Is the common 2C formula exact?

No. L≈2C+π(D1+D2)/2+(D2−D1)^2/(4C) is a common approximation. This page uses exact tangent geometry for an open two-pulley drive.

How is center distance found from belt length?

The exact length equation is monotonic for valid open-belt geometry, so the calculator solves it numerically by bisection rather than presenting the closed-form inverse of an approximation as exact.

Which diameter and length definitions apply?

Use a matching pitch/datum system from the belt manufacturer. Synchronous-belt pitch diameter and V-belt datum/effective diameter are not pulley outside diameter.

Is 120 degrees a universal minimum wrap angle?

No. Required wrap or teeth in mesh depends on belt family, profile, load and manufacturer rating procedure. This tool reports geometry without automatic acceptance.

Are speed and ratio results corrected for slip?

No. They use ideal no-slip pitch-line kinematics. Use measured speeds or a validated product-specific model when slip or creep matters.

Δωρεάν Εργαλείο Μηχανικής #087

Open Belt Geometry Calculator

Calculate exact open-belt tangent geometry from matching pitch/datum dimensions, or solve center distance numerically from a known belt length.

Exact Tangent GeometryNumerical InverseNo-Slip Reference

Geometric Results

Exact Belt Length

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Small-pulley wrap angle

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Large-pulley wrap angle

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Straight tangent span

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Directed ratio n₂/n₁ = D₁/D₂

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Pitch-line speed / driven speed

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Wrap is reported without automatic pass/fail; consult the exact belt rating procedure for minimum wrap or teeth in mesh.

Open-belt tangent geometry

θ = asin((D_L−D_S)/(2C))

L = 2√(C²−((D_L−D_S)/2)²) + π(D_L+D_S)/2 + (D_L−D_S)θ

α_S=π−2θ; α_L=π+2θ

The familiar expression 2C+π(D₁+D₂)/2+(D₂−D₁)²/(4C) is an approximation obtained from the exact geometry. Its closed-form inverse is therefore also approximate. This calculator solves the exact monotonic equation by bisection.

Gates publishes exact pitch-length geometry for belt-drive design and separately labels an approximate center-distance relation. Source: Gates Light Power and Precision Manual. Diameter terminology is also cross-checked against Gates timing-belt design και Optibelt V-belt datum system.

Selection boundary: exact geometric length is not automatically a purchasable belt designation. Select a standard product length, then solve the resulting center distance and verify wrap/teeth in mesh, tension, power rating and adjustment allowance using that product’s method.

Open Belt Geometry Calculator | Exact Length and Center Distance

Geometric Results

Open-belt tangent geometry

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