Pulley and Belt Calculator
Solve pulley diameters or rpm, then get belt speed, exact and approximate open-belt length, wrap angle on the small pulley and centre distance from a belt length.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Pulley and Belt Calculator?
A two-pulley belt drive is defined by four numbers: the diameter and speed of each pulley. Because the belt moves at one speed, driver diameter times driver rpm equals driven diameter times driven rpm. A 100 mm motor pulley at 1,750 rpm driving a 250 mm pulley turns it at 700 rpm. This calculator solves whichever of the four you leave out, with an optional slip allowance for friction belts.
It then works out the geometry that a parts catalogue asks for: the belt length for a given centre distance, using both the exact formula and the short approximation most handbooks print, or the centre distance for a belt you already have. It also gives the belt speed and the wrap angle on the small pulley, the two numbers that decide whether a friction belt will grip.
Units can be millimetres or inches. Switching converts the diameters, centre distance and belt length you already entered, and speeds stay in rpm.
- Solves driver or driven diameter or speed, with optional slip
- Exact open-belt length and the handbook approximation side by side
- Centre distance from belt length, solved exactly and by the closed-form inverse
- Wrap angle on both pulleys, belt speed in m/s and ft/min, crossed-belt length
- Millimetres or inches with in-place conversion; copy and share
How to use the Pulley and Belt Calculator
- Choose millimetres or inches, then choose which of the four values to solve for.
- Enter the other three: driver diameter and rpm, driven diameter and rpm. Add a slip percentage for V or flat belts if you want the real driven speed.
- Pick Belt length from centres and enter the centre distance, or Centres from belt length and enter the belt's pitch length.
- Read the solved value, speed ratio, belt speed, belt length (exact and approximate) or centre distance, and the wrap angles.
- Watch the warnings: wrap below 120 degrees, overlapping pulleys, or belt speed above 30 m/s.
Worked examples
Motor to fan reduction (page default)
Input
100 mm at 1,750 rpm driving 250 mm; centres 500 mm
Output
Driven 700 rpm; belt 9.16 m/s; length 1,561.05 mm exact, 1,561.03 mm approx.; wrap 162.7°
A 2.5 : 1 reduction with comfortable wrap. Pick the nearest stock belt length and use the Centres from belt length mode to find where the motor must sit.
Centre distance for a stock belt
Input
Same pulleys, 1,600 mm belt
Output
Centre distance 519.69 mm exact, 519.70 mm from the closed-form approximation
Allow adjustment either side of this for fitting the belt and for tensioning.
Inch drive on a workshop machine
Input
4 in pulley at 1,725 rpm driving 10 in; 20 in centres
Output
Driven 690 rpm; belt 1,806 ft/min; belt length 62.44 in
Belt speed in feet per minute is what V-belt rating tables use. Around 4,000 to 5,000 ft/min is often the most efficient range for classical V-belts.
Large ratio, short centres
Input
80 mm and 400 mm pulleys at 300 mm centres
Output
Exact 1,441.5 mm vs approximation 1,439.3 mm; wrap on small pulley 115.5°
Here the approximation is 2.2 mm short and the wrap angle is below 120 degrees, so a friction belt would need more tension or an idler to stop slipping.
Background and insight
For an open (uncrossed) belt the straight spans are tangent to both pulleys. With large diameter D, small diameter d and centre distance C, each span makes an angle φ = asin((D − d) / 2C) with the line of centres. The belt wraps π − 2φ radians of the small pulley and π + 2φ of the large one, so the exact pitch length is L = 2√(C² − ((D − d)/2)²) + π(D + d)/2 + (D − d)φ. This is the form in Shigley's Mechanical Engineering Design, Table 17-2.
Replacing the square root and the arcsine with the first terms of their series gives the approximation L ≈ 2C + π(D + d)/2 + (D − d)² / 4C found in Machinery's Handbook and most belt catalogues. For ordinary drives it is within a fraction of a millimetre: the default 100 and 250 mm pulleys at 500 mm centres give 1,561.05 mm exact and 1,561.03 mm approximate. The gap grows as the diameter difference approaches the centre distance, which is why the calculator shows both.
Belt makers rate drives using pitch diameters and pitch length, measured at the belt's neutral layer. For V-belts that is a little inside the sheave's outside diameter; for timing belts it is the tooth pitch line. Friction belts also creep, typically 1 to 3%, so the driven pulley runs slightly slower than the ideal ratio; timing belts do not slip.
Common use cases
Changing a machine speed
Find the pulley size that gives a target spindle, fan or pump speed from a fixed motor speed.
Ordering a replacement belt
Measure the pulleys and centre distance and get the pitch length to look up in a catalogue.
Laying out a new drive
Work back from a stock belt length to the motor position, and check wrap angle before welding a base.
Checking belt speed
Confirm the belt runs inside the manufacturer's speed limit and in its efficient range.
Tips and limitations
- Measure V-belt pulleys at the pitch diameter, not across the outer rims. Using the outside diameter overstates the ratio slightly and the belt length noticeably.
- Keep the wrap on the small pulley above about 120 degrees for friction belts. Below that, use longer centres or a backside idler.
- A common rule of thumb is a centre distance between the larger pulley diameter and three times the sum of the diameters.
- Allow tensioning travel of a few percent of the belt length, plus extra to slip the belt on without prying it over the flange.
- For timing belts the length must be a whole number of teeth; round the calculated pitch length to the nearest stock size and recompute the centres.
Frequently asked questions
How do you calculate pulley rpm?
Driven rpm = driver rpm x driver diameter / driven diameter. A 100 mm pulley at 1,750 rpm driving a 250 mm pulley gives 1,750 x 100 / 250 = 700 rpm, a little less with a slipping friction belt.
What is the formula for belt length between two pulleys?
The approximation is L = 2C + π(D + d)/2 + (D − d)² / 4C, with C the centre distance. The exact open-belt formula replaces the first and last terms with 2√(C² − ((D − d)/2)²) + (D − d) x asin((D − d)/2C). For typical drives they agree within a millimetre.
How do I find the centre distance from the belt length?
Rearranging the approximation gives C = [b + √(b² − 32(D − d)²)] / 16, with b = 4L − 2π(D + d). The calculator also solves the exact formula numerically and shows both.
What is belt wrap angle and why does it matter?
It is the arc of contact on a pulley. On the small pulley it is 180° − 2 asin((D − d)/2C). Less wrap means less grip, so friction belts below about 120 degrees tend to slip unless tension is raised or an idler adds contact.
How fast should a V-belt run?
Classical V-belts typically perform best around 20 to 25 m/s (about 4,000 to 5,000 ft/min). Standard cast iron sheaves are usually limited to roughly 30 to 33 m/s (6,000 to 6,500 ft/min) rim speed. Narrow and cogged belts may allow more. Check the maker's rating tables for your section.
Should I use outside diameter or pitch diameter?
Pitch diameter. For V-belts it is the diameter at the belt's neutral layer, slightly inside the rim; catalogues list it for each sheave. Timing pulleys list it too, and it is larger than the tooth tip diameter.
Is there an in-depth guide to the Pulley and Belt Calculator?
Yes. “Belt Length and Pulley Speed Formulas, Derived and Checked” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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