Bike spoke length calculator.

Worked example

A 32-spoke 3-cross wheel with a 600 mm ERD, a 58 mm flange diameter and 35 mm from hub centre to each flange, with a 2.6 mm spoke hole. The spoke runs from a hole on the 29 mm flange radius to a nipple seat on the 300 mm ERD radius. The angle between the two holes round the hub is 3 × 720 ÷ 32 = 67.5 degrees. Length = √(35² + 29² + 300² − 2 × 29 × 300 × cos 67.5°) − 1.3 = 290.9 mm, so a 291 mm spoke on both sides.

How it works

Length = √(W² + r² + R² − 2rR cos θ) − S/2. W is the distance from the hub centre to the flange, r is half the flange diameter, R is half the ERD, S is the spoke hole diameter and θ = 720 × crosses ÷ spokes, in degrees. It is the straight-line distance in three dimensions from the flange hole to the nipple seat, less half the spoke hole so the length is measured from under the spoke head. The tests check it against an independent vector calculation.

Damon Rinard’s widely used spoke calculator, as described by Sheldon Brown, uses the same “pure 3D trigonometry” and the same inputs: ERD, flange diameter between hole centres, flange-to-centre width, hole diameter, spoke count and crosses. ERD is the most sensitive input, so measure it rather than copying a catalogue figure; in this geometry each 2 mm of ERD error moves a spoke by about 1 mm (the tests check it).

Limits

This tool does not apply spoke stretch, nipple seat depth differences or an off-centre rim hole offset, all of which wheel builders adjust for. Use the result as a check on, not a replacement for, the hub and rim maker’s data.

Sources

Retrieved 2026-10-16. Sheldon Brown’s description of the Rinard calculator gives the inputs and says lengths are based on 3D trigonometry; the equation shown is the standard geometry and is verified in the tests against an independent calculation.

• Sheldon Brown, Damon Rinard’s Spoke Length Calculator (inputs, 3D trigonometry)
• Park Tool, Determining Spoke Length for Wheel Building (ERD, hub measurements)

FAQ

How do I calculate spoke length for a bike wheel?

Measure the rim ERD, the hub flange diameter between hole centres and the distance from the hub centre to each flange, then count spokes and crosses. The length is the 3D distance between the flange hole and the nipple seat, less half the spoke hole diameter. A 600 mm ERD, 58 mm flange, 35 mm offset, 32-spoke 3-cross wheel needs about 291 mm.

Why are the left and right spoke lengths different?

A rear or disc hub has its flanges at different distances from the hub centre, so the two sides need different lengths. Enter each distance separately and the tool returns both.

What is ERD and why does it matter?

ERD is the effective rim diameter, the diameter on which the spoke ends sit. It is the most sensitive input: an ERD that is 2 mm off moves each spoke length by about 1 mm.

How many crosses can I use?

No more than the spoke count divided by 4, so 8 for a 32-spoke wheel. Radial is 0 crosses; 2 and 3 crosses are the most common patterns.

Does this include spoke stretch?

No. The result is the geometric length to the nipple seat. Spokes stretch slightly as they are tensioned, and builders choose the nearest available length with that and the rim and nipple in mind.