Torque Calculatorτ = rF sin θ · N·m and lb·ft
Torque is the turning effect of a force: τ = rF sin θ, the force times its perpendicular distance from the pivot. Get torque in N·m and lb·ft from a force and lever arm, find an engine’s torque from its power and rpm, or work out how hard to pull a wrench to hit a torque spec on a wheel nut.
Formula verified against OpenStax — University Physics, Volume 1 · HyperPhysics, Georgia State University
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Torque inputs
θ is the angle between the wrench (lever arm) and the force. 90° gives the most torque.
Step-by-step working
What is torque?
Torque is the rotational equivalent of force: a measure of how strongly a force tends to twist an object about an axis. It depends on how hard you push, how far from the pivot you push, and at what angle.
Torque explains why door handles sit far from the hinges, why long wrenches loosen stubborn bolts, and why engine specs quote torque as well as horsepower.
Quick answers
How do you calculate torque from force and distance?
Multiply the force by the perpendicular distance from the pivot: τ = F × r. Pushing a 0.8 m-wide door at its handle with 20 N gives 16 N·m.
How do I convert N·m to lb·ft?
Multiply by 0.7376. So 200 N·m ≈ 147.5 lb·ft. To go back, multiply lb·ft by 1.3558.
How do you calculate torque from horsepower and rpm?
lb·ft = hp × 5,252 ÷ rpm, or in SI, τ = P ÷ ω. 300 hp at 5,252 rpm is exactly 300 lb·ft (406.7 N·m). The horsepower calculator runs it the other way.
Why does a longer wrench make bolts easier to undo?
Torque grows with the lever arm. Doubling the length halves the force you need for the same torque, which is why mechanics slip a pipe over a breaker bar.
Torque formula
1 N·m = 0.7376 lb·ft. ω must be in rad/s for τ = P ÷ ω.
| Symbol | Meaning | SI unit |
|---|---|---|
| τ | Torque | N·m |
| r | Lever arm (distance from pivot) | m |
| F | Applied force | N |
| θ | Angle between lever arm and force | ° |
| P | Power | W |
| ω | Angular velocity | rad/s |
How to calculate torque
- Measure the lever arm from the centre of rotation to where the force is applied.
- Find the angle between the arm and the force (90° if you push straight across).
- Multiply r × F × sin θ.
- Convert if needed: N·m × 0.7376 = lb·ft.
Worked example: tightening a wheel nut
A wheel nut needs 120 N·m and your wrench is 45 cm long. How hard must you push at right angles?
≈ 60 lbf, the force of a 27.2 kg mass hanging from the handle
An engine making 100 kW at 4,000 rpm produces τ = 100,000 ÷ (4,000 × 2π ÷ 60) = 238.7 N·m (176 lb·ft) at that speed.
Typical torque values
Approximate figures for orientation.
| Application | Torque (N·m) | Torque (lb·ft) |
|---|---|---|
| Opening a jar lid | ≈ 1–3 | ≈ 0.7–2 |
| Bicycle stem bolt | 5–6 | 3.7–4.4 |
| Car wheel nut | 80–140 | 59–103 |
| Family-car engine (peak) | 150–300 | 110–220 |
| Electric car motor (peak) | 300–700 | 220–515 |
| Large truck engine (peak) | 2,000–3,000 | 1,475–2,200 |
Common mistakes to avoid
- Using the wrench’s full length when you grip the middle. r is the distance to where the force actually acts.
- Ignoring the angle. Pushing at 45° gives only 71% of the torque.
- Using rpm directly in τ = P ÷ ω. Convert to rad/s first (× 2π ÷ 60).
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Torque Calculator: frequently asked questions
τ = rF sin θ, where r is the lever arm, F the force and θ the angle between them. With a perpendicular force it simplifies to τ = rF.
Newton-metres (N·m) in SI. In the US, pound-feet (lb·ft) and pound-inches (lb·in) are common.
No, though both can be written N·m. Torque is a turning force (a vector), while work is energy (a scalar), usually written in joules.
Power = torque × angular velocity. In US units, hp = lb·ft × rpm ÷ 5,252.
90°, where sin θ = 1. A force pushed along the line of the lever arm (0° or 180°) produces no torque.
References & sources
- OpenStax — University Physics, Volume 1 — Ch. 10.6, Torque
- HyperPhysics, Georgia State University — torque and rotational work
- NIST Special Publication 811 — Guide for the Use of the SI — conversion factors for lbf·ft
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.