Torque Calculator
Calculate Torque values for science, physics, chemistry, and engineering problems.
This torque calculator finds the rotational force (torque) produced when a force is applied at a distance from a pivot point, accounting for the angle at which the force is applied.
Enter the force, distance from the pivot, and angle, and the calculator returns the resulting torque.
Worked Calculation Examples
| Scenario | Result | Calculation Step |
|---|---|---|
| Force 50 N, lever arm 0.3 m, applied perpendicular (90°) | τ = 15 N·m | τ = 50 × 0.3 × sin(90°) = 50 × 0.3 × 1 = 15 N·m. |
| Force 80 N, lever arm 0.5 m, applied at 30° | τ = 20 N·m | τ = 80 × 0.5 × sin(30°) = 80 × 0.5 × 0.5 = 20 N·m - less torque than the perpendicular example despite a larger force, since the angle is less efficient. |
The Torque Formula
Torque = force x distance x sin(angle), where distance is the length of the lever arm from the pivot point to where force is applied, and angle is measured between the force direction and the lever arm. Torque is maximized when force is applied perpendicular to the lever arm (angle = 90 degrees, where sin = 1).
Why a Longer Lever Arm Increases Torque
For the same applied force, a longer lever arm produces more torque - this is the entire principle behind using a wrench instead of your fingers to loosen a bolt, or why door handles are placed far from the hinge rather than close to it.
How to Use the Torque Calculator
- Open the Torque Calculator and enter the values requested in the input fields.
- Check the units, percentages, dates, or time periods before reading the answer.
- Review the instant result and adjust any value to compare another scenario.
- Use the formula, example, and FAQs below to understand how the torque calculator works.
Frequently Asked Questions
What is the formula for torque?
Torque = force x distance x sin(angle), where distance is the lever arm length and angle is between the applied force and the lever arm.
When is torque maximized?
Torque is maximized when the force is applied perpendicular to the lever arm (a 90-degree angle), since sin(90°) = 1, the largest possible value for the sine function.
Why does a longer wrench make it easier to loosen a bolt?
A longer wrench increases the lever arm distance, which produces more torque for the same amount of applied force, making it easier to overcome the bolt's resistance.
How do I use this torque calculator?
Enter the known values, review the units or settings, and the calculator updates the result instantly. The formula and example on this page show how the answer is produced.
What does the Torque Calculator calculate?
Calculate Torque values for science, physics, chemistry, and engineering problems. It is designed for fast browser-based calculations without sign-up, downloads, or manual spreadsheet setup.
What formula does this torque use?
The formula is: τ = F × d × sin(θ). The lever principle behind torque was understood as early as Archimedes, who is credited with the (likely exaggerated, but illustrative) claim 'give me a lever long enough and a place to stand, and I will move the world.' Formalized within Newtonian mechanics, torque became the rotational analog of force, essential to understanding everything from a simple wrench turning a bolt to the rotational dynamics engineers calculate for engines, turbines, and machinery.
Related Calculators
Density Calculator
Calculate Density values for science, physics, chemistry, and engineering problems.
Force Calculator
Calculate Force values for science, physics, chemistry, and engineering problems.
Work Calculator
Calculate Work values for science, physics, chemistry, and engineering problems.
Kinetic Energy Calculator
Calculate Kinetic Energy values for science, physics, chemistry, and engineering problems.
Molarity Calculator
Calculate Molarity values for science, physics, chemistry, and engineering problems.
Dilution Calculator
Calculate Dilution values for science, physics, chemistry, and engineering problems.
Last updated: September 27, 2026.