Bicycle Spoke Length Calculator (Wheel Building)
One of the most error-prone steps in wheelbuilding is ordering the right spoke length: order too short and the nipple thread bottoms out before full tension; order too long and the spoke pokes past the nipple and pierces the tube. This tool uses the 30-year industry-standard Damon Rinard / Sheldon Brown formula L = √(d² + r² + R² − 2·r·R·cos α) − D/2 to compute the spoke length on one side. Rear wheels are dished, so the drive-side (DS) and non-drive-side (NDS) lengths differ — calculate each side separately. Inputs: (1) **d** — distance from rim centerline to the flange on this side; (2) **PCD** — flange spoke-hole pitch circle diameter; (3) **ERD** — effective rim diameter (nipple seat to nipple seat); (4) spoke count; (5) cross pattern. Spokes are sold in 2 mm steps, so round to the nearest 0.5 mm and pick the closest stocked length.
Check inputs: all values must be positive and finite; spoke count must be even; crosses ≤ ⌊(S/2 − 1)/2⌋.
Spoke length (per side)
—
Arc angle α
—
Flange hole diameter
Usually 2.5–2.6 mm for standard J-bend spokes.
Damon Rinard / Sheldon Brown formula: L = √(d² + r² + R² − 2·r·R·cos α) − D/2; α = 4πN/S (N = crosses, S = total spokes). On a dished rear wheel, compute each side separately. Spokes are sold in 2 mm steps, so round to the nearest 0.5 mm and pick the closest stocked length.
Formula
L = √(d² + r² + R² − 2·r·R·cos α) − D/2 d = perpendicular distance from rim centerline to the flange on this side (mm) r = PCD / 2 (flange spoke-hole pitch radius, mm) R = ERD / 2 (effective rim radius, mm) α = 4π · N / S where N = crosses, S = total spoke count D = flange hole diameter (typically 2.5–2.6 mm)
- · **Picking 0/1/2/3/4 cross**: (1) **0 cross (radial)** — spokes go straight out from hub to rim, giving the shortest, lightest, stiffest wheel — but only OK for a non-disc, non-drive front. Any disc-brake front or any rear needs ≥ 2 cross to transfer torque to the rim. (2) **2-cross** — common on rear 28/32-spoke wheels; balances stiffness and weight. (3) **3-cross** — the gold standard for 32/36-spoke rims; the default for rear, touring and heavy-loaded wheels. (4) **4-cross** — for 40/48-spoke MTB and tandem wheels; maximum torque transfer.
- · **Front vs rear dish**: a rear hub must make room for the cassette/freehub, so the drive-side (DS) flange sits closer to the centerline than the non-drive (NDS) flange (DS d ≈ 17–20 mm, NDS d ≈ 35–38 mm). As a result **DS spokes are 2–4 mm shorter than NDS spokes**. Front wheels are not dished (unless disc-braked); both sides have equal d.
- · **Measuring PCD**: (1) Spec sheet — most hub brands (DT Swiss, Chris King, Industry Nine) publish it directly. (2) By caliper — measure from the centre of one spoke hole to the centre of the diametrically opposite hole on the same flange. That distance IS the PCD. Make sure to use hole centres, not the outer edge of the flange.
- · **ERD gotchas**: brands define ERD slightly differently — DT Swiss uses "nipple-seat to nipple-seat distance" (the point where the nipple bottoms on the rim); some brands use "rim well outer diameter − 2 × spoke prep washer". If in doubt, measure yourself: thread two spokes part-way through opposite nipples and measure tip-to-tip — that's ERD.
- · **Tool tolerance vs real spokes**: the formula is exact, but real spokes are **sold in 2 mm steps** (typical stock: 248/250/252/254/256… mm). Round the computed length to the nearest 0.5 mm, then pick the closest stocked length. **Err 0.5 mm long, not short** — too short means thread bottoms out before tension; too long means the nipple still has thread to spin in.
- · **Spoke elongation**: under full tension (120–140 kgf) a spoke elongates 0.5–1 mm. Allowing 0.5 mm slack means the wheel comes up to tension at the right length. Pre-stressed spokes (e.g. DT Swiss Aerolite, factory cold-set) need no extra slack.
- · References: (1) Damon Rinard, "Bicycle Spoke Length Calculator" (rec.bicycles.tech 1996+, archived at sheldonbrown.com); (2) Sheldon Brown, "Spoke Length" (sheldonbrown.com/spoke-length.html); (3) Gerd Schraner, *The Art of Wheelbuilding* (2007), pp. 130–134; (4) Roger Musson, *Professional Guide to Wheelbuilding* (8th ed., 2018); (5) DT Swiss "Spoke Length Calculation" (dtswiss.com PDF).
Frequently asked
How different are the rear DS and NDS spoke lengths — can I just buy one length for both?
**No, do not mix**. A typical road rear has DS d ≈ 17.5 mm and NDS d ≈ 37 mm — a 19.5 mm flange asymmetry. Plugged into the formula: DS spoke ≈ 290 mm, NDS spoke ≈ 293 mm — about 3 mm difference. That sounds small but 3 mm = 6 spoke steps (2 mm each). At full tension the shorter side will thread-bottom and not reach full tension; the longer side will stick out past the nipple and puncture the tube. **Correct approach**: compute both sides and order both lengths (S/2 each). **Exceptions**: (1) un-dished front → both sides equal, one length covers all. (2) Symmetric-rim rear designs (e.g. Onyx Vesper, Velocity NoBS — offset rims compensate the dish) → both sides may differ by < 1 mm and a single length can work, but verify with the calculator. (3) Boost 148 mm rear vs standard 142 mm slightly increases DS d (17 → 19.5), reducing the gap to ~2 mm — still order both lengths.
I computed 285.7 mm but spokes are sold in 2 mm steps. Should I buy 286 or 284?
**Buy 286 mm** (round up to the next even number). **Rule of thumb: err 0.5 mm long, not short**. Why: (1) At full tension (120–140 kgf) a steel spoke elongates elastically by ~0.5 mm — so a 286 mm spoke at 130 kgf actually sits at ~286.5 mm of working length, perfect for the nipple thread; a 284 mm spoke at tension is ~284.5 mm, possibly 1 mm short → the nipple thread bottoms out before full tension. (2) A 286 mm spoke sticks out past the bottom of the nipple thread by ~1 mm (most nipples are designed to swallow 1–2 mm of overshoot) — and the rim tape protects the tube. (3) A 284 mm spoke gives less thread engagement, uneven spoke tension across the wheel, and a higher chance of fatigue failure at the J-bend. **Exception**: short-head brass nipples (DT Swiss 12 mm vs standard 14 mm) or some deep-section rims that require internal nipples need shorter spokes — follow the rim manufacturer's chart rather than blindly rounding up.
My LBS asked for the hub OLD (over-locknut dimension) — which input on this tool does it correspond to?
OLD (over-locknut dimension) is the **total width between the outer faces of the two locknuts** — i.e. hub spacing. Standard rear OLDs: 130 mm (rim-brake road), 142 mm (disc thru-axle), 148 mm (Boost MTB). Front: 100 / 110. **But OLD ≠ the tool's d** — d is **the perpendicular distance from the rim centerline to the flange on one side**, not hub width. **OLD → d**: read the hub spec sheet for "flange-to-centre distance" or "left/right flange offset" (often labelled L1, L2 or Lo, Lp). E.g. Shimano R7000 105 rear hub: L1(DS) = 17.5 mm, L2(NDS) = 37 mm — feed those as d. **Measuring it yourself**: clamp the hub vertically and use a caliper from the brake-disc / cassette-side locknut face inward to the flange centre — then subtract half the locknut thickness. Or measure FTC (flange-to-flange centre) directly and apportion based on the hub dish. **Sheldon Brown's naming**: left flange offset = "Left Center to Left Flange" = LCL; right = RCR — both map to the tool's d. No spec sheet and no caliper? Sheldon Brown maintains a hub database with thousands of measured d values: sheldonbrown.com/spoke-length.html#hubs.
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