01
Formula
Length = 2C + π(D + d) ÷ 2 + (D − d)² ÷ (4C).
Driven RPM = driver RPM × driver diameter ÷ driven diameter. The pulley calculator uses the large pulley as the driver.
Apply for financingBelt length
Belt length calculator and pulley calculator
This belt length calculator estimates an open belt around two pulleys from the center distance and the two diameters. The pulley calculator on the same card is the ratio and the driven RPM. The large pulley is treated as the driver in the speed line. It is the standard open-belt approximation, not a catalog belt number.
Belt length
78.98in
Ratio2.00
Driven RPM3,500
Driver RPM1,750
Planning estimate from the numbers you enter. Coverage, density, waste and price are assumptions, not a supplier quote or an engineering specification.
How it works
Length is twice the center distance, plus half a turn of each pulley, plus a small correction.
Belt length equals 2 times the center distance, plus pi times the sum of the diameters divided by 2, plus the square of the diameter difference divided by 4 times the center distance. All of those lengths share one unit. Thirty inches between centers, an 8 inch pulley, and a 4 inch pulley give a belt of 78.98 inches. The ratio is 2.00. If the 8 inch pulley turns at 1,750 RPM, the 4 inch pulley turns at 3,500 RPM. A crossed belt or a serpentine path with an idler is a different length. Match a stock belt to the nearest size and then move the center distance to fit. Do not assume the formula's hundredth of an inch is a belt you can buy.
02
Example
30 inch centers, 8 inch and 4 inch pulleys, 1,750 RPM.
Belt length is 78.98 inches. Ratio is 2.00. Driven speed is 3,500 RPM. Swap which pulley is the driver in your head if the small one is actually driving. The ratio is the same. The direction of the speed change is not.
03
Tips
Diameters are pitch diameters when you know them.
An outside diameter is a little larger than the pitch diameter a belt runs on. For a planning length, outside diameter is close. For a high-speed drive, use the pitch diameter the belt maker specifies.
04
Equipment
The driven machine is the purchase.
Dengaro arranges financing for shop equipment. Belt length is not a loan amount.
Important questions
Know what to expect.
Is this a v-belt part number?+
No. It is a pitch length estimate for an open belt. Manufacturers use their own numbering. Pick the closest stock belt and adjust the center distance.
What if the belt is crossed?+
Do not use this belt length calculator for a crossed belt. The wrap angles change. The page assumes an open belt.
Which pulley is the driver?+
The speed line treats the large pulley as the driver, so the small pulley spins faster. If your motor is on the small pulley, the driven speed is lower. Divide instead of multiply.
Do both pulleys need the same units?+
Yes. Inches with inches, or millimeters with millimeters. The RPM math uses the ratio, so the unit cancels there, but the belt length unit is the unit you typed.
Financing built into the sale