Spoke Length Calculator
Spoke length from hub, rim, and lacing pattern.
About this calculator
Wheel building demands precise spoke lengths — a spoke even 2 mm off can bottom out in the nipple or come up short of enough threads to hold tension safely. This calculator uses the standard trigonometric spoke-length formula built from three points that define a triangle: the rim's effective radius (half the Effective Rim Diameter, measured nipple-seat to nipple-seat), the hub flange's radius (half the flange's pitch circle diameter, where the spoke holes sit), and the flange's offset from the hub centerline. It computes the angle between a spoke and its nearest hole from your chosen cross pattern — radial (0-cross) runs spokes straight out, while 1- through 4-cross wind them at increasing angles for better torque transfer — and plugs everything into L = √(R² + H² + F² − 2RH·cos θ) − d/2, subtracting half the spoke hole diameter to account for how deep the spoke elbow seats in the flange.
Because most hubs are asymmetric (the drive-side flange sits closer to center to make room for the cassette), the calculator runs this formula twice — once per flange offset and PCD — producing distinct drive-side and non-drive-side lengths, which is why wheel-building spoke orders almost always list two different lengths. Results are also floored to the nearest whole millimeter since spokes are only manufactured in 1mm increments, and you should always round down, never up, when ordering. The most common real-world mixup is swapping ERD with BCD/rim diameter or the flange PCD with the flange-to-center offset — both are diameters and offsets respectively, and mixing them up produces spokes that are wildly wrong rather than just slightly off.
Inputs
Results
Drive-side length (mm)
293.4
How to Use This Calculator
- Enter ERD - Effective Rim Diameter (mm), Drive flange offset (mm), and Non-drive flange offset (mm).
- Set Drive flange PCD (mm), Non-drive flange PCD (mm), and Spoke hole diameter (mm).
- Adjust Spoke count, Cross pattern (0-4) as needed.
- Review the Drive-side length (mm) result.
- Use Non-drive length (mm) and Drive-side order (mm) to inform your decision.
How the result changes with ERD - Effective Rim Diameter (mm)
| ERD - Effective Rim Diameter (mm) | Drive-side length (mm) |
|---|---|
| 400 | 192.7 |
| 454 | 219.1 |
| 700 | 340.5 |
What each input means
- ERD - Effective Rim Diameter (mm)
- Effective Rim Diameter: measure from nipple seat to nipple seat across the rim.
- Drive flange offset (mm)
- Center of hub to drive-side flange center.
- Non-drive flange offset (mm)
- Center of hub to non-drive-side flange center.
- Drive flange PCD (mm)
- Pitch circle diameter of spoke holes on drive-side flange.
- Non-drive flange PCD (mm)
- Pitch circle diameter of spoke holes on non-drive-side flange.
- Spoke hole diameter (mm)
- Diameter of spoke holes in the hub flange (typically 2.4-2.8 mm).
- Spoke count
- Total number of spokes in the wheel.
- Cross pattern (0-4)
- Lacing pattern: 0 = radial, 1 = 1-cross, 2 = 2-cross, 3 = 3-cross (most common).
What each result means
- Drive-side length (mm)
- Calculated spoke length for the drive side.
- Non-drive length (mm)
- Calculated spoke length for the non-drive side.
- Drive-side order (mm)
- Drive-side length rounded down to nearest whole mm for ordering.
- Non-drive order (mm)
- Non-drive length rounded down to nearest whole mm for ordering.
- Side difference (mm)
- Difference in spoke length between drive and non-drive sides.
- Spokes per side
- Number of spokes needed per side.
- Total spokes needed
- Total spokes to purchase (add 2-4 spares recommended).
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersERD - Effective Rim Diameter (mm) = 605, Drive flange offset (mm) = 35, Non-drive flange offset (mm) = 20, Drive flange PCD (mm) = 58 = 8 input(s) provided
- Calculate Drive-side lengthDrive-side length = calcSpokeLength(flangeDistanceDrive, flangePcdDrive)293.4 = 293.4
- Calculate Non-drive lengthNon-drive length = calcSpokeLength(flangeDistanceNonDrive, flangePcdNonDrive)292 = 292
- Calculate Drive-side orderDrive-side order = floor(driveSideLength)293 = 293
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why do drive-side and non-drive-side spokes usually come out different lengths?
Most hubs are asymmetric because the drive-side flange has to sit closer to the hub's centerline to leave room for the cassette, while the non-drive-side flange sits farther out. The calculator runs the spoke-length formula separately for each side using its own flange offset and PCD, which is why the drive-side length is typically shorter than the non-drive-side length and why wheel builds almost always call for two distinct spoke lengths.
What does the cross pattern number actually change in the formula?
The cross pattern sets the angle (theta) between a spoke and its nearest hub hole via theta = 2π × cross / spokesPerSide — radial (0-cross) uses a zero angle since spokes run straight out, while higher cross numbers increase that angle, which lengthens the calculated spoke because it now has to travel a more diagonal path to reach the rim. Higher cross patterns also improve torque transfer for braking and acceleration, which is why 3-cross is the common default for most wheels.
Why does the calculator round spoke lengths down instead of up?
Spokes are manufactured in fixed 1mm increments, so the calculated length almost never lands exactly on an available size. The calculator floors both the drive-side and non-drive-side lengths because a spoke that's slightly too long can bottom out against the rim bed or protrude through the nipple, while a spoke that's a millimeter short still threads in with enough engagement to hold safe tension.
What happens if I accidentally swap ERD with rim diameter, or flange PCD with flange offset?
These are easy to confuse because they're similar-sounding measurements that feed the same formula in very different ways: ERD is specifically the nipple-seat-to-nipple-seat diameter (not the rim's outer diameter or BCD), and flange PCD (the diameter of the circle the spoke holes sit on) is a different quantity from flange offset (the distance from the hub's centerline to the flange). Mixing either pair up doesn't produce a slightly-off spoke length — it produces a length that's wildly wrong, since both terms are squared inside the square root in the formula.
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