How do I calculate belt length?

For an open drive: L = 2C + π(D₁+D₂)/2 + (D₂−D₁)²/(4C), where C is the centre distance and D the pulley diameters. The result is the pitch length, which is what you match against the belt catalogue.

What is the difference between an open and a crossed belt drive?

An open drive has the pulleys turning in the same direction and uses the (D₂−D₁)² correction. A crossed drive reverses the direction of the driven pulley and uses (D₂+D₁)² instead, which makes the belt longer.

Why does the small pulley slip first?

Because it has less wrap angle — the arc of contact is smaller — so less belt area is engaged to transmit torque. With a high speed ratio the small pulley's wrap can fall below 150°, at which point the drive must be derated or the centre distance increased.

What centre distance should I use?

At minimum, the sum of the two pulley diameters for a 1:1 ratio, and more for higher ratios because the wrap angle on the small pulley falls as the ratio rises. Greater centre distance also reduces the number of flex cycles per minute, which extends belt life.

Do I need to allow for tensioning?

Yes — the calculated length is the running length. A drive needs adjustment to tension the belt, either by moving one shaft or with an idler. Provide roughly 2% of the centre distance as adjustment range, and check that the take-up travel is enough for the belt's initial stretch.

Belt Length Calculator

Belt length for an open two-pulley drive from pulley diameters and shaft centre distance, with the wrap angles.

Page last changed 2026-10-19 · based on n/a — standard engineering relationships, no single governing revision

Quick Answer

Open belt length is L = 2C + π(D₁ + D₂)/2 + (D₂ − D₁)² ÷ (4C). The third term is a small correction for unequal pulleys — for equal pulleys it vanishes and the length is simply 2C + π·D.

Belt Length

Driver pulley diameter (in)

Driven pulley diameter (in)

Centre distance (in)

The Formulas Used

Open belt: L = 2C + π(D₁ + D₂)/2 + (D₂ − D₁)² ÷ (4C)
Crossed belt: L = 2C + π(D₁ + D₂)/2 + (D₂ + D₁)² ÷ (4C)
Wrap angle on the small pulley: θ = 180° − 2·asin((D₂ − D₁) ÷ 2C)

Wrap Angle Governs How Much Power the Belt Can Carry

The belt transmits torque only where it is in contact with the pulley, so the small pulley's wrap angle sets the drive's capacity — and the small pulley always has the smaller wrap, which is why it is the one that slips.

The formula is unforgiving about ratio. With equal pulleys the wrap is 180° on both. With a 2:1 ratio and a centre distance of only twice the large pulley diameter, the small pulley's wrap falls to well under 150°, and the drive's power capacity drops with it. The standard remedy is to increase the centre distance, which is cheaper than changing the belt. As a rule, centre distance should be at least the sum of the two pulley diameters for a 1:1 drive, and more for high ratios.

Frequently Asked Questions

How do I calculate belt length?: For an open drive: L = 2C + π(D₁+D₂)/2 + (D₂−D₁)²/(4C), where C is the centre distance and D the pulley diameters. The result is the pitch length, which is what you match against the belt catalogue.
What is the difference between an open and a crossed belt drive?: An open drive has the pulleys turning in the same direction and uses the (D₂−D₁)² correction. A crossed drive reverses the direction of the driven pulley and uses (D₂+D₁)² instead, which makes the belt longer.
Why does the small pulley slip first?: Because it has less wrap angle — the arc of contact is smaller — so less belt area is engaged to transmit torque. With a high speed ratio the small pulley's wrap can fall below 150°, at which point the drive must be derated or the centre distance increased.
What centre distance should I use?: At minimum, the sum of the two pulley diameters for a 1:1 ratio, and more for higher ratios because the wrap angle on the small pulley falls as the ratio rises. Greater centre distance also reduces the number of flex cycles per minute, which extends belt life.
Do I need to allow for tensioning?: Yes — the calculated length is the running length. A drive needs adjustment to tension the belt, either by moving one shaft or with an idler. Provide roughly 2% of the centre distance as adjustment range, and check that the take-up travel is enough for the belt's initial stretch.

Value Sources

References and calculation methods used for this page are listed below. Numbered markers connect table columns where present. A reference listing does not itself establish that every value has been independently checked.

#	Source	Type	Revision / method
[1]	Values computed in your browser	derived	Evaluated locally from the formulas shown on the page. No data leaves the device.

Data Sources

Standard	Revision	What it covers on this page
Formulas as shown on this page	n/a — standard engineering relationships, no single governing revision	every value this calculator produces

Verification scope

No page-specific independent source review is recorded here. The listed references and formulas explain the basis of the compilation; automated consistency checks do not verify the original sources or establish product conformity.

Derived values — the following values on this page are calculated, not taken directly from the standard:

Value	How it is derived
All outputs	Computed in the browser from the formulas above. No data leaves the device.

Outputs are computed from the formulas shown. Verify against the governing standard for design or acceptance work.

Accuracy and use. Use the source notes and recorded verification scope above to assess each value. Calculated values follow the stated derivations; compilation values may lack a confirmed original document or product condition. No warranty, express or implied, is made as to the accuracy or completeness of this information, and no liability is accepted for any loss or damage arising from its use. Engineering reference data is provided for guidance in preliminary work — before a value is used for design, fabrication or acceptance testing, verify it against the current revision of the governing standard and against your own inspection. The user assumes all risk and responsibility in connection with the use of this information.

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Plain text

Engineering Reference. "Belt Length Calculator." https://refmanual.com/calculators/belt-length/ (accessed 2026-10-19). Data from Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision.

BibTeX

@misc{belt-length,
  title        = {Belt Length Calculator},
  author       = {{Engineering Reference}},
  howpublished = {\url{https://refmanual.com/calculators/belt-length/}},
  note         = {Accessed: 2026-10-19},
  source       = {Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision}
}

RIS (EndNote, Zotero, Mendeley)

TY  - ELEC
TI  - Belt Length Calculator
AU  - Engineering Reference
PB  - Engineering Reference
UR  - https://refmanual.com/calculators/belt-length/
PY  - 2026
DA  - 2026-10-19
N1  - Source: Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision
ER  -