# Belt Length Calculator

Calculate V-belt or flat belt length from pulley diameters and center distance. Includes speed ratio and wrap angles for open and crossed belts.

## What this calculates

When designing or replacing a belt drive, you need to know the exact belt length for your pulley setup. This calculator uses the standard engineering formula for both open and crossed belt configurations, giving you the belt length, speed ratio, and wrap angles on each pulley.

## Inputs

- **Large Pulley Diameter (D)** (in) — min 0
- **Small Pulley Diameter (d)** (in) — min 0
- **Center Distance (C)** (in) — min 0
- **Belt Configuration** — options: Open (standard), Crossed — Open belts are standard. Crossed belts reverse rotation.

## Outputs

- **Belt Length** (in) — Total belt length required
- **Belt Length** (mm) — Belt length in millimeters
- **Speed Ratio** — Large:Small pulley speed ratio
- **Wrap Angle (Large Pulley)** (°) — Belt contact angle on the large pulley
- **Wrap Angle (Small Pulley)** (°) — Belt contact angle on the small pulley

## Details

The standard formula for open belt length is:

L = 2C + (pi/2)(D + d) + (D - d)² / (4C)

Where D is the large pulley diameter, d is the small pulley diameter, and C is the center-to-center distance.

For a crossed belt (where the belt forms an X between pulleys, reversing rotation):

L = 2C + (pi/2)(D + d) + (D + d)² / (4C)

  - Speed ratio = D/d. If the large pulley is the driver, the small pulley spins faster by this ratio

  - Wrap angle is the contact arc on each pulley. More wrap angle means better grip and less slipping

  - The small pulley in an open belt always has a smaller wrap angle, making it the more likely to slip

These formulas are accurate for V-belts, flat belts, and timing belts. For V-belts, manufacturers catalog belts in standard lengths, so round your result to the nearest available size. For timing belts, the length must match the tooth pitch exactly.

## Frequently Asked Questions

**Q: What is the difference between open and crossed belts?**

A: An open belt runs straight between two pulleys and both rotate in the same direction. A crossed belt forms an X shape between the pulleys, causing them to rotate in opposite directions. Crossed belts have more contact area on each pulley (larger wrap angles) but the belt wears faster due to friction at the crossing point.

**Q: Why does wrap angle matter?**

A: Wrap angle is the arc of contact between the belt and pulley. A larger wrap angle means more friction surface, so the belt can transmit more power without slipping. The small pulley in an open belt drive always has less wrap angle and is usually the limiting factor for power transmission. If wrap angle drops below about 120 degrees, consider a belt tensioner.

**Q: How do I find the right belt size from this result?**

A: V-belts come in standard lengths (measured along the inside or outside depending on the standard). Calculate the required length here, then look up the closest standard belt size in a catalog. Common belt standards include A, B, C, D sections for classical V-belts and 3V, 5V, 8V for narrow V-belts. The belt number usually indicates the outside circumference in inches.

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Source: https://vastcalc.com/calculators/physics/belt-length
Category: Physics
Last updated: 2026-04-08