Torque Calculator helps you compute how strongly a force turns something. You use it to convert between N·m, lb·ft, and in·lb, and to calculate missing values like force or lever arm when you know the other inputs.
This guide explains the torque formula, what each variable means, and how to choose correct units. It also includes practical examples and a quick FAQ for the most common questions.
What Is Torque?
Torque is the rotational effect of a force. If you push a wrench farther from the bolt, you usually get more turning force even with the same push. That “turning strength” is torque.
In physics, torque depends on three things:
- Force applied (how hard you push or pull)
- Lever arm distance from the pivot to where the force acts
- Angle between the force direction and the lever arm
Torque Formula (Core Concepts)
The most common torque equation is:
τ = r · F · sin(θ)
- τ = torque
- r = lever arm (distance from pivot to point of force application)
- F = force
- θ = angle between force and lever arm
When the force is applied perpendicular to the lever arm, θ = 90°, so sin(90°) = 1 and the formula simplifies to:
τ = r · F
Common Torque Units (and What They Mean)
Torque units combine a force unit with a distance unit. The most widely used units are:
| Unit | Meaning | Typical Use |
|---|---|---|
| N·m | Newtons × meters | Engineering, automotive specs |
| lb·ft | Pounds-force × feet | US automotive, mechanical work |
| in·lb | Pounds-force × inches | Small fasteners, tools |
A Torque Calculator should convert units consistently so you don’t mix inches with feet or newtons with pounds.
How the Torque Calculator Works
This Torque Calculator computes torque from force and lever arm, using the angle term. It also supports computing torque in multiple unit systems.
Inputs you typically need:
- Force (F) and its unit (N or lbf)
- Lever arm (r) and its unit (m, ft, or in)
- Angle (θ) in degrees (default 90° for perpendicular force)
Output:
- Torque (τ) in your selected torque unit (N·m, lb·ft, or in·lb)
Angle Matters: Perpendicular vs. Non-Perpendicular Force
Torque depends on the effective component of force that causes rotation. The term sin(θ) captures that.
- If θ = 90°, sin(θ) = 1 → maximum torque for that force and lever arm.
- If θ = 0°, sin(θ) = 0 → no torque (force goes straight toward/away from the pivot).
- If θ is between 0° and 90°, you get partial torque.
In real jobs, the force direction may not be perfectly perpendicular. Using the angle input makes your estimate more accurate.
Step-by-Step: Using the Torque Calculator
- Choose your force unit (Newtons or pounds-force).
- Enter the lever arm distance from the pivot to where the force is applied.
- Set the angle θ between the force direction and the lever arm.
- Select the output torque unit you want.
- Read the computed torque result.
If you only know that the force is perpendicular to the lever arm, set θ to 90° and the calculator will simplify to τ = r·F.
Practical Examples (Real-World Use Cases)
Example 1: Tightening a Bolt with a Wrench
Suppose you apply a force of 400 N using a wrench that is 0.30 m long, and the force is perpendicular to the wrench handle (θ = 90°). The torque is:
τ = r·F·sin(90°) = 0.30 · 400 · 1 = 120 N·m
You could then convert that to lb·ft if your vehicle manual lists torque in US units.
Example 2: Estimating Torque from a Motor and Load
A motor applies a rotational force equivalent to a certain torque. If you know the effective lever arm and the force component at the contact point, you can estimate the torque needed.
For instance, if a mechanism applies 250 lbf at a lever arm of 2.0 ft with a 60° angle, then:
τ = r·F·sin(60°) = 2.0 · 250 · 0.866 ≈ 433 lb·ft
This helps compare your setup against design targets or safety limits.
Common Mistakes to Avoid
- Mixing units: inches with feet, or lbf with N, without converting.
- Forgetting the angle: using τ = r·F when the force is not perpendicular.
- Using the wrong lever arm: the lever arm is measured from the pivot to the line of action of the force (or the point where the force effectively acts).
- Confusing torque with power: torque is a rotational force; power is how fast work is done.
Frequently Asked Questions
What is the formula for torque in a Torque Calculator?
Most torque calculators use τ = r · F · sin(θ). Here τ is torque, r is the lever arm distance from the pivot, F is the applied force, and θ is the angle between the force direction and the lever arm. If θ = 90°, sin(θ) = 1.
When should I use sin(θ) instead of τ = r · F?
Use sin(θ) when the force is not perpendicular to the lever arm. If the force is perpendicular, θ = 90° and sin(θ) equals 1, so τ = r · F matches the full equation. When θ is unknown, assume perpendicular only if that’s physically true.
How do I convert N·m to lb·ft?
Convert using a fixed unit ratio: 1 N·m ≈ 0.73756 lb·ft. If your calculator outputs N·m, multiply by 0.73756 to get lb·ft. Reverse it for lb·ft to N·m by dividing by 0.73756. Always keep consistent torque units.
What units can I enter for force and lever arm?
Torque uses a force unit and a distance unit. You can enter force in N or lbf, and lever arm in meters, feet, or inches. The calculator combines them correctly and then reports torque in your chosen unit. Avoid mixing distance units unless you convert.
Why does my torque result look too high or too low?
Most errors come from angle and lever arm assumptions. If you used θ = 90° but the force is angled, torque will be overestimated. If you measured the lever arm from the wrong point, r will be wrong. Also check that you didn’t mix inches and feet.