Calculator Inputs
Example Data Table
| Layout | Driver Ø | Driven Ø | Center distance | Thickness | Allowance | Base length | Recommended | Wrap small / large |
|---|---|---|---|---|---|---|---|---|
| Open | 200 mm | 100 mm | 500 mm | 5 mm | 2% | 1491.947 mm | 1521.786 mm | 168.52° / 191.48° |
| Crossed | 250 mm | 150 mm | 600 mm | 0 mm | 0% | 1894.985 mm | 1894.985 mm | 218.94° / 218.94° |
| Open | 8 in | 4 in | 20 in | 0.2 in | +1 in | 59.678 in | 60.678 in | 168.52° / 191.48° |
| Open | 120 mm | 120 mm | 400 mm | 0 mm | +10 mm | 1176.991 mm | 1186.991 mm | 180.00° / 180.00° |
Formula Used
Symbols: D = larger effective pulley diameter, d = smaller effective diameter, C = center distance.
Crossed: sin(α) = (D + d) / (2C), θboth = π + 2α
Thickness adjustment: when enabled, the effective diameter is approximated as D + t, placing the belt’s pitch line near mid-thickness.
How to Use This Calculator
- Choose open or crossed layout to match your routing.
- Select units (mm or inches) and enter both pulley diameters plus center distance.
- Optionally enable thickness adjustment if you have belt thickness data.
- Add an allowance (percent or fixed) for take-up travel or installation margin.
- Choose a rounding rule and increment to align with standard belt lengths.
- Press Calculate. Download CSV or PDF to document the design.
Center distance and geometry constraints
Center distance C controls feasibility and sensitivity. For open belts, require 2C > (D − d); for crossed belts, 2C > (D + d). Near these limits, the correction term (…)/(4C) becomes large, so small diameter errors can shift length by several millimeters. Measure shaft centers, and confirm pulley alignment before finalizing a belt.
Effective diameters and pitch line selection
The equations work on the belt’s pitch line, not always the outside pulley diameter. With thickness enabled, the tool estimates effective diameter as D + t, placing the pitch line near mid-thickness. Use catalog pitch diameters for V-belts and timing belts when available because groove geometry can move the pitch radius more than thickness alone.
Allowance planning for installation and take-up
Add allowance to cover tensioning travel and manufacturing tolerance. For fixed centers with an idler, 1–3% slack is a practical starting range; then set tension to the supplier specification. For adjustable centers, a fixed allowance (for example +10 mm or +0.5 in) maps directly to slide travel. Keep allowances smaller on long spans to limit vibration, and record the margin for repeat builds. The report shows base and allowance lengths for traceability.
Wrap angle, traction, and power checks
Wrap angle affects traction and power because frictional grip increases with contact. The calculator reports wrap on the small pulley and warns below 120° in open layouts. If wrap is low, increase C, increase the small pulley diameter, add an idler, or use a crossed layout. When RPM is entered, belt speed is v = π·D1·n/60; values above 30–60 m/s may need guarding and vibration checks. Combine wrap, speed, and service factors to confirm slip margin.
Rounding to standard lengths and documentation outputs
Belts are sold in standard lengths, so rounding avoids non-stock specifications. Choose “nearest” when center distance is adjustable, “round up” when you prefer extra take-up margin, and “round down” only when tensioning travel is generous. Set increments like 5 mm or 0.25 in to match catalogs. Verify whether the supplier lists inside length, outside length, or pitch length and align your rounding target accordingly. Export CSV for analysis and PDF for design reviews.
FAQs
Which diameter should I enter: outside, pitch, or datum?
Enter pitch diameter when available. If you only have outside diameters, enable thickness and enter belt thickness to approximate the pitch line. For grooved V-belt pulleys, supplier pitch diameters give the most reliable length estimates.
Why does the calculator show an “invalid geometry” error?
The center distance is too small for the chosen layout. Open belts require 2C greater than (D − d). Crossed belts require 2C greater than (D + d). Increase C or select different pulley diameters.
What allowance value should I use?
Use percentage allowance when you want a proportional margin, typically 1–3% for installation and take-up. Use fixed allowance when you know the exact slide or tensioner travel, such as +10 mm or +0.5 in.
How do I choose the rounding increment?
Match the increment to your belt catalog steps. Common choices are 5 mm, 10 mm, or 0.25 in. If your center distance is fixed, use smaller increments to avoid large tension changes when selecting a standard size.
What does wrap angle tell me?
Wrap angle is the belt contact angle on the pulley. Higher wrap usually increases traction and reduces slip risk. If small-pulley wrap is low, consider a larger small pulley, greater center distance, an idler, or a crossed layout.
How is belt speed calculated and why is it useful?
Belt speed is computed from driver diameter and RPM using v = π·D1·n/60. It helps check noise, heat, and safety. Very high speeds may require different belt types, improved guarding, and tighter alignment control.