L = √( W² + (d/2)² + (D/2)² − 2 · (d/2) · (D/2) · cos α ) − s/2
Spoke length calculator
Spoke lengths for each side of a wheel from the rim's ERD, the hub's flange diameters and centre-to-flange distances, spoke count, lacing and hole size — with rounding advice, bracing angles, the left/right tension ratio, rim offset, and an ERD-from-measurement helper.
Added
How to use it
Enter the rim’s ERD (effective rim diameter — the diameter at the ends of the spokes, where the nipples seat), the number of spokes, and for each hub flange the flange diameter (the diameter of the circle through the spoke holes, centre to centre), the centre-to-flange distance (from the middle of the hub, between the locknuts, to the middle of that flange) and the lacing. The flange hole diameter (2.4–2.7 mm, usually 2.6) and a rim offset for asymmetric rims complete it. The presets are typical examples for each kind of hub and rim — not a particular product — so they show the shape of the answer; for a real build, measure or use the maker’s specification sheet.
The formula (the law of cosines between the hub hole and the rim hole, used by every spoke calculator, and given in Rohloff’s handbook in numeric form):
with D the ERD, d the flange diameter, W the centre-to-flange distance, s the flange hole diameter, and α = 720° × crosses ÷ spokes the angle the spoke turns through around the axle (0 for radial). It is checked against Rohloff’s worked example (ERD 539, 100 mm hole circle, 32 spokes 2-cross: 238 mm) and against a 3-D distance computation.
-
Rounding: spokes come in whole millimetres. Park Tool’s advice when the two sides differ: 1 mm — one length, the longer; 2 mm — one length, the average; 3 mm or more — two lengths. Aim for the spoke end to finish flush with the top of the nipple head; a little short (under ~1 mm) is fine, long spokes can bottom out in the nipple before the wheel is tight.
-
Bracing angle — each side’s spoke angle from the wheel’s plane; a wider angle makes a laterally stiffer wheel.
-
Tension ratio — spokes on the side with the flange closer to the centre (the drive side of a rear wheel, the non-disc side of a disc front) pull at a steeper angle, so for the rim to be centred the other side runs slacker: TL · WL / LL = TR · WR / LR.
-
Rim offset — asymmetric rims put the spoke holes off the centre line (toward the left), which evens the tensions: the right centre-to-flange grows by the offset and the left shrinks.
-
Measure the ERD — Park Tool’s method with two spokes and nipples; Use this ERD copies the result up.
Limits
-
The answer is only as good as the measurements; ERDs printed by makers are sometimes a millimetre or two out, and hub figures vary by model year.
-
Straight-pull hubs, paired-spoke rims, 2:1 lacing (different spoke counts per side) and different spoke counts on a hub’s flanges are not covered.
-
Spoke stretch under tension (a fraction of a millimetre) and nipple length are ignored, as most calculators do.
Related: gearing calculator, tyre pressure, maintenance log, power and climbing.
Linking to an example
| Parameter | Meaning | Example |
|---|---|---|
|
Effective rim diameter (mm) |
|
|
Rim example: |
|
|
Hub example: |
|
|
Spokes in the wheel |
|
|
Crosses, left and right (0 = radial) |
|
|
Flange (hole-circle) diameter, left and right (mm) |
|
|
Centre to flange, left and right (mm) |
|
|
Flange hole diameter (mm) |
|
|
Rim offset (mm, spoke bed moved left) |
|
Presets (?example=<name>):
example= |
Shows |
|---|---|
|
a 32-spoke road rear, 3-cross both sides, on a 600 mm ERD rim |
|
a 20-spoke radial road front on a 30 mm rim |
|
a 28-spoke Boost rear, 3-cross, on a 29″ rim |
|
the road rear on a rim with 3 mm offset: tensions closer to even |
|
Rohloff’s handbook example: ERD 539, 32 spokes 2-cross → 238 mm |
Feedback is a gift. Something to improve, a feature to add, or a bug? Tell me.
Runs entirely in your browser; nothing you type leaves this page.