect depends on where and in what direction the force is applied.

The simplest example is opening a door. It opens most easily when you push the handle far from the hinge (the axis), and needs more force near the hinge. Torque arises from the combination of the distance from the axis and the magnitude of the force.

Torque plays a central role in designing and analyzing mechanical systems — from a car engine’s rotational force and bicycle pedal force to the force of screwdrivers and wrenches and even electric motor output.

This calculator takes a force and a distance from the axis and computes the torque magnitude when the force acts perpendicular to the distance. It serves as an educational tool for rotational mechanics and a practical tool that gives engineers accurate torque data for machine design, structural analysis, and power system development.

Term Glossary

Torque
The tendency of a force to rotate an object about an axis; proportional to the force and the distance (lever arm) to the axis, with unit N·m.
Lever Arm
The perpendicular distance from the axis to the point where the force is applied. The farther it is, the greater the torque from the same force.
Newton-meter (N·m)
The international unit of torque, representing the rotational effect of a 1 N force applied at a 1 m arm length.

  1. Enter the applied force in newtons (N).
  2. Enter the distance from the pivot point to where the force is applied, in meters (m).
  3. Enter the angle between the force and the lever arm in degrees.
  4. Click calculate and the torque is computed in newton-meters (N·m).

10 N × 2 m at 90°

Applying a 10 N force at 90° at a distance of 2 m from the axis gives a torque of 10 × 2 × sin(90°) = 20 N·m.

50 N × 0.3 m at 90°

Applying a 50 N force at 90° to a 0.3 m wrench gives a torque of 50 × 0.3 × sin(90°) = 15 N·m.

20 N × 1 m at 30°

Applying a 20 N force at 30° at a distance of 1 m, since sin(30°) = 0.5, gives a torque of 20 × 1 × 0.5 = 10 N·m.

Basic Torque Formula

τ=rFsin⁡(θ)\tau = r F \sin(\theta)
  • τ (tau): torque, international standard unit newton-meter (N·m)
  • r (radius): distance from the axis to the force point (lever arm), unit meter (m)
  • F (Force): applied force, unit newton (N)
  • θ (theta): the angle between the distance vector and the force vector

Simplified Formula (Perpendicular Force)

When the force acts perpendicular to the lever arm (θ = 90°), sin(90°) = 1, so:

τ=rF\tau = r F

Example

What is the torque when a 50 N force is applied with a 0.5 m wrench?

τ=0.5 m×50 N=25 N\cdotpm\tau = 0.5\,\text{m} \times 50\,\text{N} = 25\,\text{N·m}

Therefore the torque is 25 newton-meters.

How to Maximize Torque

There are three key factors for maximizing torque.

  • Apply more force: pushing or pulling harder increases torque.
  • Lengthen the lever arm: apply force as far from the axis as possible.
  • Angle at 90°: torque is maximal when the force is perpendicular to the lever arm.

Real-Life Applications

  • Tool Use

    Wrenches, spanners, and screwdrivers all use the principle of torque. A torque wrench is used to tighten to a specific torque value.

  • Automobile

    Maximum torque is the greatest rotational force an engine can produce, determining performance when starting off or climbing hills.

  • Bicycle

    Pedaling turns the crank, generating torque; gear shifting adjusts the torque relationship.

Right-Hand Rule

Torque is a vector quantity whose direction is given by the right-hand rule: curl the fingers of the right hand in the rotation direction, and the thumb points along the torque vector.

Unit Conversion

  • 1 N·m = 1 joule (J)
  • 1 kgf·m = 9.80665 N·m
  • 1 ft·lbf = 1.35582 N·m
  • 1 in·lbf = 0.11298 N·m

QWhat is torque?

Torque is a physical quantity that describes the tendency of a force to rotate an object about an axis — the rotational analogue of force. Its unit is the newton-meter (N·m).

QWhat is the torque formula?

Torque is calculated as τ = rF sin(θ), where r is the distance from the axis (lever arm), F is the applied force, and θ is the angle between the force and the lever arm.

QWhat does the unit N·m mean?

N·m (newton-meter) is the torque from a 1 newton force applied perpendicularly at a 1 meter arm. Although torque and energy share the same-looking unit, torque is a vector while energy is a scalar.

QWhy does the angle matter?

Torque is proportional to the perpendicular component of the force, so it is maximum when the force is perpendicular (90°) to the lever arm. At 0° or 180° the torque is zero, and oblique angles reduce the effective rotation.

QWhat is the difference between torque and force?

Force pushes or pulls an object in a straight line, while torque rotates an object about an axis. The same force produces different torque depending on the distance from the axis and the angle.

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