Technical reference: spoke length and tension calculations

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This reference is for anyone reproducing the calculations or reviewing an implementation. It collects the inputs, expected outputs and sources used in the software tests. Measuring the parts, checking meter calibration and inspecting the physical wheel require separate checks.

If you are preparing a build, start with the wheelbuilding guide or how to measure ERD. This page provides the numerical reference detail.

Two spoke-length cases

In the length calculator, use manual entry and J-bend. Set the same geometry on both sides, with evenly spaced holes and 16 spokes per side:

Input	Value
ERD	600 mm
Total spoke count, N	32
Flange hole-circle diameter, PCD	58 mm on each side
Centre-to-flange distance, W	35 mm on each side
Hub spoke-hole diameter, s	2.6 mm
Rim offset, OSB	0 mm
Stretch allowance in the engine	0 mm

The equation follows the cosine rule and axial Pythagoras described by John Allen. Here the flange and rim radii are 29 and 300 mm. Subtract half the hub hole diameter, 1.3 mm, for the J-bend correction.

Crosses on both sides	Angle, 720 × crosses / N	Raw length on each side
3-cross	67.5°	290.9453 mm
Radial (0-cross)	0°	271.9508 mm

These are reference values before stock-size rounding. The interface shows the raw result to one decimal place; the tests use four decimals to detect software changes. Physical precision depends on the input measurements. Building radially also requires the hub maker to permit that pattern on the particular hub.

These length cases use only the geometry in the table. A real wheel’s ERD must reflect where the spoke ends with the chosen nipples and washers. When comparing figures from different sources, check that they all use the same reference point.

Park TM-1 conversion

In the tension tool, select Park Tool TM-1 (park-tm1) and the round steel 2.0 mm profile (steel-round-2.0). The diameter is that of the section where you take the reading. The registered source is parktool.com TM-1 conversion table PDF, version 2024, linked to Park Tool’s PDF.

Dial reading	Expected conversion
22	86 kgf, a table point
23	96 kgf, the next table point
22.5	91 kgf, linear interpolation: 86 + 0.5 × (96 − 86)
Below 17 or above 28	Rejected: `outOfRange`, tension `null`

The endpoints 17 and 28 are included. The existing tests reject readings 0 and 99. These kgf figures are the conversions of those readings. Choose build targets according to the components. The source version identifies the table used; check each meter’s calibration using its manufacturer’s procedure.

What the tests cover

The lacing diagram models evenly spaced J-bend holes and equal counts on each side: 8 to 144 spokes in total, divisible by four, with integer crosses from zero to floor(N/8) per side. These are the drawing model’s limits. Check clearances and build restrictions against the hub and rim documentation.

Check	What is checked	What is not checked
Length	Fixed results and independent sides	Actual dimensions, thread engagement or fit
OSB	Offset sign and agreement between engine and drawings	Orientation of your physical rim
Straight-pull	Additive length offset; viewer rejects an unknown layout	Hub-specific hole layout or clearances
Tension	Table points, interpolation and range rejection	Instrument accuracy, safe targets or completed-wheel safety

Download the reference inputs and expected outputs as JSON, revision 2026-09-09, to repeat these cases without repository access. The project’s automated tests also check this file. In a local checkout, run:

npx vitest run src/lib/reference-checks.test.ts

Passing means these software assertions hold. Before using the results on a wheel, measure the parts, check calibration and follow the component manufacturers’ limits.