Pulley Speed Calculator
The belt drive's speed trade: driven rpm from the diameter ratio, the belt's linear speed at the rim, and the torque inverse that pays for it.
Pulley Speed Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Two-pulley open belt; no idlers or multi-stage
- Ideal torque — slip and losses not priced
In short: A 100 mm driver turning 1,800 rpm belts a 200 mm driven pulley to 900.000000 rpm — the ratio D1/D2 halves the speed and, in the same breath, doubles the ideal torque, because power is the conserved thing and speed is what gets sold. The belt itself runs at 9.424778 m/s at the driver rim — π·D·N/60 — comfortably inside the classical V-belt range where centrifugal force has not yet begun lifting the belt off its grip.
Formula
N₂ = N₁ × D₁/D₂ ··· v = π·D·N/60 ··· torque × = D₂/D₁ (ideal)
A belt drive is a friction gear: the rim speed of one pulley is the rim speed of the other, so speed trades inversely with diameter and torque trades the other way. The arithmetic is conservation dressed in a v-belt; slip (one to two percent honest) and the wrap angle are the corrections reality adds.
Worked Example
- Enter the driver diameter and its rpm.
- Enter the driven pulley diameter.
- Read the driven speed and the torque trade.
- Check the belt speed stays in the sane range.
Defaults: 100 mm at 1,800 rpm driving 200 mm → 900.000000 rpm, ratio 2:1, belt 9.424778 m/s. The overdrive check: swap the diameters — 3,600.000000 rpm at the driven shaft, torque halved. Same belt, opposite trade.
Strengths & Limits Of This Model
Where this engine is strong
- Speed and torque trade in one read
- Belt speed checked beside the ratio
Where it stops
- No wrap-angle capacity model
- No belt-section selection
Practical Use Cases
Motor matching
fan and pump speed setting
Conveyor drives
torque at the drum
Teaching
the conservation with a belt
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.
Pulley Speed Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does a bigger driven pulley slow the output?
Because both pulleys share one belt, and the belt moves at one linear speed: a larger circumference unwinds that speed more slowly in rotations. Diameter is the exchange rate between belt metres and shaft turns, so doubling the driven diameter halves the driven rpm — and the torque doubles in the same handshake, since power on each shaft is the same power.
What does the belt speed tell me?
It is the rim speed — π·D·N/60 — and every part of the drive lives with it: centrifugal force grows with its square, lifting the belt off the pulley and starving the grip at high speed. Classical V-belts are happy near the default's 9.424778 m/s; past roughly 25–30 m/s the design conversation changes to cogs or timing belts. The card exists so speed is checked, not assumed.
How much slip should I budget?
One to two percent for a properly tensioned V-belt is the honest allowance — belt creep through the arc of contact, not the squeal of a loose drive. Squeal is tension or alignment speaking, not arithmetic. If the driven speed must be exact, budget the slip explicitly or move to a toothed belt, which refuses to slip by construction.
Is torque really multiplied exactly by the ratio?
Ideally yes — torque ratio equals D₂/D₁, the mirror of the speed ratio, because power is torque times speed and the belt does not mint power. Real drives pay bearing and belt losses of a few percent, which the ideal card ignores by design. The number is the promise; the coupling collects the tax, and the pump power page prices that kind of tax elsewhere.
Why is the single-stage ratio capped near 6:1?
Because the small pulley's arc of contact shrinks as the ratio grows, and grip lives in that arc — below roughly 120 degrees of wrap the belt starts surrendering under load. Big ratios want two stages in series, each keeping its wrap, or a flat idler pushing the belt onto the small pulley. The ratio is free; the wrap is the currency that buys it.
Can I mix units — inches for one pulley?
The ratio cancels units only when BOTH diameters use the same unit: the formula reads D₁/D₂ and any consistent stick works, millimetres or inches alike. The belt speed card is different — it assumes millimetres to produce m/s. Enter both diameters in one unit and the speed trade is unit-blind; only the linear speed cares.
What if the driven pulley is the SMALLER one?
Then the drive is an overdrive: the driven shaft spins faster than the motor and the available torque drops by the same factor. The page names the trade either way — reduction is slower and stronger, overdrive faster and weaker — because the belt does not know which direction the designer intended, only which pulley is bigger.
How does this differ from the gear page?
The belt trades speed by DIAMETER through friction; the gear page trades it by TEETH through positive interlock. The arithmetic rhyme is exact — ratio in, speed divided, torque multiplied — but the belt can slip a percent and needs its wrap angle, while the gear cannot slip and instead carries mesh efficiency. Same conservation, two different contracts with reality.