Bike Spoke Length Calculator
Calculate the exact spoke length needed for any wheel build from rim ERD, hub flange dimensions, and lacing pattern. Essential before ordering spokes for a custom or replacement wheel.
About this calculator
Spoke length is calculated using a 3-D distance formula derived from the geometry of the wheel triangle formed by the rim, hub flange, and spoke. The formula is: L = √((ERD/2)² + (PCD/2)² + offset² − 2 × (ERD/2) × (PCD/2) × cos(cross × 2π / n)), where ERD is the effective rim diameter (the diameter at the spoke nipple seat), PCD is the hub pitch circle diameter (flange hole circle), offset is the lateral distance from the wheel centerline to the flange, cross is the lacing pattern (0 = radial, 1 = 1-cross, 2 = 2-cross, 3 = 3-cross), and n is the total spoke count. The cosine term accounts for the angular offset between the spoke's hub hole and the corresponding rim hole introduced by the cross pattern. A radial build (cross = 0) gives the shortest spokes; each additional cross adds length. Drive-side and non-drive-side flanges always have different offsets on rear wheels and must be calculated separately.
How to use
Build a 32-spoke, 3-cross rear wheel. Rim ERD = 584 mm, hub PCD = 58 mm, drive-side flange offset = 17 mm. Step 1 — half values: ERD/2 = 292, PCD/2 = 29. Step 2 — angle: cos(3 × 2π / 32) = cos(1.1781) ≈ 0.3827. Step 3 — inside the square root: 292² + 29² + 17² − 2 × 292 × 29 × 0.3827 = 85264 + 841 + 289 − 6485 ≈ 79909. Step 4 — L = √79909 ≈ 282.7 mm. Order 283 mm spokes for the drive side (always round up 0.5–1 mm for threading clearance).
Frequently asked questions
What is effective rim diameter (ERD) and how do I measure it accurately?
ERD is the diameter of the circle where spoke nipples seat inside the rim — not the outer rim diameter or the bead seat diameter. It is the most critical measurement for spoke length accuracy; a 2 mm error in ERD produces nearly a 1 mm error in spoke length. The most reliable way to measure ERD is to thread two known nipples into opposite spoke holes, attach a spoke to each, and measure the distance between spoke tips, then add twice the nipple length (typically 12 mm for standard brass nipples). Alternatively, many rim manufacturers publish ERD in their specifications. Always verify with a physical measurement because published values sometimes vary by production batch.
How does the spoke lacing cross pattern affect spoke length and wheel strength?
Each additional cross in the lacing pattern increases spoke length because the spoke must travel further around the hub before heading to the rim. Going from radial (0-cross) to 3-cross on a typical 32-hole wheel adds roughly 8–12 mm of spoke length. Beyond length, the cross pattern dramatically affects wheel characteristics: radial lacing is stiffest laterally and lightest but puts high stress on hub flanges, making it unsuitable for rear drive-side spokes. A 3-cross pattern transfers torque efficiently and is the standard for rear wheels. A 2-cross is a common compromise for front wheels where lateral stiffness matters but flange stress must be managed.
Why do I need to calculate drive-side and non-drive-side spoke lengths separately on a rear wheel?
On a rear wheel the hub is dished — the flanges are not equidistant from the wheel centerline. The drive side (sprocket side) flange sits closer to the center to make room for the cassette, giving it a smaller lateral offset. The non-drive side flange sits further out, with a larger offset. Because offset appears in the spoke length formula, the two sides require different spoke lengths, typically differing by 1–4 mm on modern wide-ratio cassette hubs. Using the wrong length on either side results in spokes that bottom out in nipples or protrude dangerously through the rim bed, so always calculate both sides independently.