Pitch-line geometry, not belt selection

Controlled Synchronous-Belt Geometry Calculator

Calculate the ideal open-drive pitch path from a documented center distance, or solve center distance for an entered integer belt tooth count. No catalogue size, tooth profile, power capacity or tension is selected.

Exact ideal geometryNo forced even countNo profile substitutionNo power rating

Controlled two-pulley calculation

Do not order or rate a drive from this result. Confirm an actual belt and matching pulleys in the current manufacturer catalogue and design method. Width, tooth profile, minimum pulley, teeth in mesh, speed, service factor, transmitted power, tension, tolerances, installation travel, alignment, environment and safety requirements remain outside this geometry model.

Calculation modeThe unused input becomes blank and read-only
Documented tooth pitch p (mm)Positive plain decimal from the controlled belt/pulley family
Pulley 1 tooth count z₁Whole number; computational minimum 2 is not a design recommendation
Pulley 2 tooth count z₂Whole number from the documented compatible pulley
Center distance C (mm)Used in pitch-path mode; must keep the ideal pitch circles separate
Entered belt tooth count NUsed in center mode; must be an actual candidate from a controlled catalogue or record
Belt, pulley and source recordRecord manufacturer, family/profile, part or catalogue revision, pitch and pulley designations
I confirm that the pitch and both pulley tooth counts belong to one documented, mutually compatible belt/pulley family; matching pitch alone does not prove profile compatibility.
I understand that adjacent integer tooth counts are arithmetic only, not stock sizes, and that this result does not verify power capacity, tension, installation or safety.

Ideal pitch-line result

გაანგარიშება

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Pitch and pulley teeth

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Center distance

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Pitch-path length and count

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Pitch diameters

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Ideal wrap angles

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Tooth and speed ratios

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Integer-pitch information

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Ideal open-drive pitch-line geometry

rᵢ = zᵢ × p / (2π)
δ = |r₂ − r₁| ; α = asin(δ / C)
s = √(C² − δ²)
L = 2s + r_small(π − 2α) + r_large(π + 2α)
ჩრ_{საჭირო} = L / p

This is the exact planar geometry of two circular pitch lines joined by straight external tangents. It is not the common truncated approximation 2C + π(D₁+D₂)/2 + (D₂−D₁)²/(4C). Center mode solves the same exact ideal geometry by bisection until the entered integer pitch length N·p is met.

Real pulley outside diameters, tooth geometry, belt neutral axis, manufacturing tolerances and installation tension are product-specific. The computational non-overlap condition C > r₁+r₂ is conservative pitch-circle geometry, not a manufacturer clearance requirement.

Standards and catalogue boundary

ISO 13050:2022, Edition 3 covers specified metric curvilinear profile systems and includes pitch spacing, length, pulley geometry and tolerances. A common numerical pitch does not make proprietary or ISO profiles interchangeable.
ISO 5295:2023, Edition 4 establishes power-rating and centre-distance formulae for trapezoidal belts only and explicitly does not apply to curvilinear synchronous belts. This page does not use it to rate HTD or GT products.
The official Gates PowerGrip GT3 manual says exact center distance is found by convergence between center-distance and belt-length equations, and that synchronous-belt pitch length increments are multiples of pitch. It requires catalogue and power-rating steps beyond geometry.
There is no universal even-tooth rule. An official Gates GT3 product record lists a 105 mm, 3 mm-pitch belt with 35 teeth; current catalogue availability must be checked by exact family and part.

Official evidence

Gates PowerGrip GT3 Drive Design Manual

Official design procedure, stock tables, exact center-distance iteration, pitch-length increments, profile distinctions, tolerances and installation considerations.

Gates GT3 105-3MGT product record

Official example with 105 mm pitch length, 3 mm pitch and 35 teeth, directly disproving automatic even-tooth rounding.

ISO 13050:2022, Edition 3

Official current-status and scope page for specified metric curvilinear synchronous belt and pulley systems.

ISO 5295:2023, Edition 4

Official scope page: power rating and centre distance for trapezoidal belts only, not curvilinear belts.