Torque Calculator
The turning price of a force: τ = F·r·sinθ, where the angle decides how much of your pull actually twists — and why long wrenches and distant door handles are the same bargain.
Torque Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Magnitude only — rotation direction is a sign this page strips
- Rigid arm, point force; no friction at the pivot
In short: Push 150 N on a 0.3 m wrench at 90°: τ = 150 × 0.3 × 1 = 45.000000 N·m (33.190297 lbf·ft). The angle is the leverage: at 30° the same push twists only 22.500000 N·m, and along the arm (0°) it turns NOTHING — pulling along the wrench is expensive posture, not torque. The balance card translates: 45 N·m would hold 15.295743 kg hanging at the same radius, because torque is what seesaws price in. This is the whole reason door handles live far from hinges and breaker bars exist: the force is what you have; the radius is what you choose.
Formula
τ = F·r·sinθ · balance: m = τ/(g·r) · 1 lbf·ft = 0.45359237 × 9.80665 × 0.3048 N·m
Torque is force's rotational currency: the component of force perpendicular to the arm, times the arm. The sinθ keeps only the twisting share — at 90° everything twists, along the arm nothing does. The balance card converts torque into the hanging mass that would fight it at the same radius, which is what a see-saw, a beam balance and a torque wrench all measure.
Worked Example
- Enter the force and the arm from the axis to where it acts.
- Set the angle between them — usually 90° on a wrench held square.
- Read torque in N·m (and lbf·ft, derived from the exact pound).
- Read the balance card before choosing a shorter tool: the radius is the purchase.
Defaults: 45.000000 N·m at 90°; 22.500000 at 30°; zero along the arm. Same torque balances 15.295743 kg at 0.3 m — or 7.647872 kg at 0.6 m, because the far side's radius does the scaling.
Strengths & Limits Of This Model
Where this engine is strong
- Balance card converts twist to the hanging mass it holds
- lbf·ft derived from exact definitions
Where it stops
- No rotational dynamics (τ = Iα) on this page
- No compound levers or gear trains
Practical Use Cases
Workshop
wrench settings and breaker-bar honesty
Engineering
actuator sizing against a load arm
Teaching
why the see-saw balances, with numbers
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Torque Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does a longer wrench loosen the same bolt?
Because torque multiplies the arm: the same grip at 0.6 m twists twice what it does at 0.3 m. The bolt does not know how hard you pushed — only how much twist arrived, and the radius is half the product. Breaker bars are not cheating; they are the law, applied honestly.
Why do door handles sit far from the hinge?
Maximum arm. Every centimetre of width is a multiplier on whatever push you spare, and near the hinge the arm — and the twist you can buy — collapses toward zero. The page's leverage card is that doorway, priced.
What does the angle actually do?
sinθ keeps the twisting component: at 90° the full force turns, at 30° half of it, along the arm none. Pulling along the wrench loads your wrists and turns nothing — the page prints the zero so the posture has a price tag.
Is torque energy? Both use force times distance.
No, and the unit naming keeps the border: torque is newton-METRES, energy is NEWTON-metres called joules. Work needs force along a DISPLACEMENT; torque is force against an ARM with nothing moved. A stuck bolt absorbs your torque all day and banks zero joules.
What does the balance card mean physically?
A see-saw balances when the torques match: m·g·d on one side equals your τ on the other. The card prices the hanging mass that would exactly fight your twist at the same radius — 15.295743 kg here. It is why a child can lift an adult on a see-saw given the longer arm.
Why quote lbf·ft as well?
Because workshop torque wrenches are sold in it. The conversion is derived live from the exact pound and foot — 0.45359237 × 9.80665 × 0.3048 — so the digits are definitions, not a rounding somebody remembered.
Where does the sign of torque go?
This page prices magnitude; direction (clockwise vs counter-clockwise) is a bookkeeping sign the same law carries. Two opposing torques on one shaft cancel exactly like opposing forces — the rotational ledger keeps signs for the same reason the momentum page does.
How does this connect to moment of inertia?
As force connects to mass: τ = I·α is the rotational second law, where I (the moment of inertia page, later in the category) prices how stubborn the spinning mass is. Torque is the cause; spin-up is the effect; this page prices the cause.