What is the formula for spoke length?

L = √(R² + r² + W² − 2·R·r·cos α) − s/2. R is half the ERD, r is half the flange hole-circle diameter, W is the flange distance from the hub centerline, α = 720° × crosses ÷ total spokes, and s is the hub spoke-hole diameter. For a 32-spoke 3-cross wheel, α = 720 × 3 ÷ 32 = 67.5°.

How do I measure a rim for spoke length (ERD)?

Thread a nipple onto each of two spokes of known length until the spoke end is flush with the bottom of the nipple slot. Drop them through opposite rim holes, pull them tight toward the center, and measure the gap between the two spoke ends. ERD = spoke A + spoke B + gap. Repeat at another pair of holes and average.

Can I use the ERD printed by the rim maker?

Yes, as a starting point. Published ERD values can differ from your rim by a millimeter or two, and nipple length or washers change the real seat position, so measuring the rim you have is more reliable.

How should I round the calculated spoke length?

Spokes come in 1 mm or 2 mm steps depending on brand. Round to the nearest size you can buy. When a result falls between two sizes, most builders take the shorter one because spokes stretch slightly once tensioned and the rim bed compresses a little.

Why are the left and right spoke lengths different?

On a rear wheel the cassette pushes the drive-side flange closer to the centerline, and on disc hubs the rotor side moves too. A smaller flange offset W gives a shorter spoke, and different flange diameters change the length as well.

Which cross patterns work with my spoke count?

Crossed lacing needs a spoke count divisible by 4, and the lacing angle 720° × crosses ÷ spokes must stay below 180°. In practice 3-cross suits 32 and 36 spokes, 2-cross suits 24 and 28, and 0-cross is radial lacing.

Does this work for straight-pull hubs?

Not directly. Straight-pull spokes leave the flange tangentially, so their geometry differs from J-bend spokes. Use the hub maker's method or calculator for straight-pull and other proprietary systems.

Spoke Length Calculator

Calculate left and right bicycle spoke lengths from rim ERD and hub measurements, with rounding to orderable sizes and a guide to measuring the rim.

Spoke length L = √(R² + r² + W² − 2·R·r·cos α) − s/2, where R = ERD ÷ 2, r = hub flange hole-circle diameter ÷ 2, W = center-to-flange distance, α = 720° × crosses ÷ total spokes, and s = hub spoke-hole diameter.

Rim and hub measurements

All dimensions in millimeters. Measure to 0.1 mm where you can.

Effective rim diameter (ERD)

Total spokes in wheel

Hub spoke-hole diameter

Rim offset, + = holes toward left / non-drive (0 = symmetric)

Left / non-drive Flange hole-circle diameter Center to flange Cross pattern

Right / drive Flange hole-circle diameter Center to flange Cross pattern

Left spoke

–

Right spoke

–

Lacing angle:

Side difference:

If ERD is off by ±1 mm:

Ordering estimate for J-bend spokes. Check the rim, nipple and hub dimensions before you buy; straight-pull hubs need the maker's method.

Measured ERD helper

Two spokes with nipples seated in opposite rim holes, pulled taut: add both spoke lengths and the gap between their ends.

Spoke A

Spoke B

End gap

ERD = spoke A + spoke B + gap.

Building the wheel next? Balance it with the spoke tension calculator, or work out ratios with the bicycle gear calculator.

How to measure the rim for spoke length (ERD)

ERD is the diameter where the spoke ends sit inside the nipples in a built wheel. It is smaller than the rim's outside diameter and is not the tire bead-seat size, so two 700c rims with the same 622 mm bead seat can differ a lot: around 600 mm for a shallow box-section rim, and in the low 500s for a deep aero rim.

Two-spoke method

Measure two identical spokes with a spoke ruler or caliper.
Thread a nipple on each until the spoke end reaches the bottom of the screwdriver slot. Add rim washers if you will use them.
Drop the spokes through two opposite rim holes and pull them toward the center.
Measure the gap between the two spoke ends to 0.1 mm.
ERD = spoke A + spoke B + gap. Repeat at another pair of holes and average.

Caliper method and hub measurements

Rim: measure the outside diameter, then the depth from the rim edge to the bottom of the nipple slot. ERD = outside diameter − 2 × depth.
Flange hole circle: measure from the center of one spoke hole to the center of the hole directly opposite.
Center to flange: half the over-locknut width minus the distance from that locknut face to the middle of the flange.
Spoke hole: usually 2.4–2.7 mm; a small error here barely changes the result.

Rounding to a spoke you can buy

Spokes are sold in 1 mm or 2 mm steps. Take the nearest stocked size, and when a result falls between two sizes, go shorter: spokes stretch a little under tension. If the two sides round to the same size, one length does the whole wheel; a gap of 2 mm or more usually means ordering two lengths.

Quick answer

Example: ERD 600 mm, 32 spokes laced 3-cross, 44 mm flanges set 35 mm (left) and 20 mm (right) from center, 2.6 mm holes: α = 67.5°, left 293.1 mm and right 291.7 mm, so order 293 mm and 292 mm spokes.

Enter your rim and hub measurements to get both lengths.

Summary

The calculator uses the standard three-dimensional spoke length formula found in wheel-building references: the law of cosines across the wheel plane for the rim radius, flange radius and lacing angle, plus the flange offset at right angles to it, minus half the hub spoke-hole diameter. Each side of the wheel gets its own result because rear and disc hubs have different flange offsets and sometimes different flange sizes. It also shows how much a 1 mm ERD error moves the answer and gives the nearest whole and even sizes for ordering. Everything runs in your browser.

How it works

Measure the rim ERD (effective rim diameter) with two spokes and nipples, or take it from the rim maker and check it.
Measure each hub flange hole-circle diameter (center of one spoke hole to the center of the opposite hole).
Measure each flange distance from the hub centerline: half the over-locknut width minus the locknut-to-flange distance.
Enter the total spoke count, the cross pattern for each side, and the hub spoke-hole diameter.
If the rim has an off-center spoke bed, enter the offset as a positive number when the holes sit toward the left (non-drive) side, as on most asymmetric rear rims; leave it at 0 for symmetric rims.
Calculate, then round each side to an orderable size using the nearest-size figures and the rounding notes.

Use cases

Order spokes for a new bicycle wheel build.
Find the different drive-side and non-drive-side lengths on a dished rear wheel.
Check lengths for a disc-brake front wheel with unequal flange offsets.
Compare 2-cross, 3-cross and radial lacing before ordering.
See how much a rim ERD measurement error changes the spoke length.
Re-use an old hub with a new rim and confirm the spokes still fit.

Frequently Asked Questions

Last updated: 2026-10-08 · Reviewed by Nham Vu