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Torque Calculator

Physics

Calculate rotational torque using τ = r × F × sin(θ). Enter lever arm length, force, and angle to get torque in newton-meters instantly, with a formula breakdown.

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Torque

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This calculator computes your Torque from the values you enter.

Inputs
Lever Arm LengthForceAngle Between Force and Lever Arm
Outputs
Torque

What is a Torque?

The Torque Calculator computes rotational torque using τ = r × F × sin(θ) — the turning effect produced by a force applied at a distance from a pivot point. Enter a lever arm length, a force, and the angle between the force and the lever arm (defaulting to 90°, the most efficient angle), and the calculator instantly returns the torque in newton-meters.

Torque is the rotational analog of force, central to understanding how wrenches, engines, motors, and any rotating mechanical system work. This general-purpose calculator handles any lever-arm-and-force scenario in physics or mechanical engineering — distinct from the Bolt Torque Calculator, which is a specialized fastener-spec tool for determining correct bolt tightening torque.

If you need the linear-motion equivalents of work or power, use the Work Calculator or Mechanical Power Calculator.

How to use this Torque calculator

  1. Enter the lever arm length — the distance from the pivot point to where the force is applied, in meters.

  2. Enter the force — the magnitude of the applied force, in newtons.

  3. Enter the angle — the angle between the force direction and the lever arm, in degrees (90° for the default perpendicular case).

  4. Read the torque result — the highlighted result shows the torque in newton-meters.

  5. Check the step-by-step breakdown — expand the calculation steps to see the exact formula substitution, and compare with the Bolt Torque Calculator if your specific application involves fastener tightening specs.

Formula & Methodology

Torque formula:
τ = r × F × sin(θ)

Variable definitions:
- r — lever arm length (meters)
- F — applied force (newtons)
- θ — angle between force and lever arm (degrees)
- τ — torque (newton-meters)

Worked example:

A 0.3 m wrench has 80 N of force applied perpendicular to it (θ = 90°).

Step 1 — Apply the formula: τ = 0.3 m × 80 N × sin(90°) = 0.3 × 80 × 1 = 24 N·m

This means 24 newton-meters of torque are applied — enough to tighten many standard bolts, though the exact required torque depends on the bolt's size and material specification (see the Bolt Torque Calculator for that specialized use case).

Note: This calculator computes the torque from a single applied force. Real-world systems with multiple forces or a distributed load require summing the torque contributions from each force separately.

Frequently Asked Questions

Torque is calculated as τ = r × F × sin(θ), where r is the lever arm length in meters, F is the applied force in newtons, and θ is the angle between the force direction and the lever arm. The result is expressed in newton-meters (N·m). This calculator applies that formula directly to whatever values you enter.
Only the component of force perpendicular to the lever arm produces rotation — the sin(θ) term accounts for this. When force is applied exactly perpendicular to the lever arm (θ = 90°), sin(θ) = 1 and the full force contributes to torque, which is the most efficient angle. When force is applied along the lever arm (θ = 0°), sin(θ) = 0 and no torque is produced at all.
90° represents the most common and most efficient scenario — force applied perpendicular to the lever arm, such as pushing straight down on a wrench handle. This maximizes torque for a given force and lever arm length, which is why tools are typically designed and used this way.
This calculator computes general rotational torque (τ = r × F × sin(θ)) for any lever-arm-and-force scenario in physics or engineering. The [Bolt Torque Calculator](/bolt-torque-calculator/) is a specialized fastener-spec tool that determines the correct tightening torque for specific bolt sizes and grades, which is a different application entirely.
Lever arm length is entered in meters (m), force in newtons (N), and angle in degrees (°), producing torque in newton-meters (N·m) — the SI unit of torque. If your measurements are in other units, convert them to meters and newtons first for an accurate result.
Tightening a typical bolt might require 20–50 N·m of torque, opening a stubborn jar lid might involve a few N·m applied at the lid's small radius, and a car engine might produce 200–400 N·m of torque at its crankshaft — illustrating the wide range of torque values in daily life and engineering.
Torque increases linearly with lever arm length for a fixed force and angle — doubling the lever arm doubles the torque. This is why a longer wrench or breaker bar makes it easier to loosen a stuck bolt: the same hand force applied farther from the pivot point produces more torque.
In rotational motion, torque plays a role analogous to force in linear motion — rotational work equals torque multiplied by angular displacement, and rotational power equals torque multiplied by angular velocity. Compare with the [Work Calculator](/work-calculator/) and [Mechanical Power Calculator](/mechanical-power-calculator/) for the linear-motion equivalents.
Yes — many real-world scenarios involve force applied at an angle other than perpendicular to the lever arm, such as pushing on a wrench handle at a slight angle rather than straight down. This calculator's sin(θ) term correctly reduces the effective torque in those cases.
Torque calculations are fundamental to motor and engine specifications (torque curves define usable power across speeds), gear system design (torque changes as gears change speed ratios), fastener tightening specifications, and any rotating machinery from wind turbines to power tools.
Force is a straightforward push or pull measured in newtons, while torque is the rotational effect of a force applied at a distance from a pivot point, measured in newton-meters. The same force can produce very different torque depending on how far from the pivot it's applied and at what angle.
To maximize torque for a given force, apply it at the longest practical lever arm length and at exactly 90° to that lever arm (perpendicular), since both a longer lever arm and a 90° angle increase the resulting torque, as shown directly in the τ = r × F × sin(θ) formula.
Also known as
torque formula calculatorrotational force calculatormoment of force calculatorlever arm torque calculatortau = rF sin theta calculator