What this calculator does
The Belt & Pulley Calculator solves the everyday belt-drive questions in a workshop: how long a belt you need to span two pulleys of known diameter at a given center distance, how fast the driven pulley will turn, how fast the belt itself travels, and what the speed ratio of the drive is.
It works for open (uncrossed) belt drives — flat belts, V-belts on stepped pulleys, and timing belts alike — in metric millimeters or imperial inches, entirely in your browser.
How to use the Belt & Pulley Calculator
- Choose the unit system: millimeters or inches. All dimensions use the same unit.
- Enter the driver pulley diameter D1 (the pulley attached to the motor) and the driven pulley diameter D2.
- Enter the center distance C — the distance between the two pulley shafts. It should be comfortably larger than half the sum of the diameters, otherwise the pulleys will collide.
- Optionally enter the driver speed in RPM to get the driven speed, the ratio, and the belt speed.
- Click "Calculate" to see the belt length and, if a speed was given, the drive data.
Formulas
The belt-length formula is the classic open-belt approximation, accurate for equal and unequal pulleys whenever the wrap angles are large — which is the case in normal drives. Because belts are sold in standard nominal lengths, round the result to the nearest available size and adjust the center distance with the tensioner or slotted mounts.
Examples
- A motor pulley of 100 mm driving a pulley of 200 mm at a center distance of 500 mm: L = 2 × 500 + (π/2) × 300 + (100² ÷ 2000) ≈ 1,476 mm — order a nominal 1,500 mm belt and take up the slack with the tensioner.
- With the motor running at 1,450 RPM: the driven pulley turns at 1,450 × 100 ÷ 200 = 725 RPM (ratio 2 : 1), and the belt speed is π × 0.1 m × 1,450 ÷ 60 ≈ 7.6 m/s — well within the limit of a standard V-belt (below about 30 m/s).
- In inches: a 2" pulley driving a 4" pulley at 20" center distance: L = 40 + (π/2) × 6 + (2² ÷ 80) ≈ 49.5 inches; at 3,450 RPM the small pulley drives the large one at 1,725 RPM.
Frequently asked questions
Does this work for V-belts and timing belts?
Yes, with a caveat. The geometry (length, speeds, ratio) is the same for any open belt. For actual purchasing, though, use the pitch or outside diameter relevant to your belt type: V-belts are specified by their effective width profile (A, B, SPZ...), and timing belts need the pulley's pitch diameter and tooth pitch, since the teeth must mesh exactly.
What about crossed belts?
For a crossed (figure-eight) drive, which reverses the rotation direction, the length is L = 2C + (π/2) × (D1 + D2) + (D1 + D2)² ÷ (4C) — the last term uses the sum instead of the difference, so crossed belts are always longer.
Why is the driven pulley speed exact but the belt speed approximate?
The speed ratio follows strictly from the pitch diameters, so for equal contact (no slip) it is exact. The belt speed uses the driver diameter, and small differences between nominal and pitch diameter, plus possible slip of a few percent under load, make real values slightly different.
How much tension and center distance should I use?
Keep the center distance at least as large as the larger pulley diameter, and preferably between one and two times (D1 + D2). Too short a distance means small wrap angles and slipping; too long a belt flaps and wastes energy. Provide a tension adjustment of at least 2–3% of the belt length.
Can I use it for more than two pulleys?
No — the formula covers a single two-pulley span. For multi-pulley (serpentine) layouts, compute each straight segment and each arc between contact points, or measure the old belt path with a string.
Is my data saved or sent anywhere?
No. Every calculation runs in your browser, and nothing you type is stored or sent to a server.
Related calculators
Other free calculators commonly used with this tool: Gear Ratio Calculator, Bolt Torque Calculator, and Cutting Speed & Feed Calculator.
Want a deeper walkthrough? Read our belt length guide.