Calculate belt length, pulley diameters, or spacing by entering any 3 values in inches, feet, cm, or m for two pulleys and belt runs.
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Belt Length Formula
The calculator uses the standard approximate open-belt length formula when you solve for belt length from two pulley diameters and the center-to-center distance.
BL = (pi/2)*(D + d) + 2*C + ((D - d)^2)/(4*C)
When solving for the length between pulleys, the calculator uses this rearranged form:
C = (BL - (pi/2)*(D + d))/2
When solving for a missing pulley diameter, the calculator estimates the missing diameter from the belt length and center distance:
D = 2*(BL - 2*C)/pi
d = 2*(BL - 2*C)/pi
- BL = belt length
- D = diameter of the larger pulley
- d = diameter of the smaller pulley
- C = center-to-center distance between the two pulley shafts
- pi = 3.14159265…
All inputs are converted to inches for the calculation, then the result is converted back to the unit you selected. You can enter any three values and leave one field blank. The calculator then solves for the blank field.
- Belt length mode: uses both pulley diameters and the center distance to estimate the required open-belt length.
- Center distance mode: uses belt length and both pulley diameters to estimate the distance between pulley centers.
- Missing pulley diameter mode: uses belt length and center distance to estimate the blank pulley diameter.
Common Belt Length Units and Conversions
The calculator accepts inches, feet, centimeters, and meters. Internally, values are converted to inches before solving.
| Unit | Equivalent in inches | Common use |
|---|---|---|
| 1 inch | 1 in | Small pulleys, automotive belts, shop measurements |
| 1 foot | 12 in | Long center distances or large belt runs |
| 1 centimeter | 0.393701 in | Metric pulley measurements |
| 1 meter | 39.3701 in | Long metric belt layouts |
What to Measure Before Calculating
| Input | How to measure it | Important note |
|---|---|---|
| Larger pulley diameter | Measure straight across the pulley through its center. | Use the belt pitch diameter when available, not just the outer rim diameter. |
| Smaller pulley diameter | Measure straight across the smaller pulley through its center. | Keep units consistent, or use the unit dropdowns to convert automatically. |
| Length between pulleys | Measure from the center of one pulley shaft to the center of the other shaft. | This is center distance, not the open gap between pulley edges. |
| Belt length | Use the belt pitch length or measured loop length. | Real belts may require adjustment for tensioning range and manufacturer sizing. |
Example Belt Length Calculations
Example 1: Calculate belt length
Suppose the larger pulley diameter is 8 in, the smaller pulley diameter is 4 in, and the center distance is 24 in.
BL = (pi/2)*(8 + 4) + 2*24 + ((8 - 4)^2)/(4*24)
BL = 18.8496 + 48 + 0.1667 = 67.0163 in
The estimated belt length is 67.0163 inches.
Example 2: Calculate length between pulleys
Suppose the belt length is 80 in, the larger pulley diameter is 10 in, and the smaller pulley diameter is 6 in.
C = (80 - (pi/2)*(10 + 6))/2
C = (80 - 25.1327)/2 = 27.4336 in
The estimated center-to-center distance is 27.4336 inches.
Belt Length Calculator FAQ
What does length between pulleys mean?
Length between pulleys means the center-to-center distance between the pulley shafts. It is not the distance between the outer edges of the pulleys. To measure it, measure from the center of the first shaft to the center of the second shaft.
Should I use outside diameter or pitch diameter?
Use pitch diameter if you have it. Belt length formulas are most accurate when the pulley diameter represents the effective path of the belt. Outside diameter can give a close estimate in some cases, but it may be less accurate for V-belts, timing belts, and grooved pulleys.
Why is the calculated belt length not exactly the belt size I can buy?
Manufactured belts are sold in standard sizes, and real installations need allowance for tensioning and adjustment. If the calculated value falls between available belt sizes, choose a size that fits the adjustment range of your tensioner or movable pulley mount.
