How to use the bike wheel spoke length calculator
- Enter the effective rim diameter (ERD), the diameter where the spoke ends inside the rim. The rim maker publishes it, or you can measure it.
- Enter the flange diameter (the circle through the spoke holes) and the flange offset (the distance from the hub center to the flange) for each side. Rear hubs usually differ left and right.
- Enter the total number of spokes and the crossings per spoke, where 0 is radial and 3 is the classic three cross pattern.
- Read the left and right spoke lengths in millimeters. Spokes come in whole millimeter sizes, so pick the nearest.
Formula
angle = 720 x crossings / number of spokes, in degrees
length = sqrt(R^2 + r^2 + w^2 - 2 R r cos(angle)) - hole diameter / 2
R = ERD / 2, r = flange diameter / 2, w = flange offset
A spoke runs from a hole on the hub flange to a hole in the rim. The rim hole is at radius R, the hub hole at radius r and angle apart around the axle, and the hub hole sits w to the side of the rim centerline. The last term takes off half the hole diameter for the spoke elbow.
A 32 spoke wheel laced three cross
With an ERD of 600 mm, flanges 58 mm across and offsets of 35 mm on the left and 20 mm on the right, the angle is 720 x 3 / 32 = 67.5 degrees. The left spoke is sqrt(300^2 + 29^2 + 35^2 - 2 x 300 x 29 x cos 67.5) - 1.3 = 290.95 mm and the right is 289.53 mm, so you would buy 291 mm and 290 mm spokes.
A 28 spoke wheel with an ERD of 559 mm, 44 mm flanges, a 35 mm offset, two cross and 2.4 mm holes gives 267.43 mm. A radial wheel with 36 spokes, an ERD of 622 mm, 45 mm flanges and a 28 mm offset gives 288.56 mm. All three agree with the straight line distance between the two holes in three dimensional coordinates.
Measuring your own parts
Use a caliper for the flange diameter and offset, and the rim maker or a measuring method for ERD, because a small error in ERD carries straight into the spoke length. The default numbers on this page are examples, not a recommendation for any hub or rim.
Different calculators subtract the elbow or the hole differently and round at different points, so two correct tools can disagree by about a millimeter. Check the result with the maker of your spokes, and confirm the thread length is enough for your nipples.
Related bike tools
Gear choices change speed and effort, which the Gear Ratio Calculator shows, and the Bike Frame Size Calculator helps with fit. For training zones from power, use the Cycling Power Zones Calculator.
More maker tools
For other hobby and building projects, try the IBU Calculator, Cone Pattern Calculator and Circle Skirt Calculator.
Assumptions and limits
- The spoke runs in a straight line between the hub hole and the rim hole.
- Both flanges have the same number of holes and the pattern is the same on both sides.
- The elbow allowance is half the hole diameter, with an example of 2.6 mm.
- All measurements are in millimeters.
Frequently asked questions
How do I calculate spoke length for a bike wheel?
Find the angle from the crossings and spokes, then take the straight line distance between the hub hole and the rim hole and subtract half the hole diameter. This page does that for each side.
What is ERD on a bicycle rim?
Effective rim diameter is the diameter of the circle where the spoke ends sit inside the rim. It is not the outside size of the rim, and it comes from the rim maker or a measurement.
Why are the left and right spokes different lengths?
Hub flanges are not centered, especially on rear wheels, so one side has a larger offset and a different distance to the rim.
How many crossings should I use?
It depends on the spoke count and the hub. This page only works out the length for the number you choose, up to the most that fits your spoke count.