Spoke Length Calculator for US Wheel Builders
The law-of-cosines formula, hub presets for 12 popular American-market hubs, a cross-pattern comparison chart, and a full PDF wheel build spec sheet. All free, all in one place, all built around the way American cyclists actually work.
Law-of-Cosines Spoke Geometry: Drive-Side and Non-Drive Computation
Rim Measurement
Drive-Side Hub (Right Side)
Non-Drive-Side Hub (Left Side)
Lacing Configuration
Hub Presets and Component Reference Data for American Riders
The hub preset dropdown above is not a convenience feature; it is a quality-control tool. The single most common error in spoke length calculation is entering the wrong hub measurement, and the most common reason for entering the wrong measurement is measuring the wrong thing. Hub flange diameter is not the outer diameter of the flange body. It is the Pitch Circle Diameter (PCD), which is the diameter of the circle that passes through the center of each spoke hole. To measure it correctly, you place digital calipers across two spoke holes that are directly opposite each other and measure center-to-center. The outer edge of one hole to the inner edge of the other, then add the hole diameter.
Center-to-flange distance (sometimes called CTF or hub offset) is equally easy to get wrong. It is measured from the midpoint between the two outer locknut faces (the same reference point used to define Over Locknut Distance) to the center of each flange. Not the inner face of the flange, not the outer face. The center. On rear hubs this measurement differs between sides because the cassette body forces the drive-side flange closer to center to make room for the sprockets. This asymmetry is the reason your rear wheel has two different spoke lengths.
The presets in this calculator are derived from published manufacturer documentation and community-verified measurements. They are labeled as approximate because hub tolerances vary between production batches and because some manufacturers update their specifications without changing the model name. Always verify the preset values against your specific hub before placing a spoke order, especially for high-end hubs where a 0.5 mm error in flange PCD changes your calculated spoke length by nearly a millimeter.
Published Hub Flange Specifications for Common US-Market Hubs
| Hub Model | DS Flange PCD | DS CTF Offset | NDS Flange PCD | NDS CTF Offset | Spacing |
|---|---|---|---|---|---|
| DT Swiss 240 Road Rear (CL) | 44.5 mm | 17.4 mm | 44.5 mm | 34.1 mm | 130mm QR |
| DT Swiss 240 Road Front (CL) | 44.5 mm | 17.0 mm | 44.5 mm | 17.0 mm | 100mm QR |
| DT Swiss 350 MTB Rear (Boost) | 44.5 mm | 16.8 mm | 44.5 mm | 34.5 mm | 148mm Boost |
| Shimano 105 / Ultegra Road Rear | 44.0 mm | 17.2 mm | 44.0 mm | 34.5 mm | 130mm QR |
| Shimano XT M8100 MTB Rear | 44.0 mm | 17.5 mm | 44.0 mm | 36.0 mm | 148mm Boost |
| Chris King R45D Road Rear | 43.5 mm | 18.3 mm | 43.5 mm | 35.5 mm | 130mm QR |
| Industry Nine 1/1 Road Rear | 46.0 mm | 17.5 mm | 46.0 mm | 33.5 mm | 130mm QR |
| Generic Road Hub Front (100mm) | 48.0 mm | 17.0 mm | 48.0 mm | 17.0 mm | 100mm QR |
All values are approximate. Verify against your hub’s individual spec sheet before ordering spokes. Manufacturer tolerances typically span plus or minus 0.5 mm.
ERD, Flange Diameter, and Cross Pattern: The Three Variables That Matter
This calculator has six input fields, but three of them do most of the mathematical heavy lifting. Understanding exactly what each one measures and why it behaves the way it does in the formula will save you from building a wheel that comes back to the truing stand in a hundred miles.
ERD: The Most Important Number You Probably Measured Wrong
Effective Rim Diameter is not the tire bead diameter, not the ISO rim size, and not the outer diameter of the rim. It is the diameter of the circle formed by the points where spoke ends seat inside the rim channel when the nipples are fully threaded in and under tension. Rim manufacturers publish ERD values, but these published numbers are often rounded and sometimes based on a specific nipple style that may not match what you are using. A brass nipple seats at a slightly different depth than an aluminum nipple of the same thread length.
The most reliable way to measure ERD is with two old spokes. Thread nipples onto both spokes all the way to the nipple’s head, insert the spoke tips into two directly opposing spoke holes in the rim until they cannot go further, and then measure the distance from spoke tip to spoke tip. Add the diameter of one spoke head (typically 2.6 mm for a standard J-bend spoke) and you have your ERD. A 2 mm error in ERD measurement translates to a 1 mm error in calculated spoke length, which can be enough to make the spoke protrude beyond the nipple slot and puncture your rim tape or inner tube.
Flange PCD and the Law-of-Cosines in Practice
The flange PCD (Pitch Circle Diameter) determines how far the spoke hole sits from the center of the wheel. In the law-of-cosines formula, this appears as R_fl (the flange radius, which is half the PCD). A larger flange moves the spoke attachment point further from the center, which shortens the spoke for a given crossing pattern because less diagonal distance is needed to reach the rim. This is why large-flange hubs, popular in track cycling and older touring builds, produce notably shorter spokes than typical road racing hubs with their smaller flanges.
The formula also uses the center-to-flange distance (O) as its third spatial dimension. The formula is working in three dimensions: R_rim defines the radial position of the rim nipple, R_fl defines the radial position of the spoke hole on the flange, and O defines the axial (lateral) offset between the two planes. The Pythagorean relationship between these three values is what the square root resolves.
Cross Pattern: The Angle That Changes Everything
The crossing number k determines the angle between the spoke’s attachment point on the hub flange and where it lands on the rim. In the formula this appears in the cosine term: cos(2 x pi x k / n), where n is the number of spokes per side. When k equals zero (radial lacing), the cosine term equals 1 and the spoke runs perfectly straight from hub to rim. As k increases, the cosine term decreases toward negative values, which increases the value under the square root and therefore increases spoke length. This is why 3-cross spokes are longer than radial spokes on the same wheel: the spoke must travel further to cross its neighbors.
R_rim = ERD / 2
R_fl = flange_PCD / 2
O = center-to-flange distance
k = crossing number (0=radial, 1, 2, 3, 4)
n = spokes per side (total spoke count / 2)
hole_dia = spoke hole diameter in flange
This formula is derived from the same geometric principles found in “The Bicycle Wheel” by Jobst Brandt (the definitive engineering reference on wheel mechanics) and matches the calculation used in the DT Swiss professional spoke calculator and SpocalC. The result is the straight-line distance from the spoke’s elbow at the hub flange to the nipple seat in the rim, minus the spoke hole radius to account for where the spoke head actually seats.
How Does the Crossing Number Change Your Final Millimeter Result?
The cross-pattern comparison chart built into this calculator shows something that no other free online spoke calculator currently offers: a side-by-side visual of how radial through 4-cross lacing affects spoke length for your specific wheel configuration. Most riders and even some mechanics have a general sense that crossing pattern matters, but the chart makes the magnitude concrete.
On a typical 32-spoke road rear wheel with a DT Swiss 240 hub and an ERD of 584 mm, switching from radial lacing to 3-cross increases drive-side spoke length by approximately 5 to 7 mm. This is significant: spokes are ordered in 2 mm increments, so a miscalculation of your crossing number can mean your order arrives two full sizes wrong. The chart instantly shows you this spread across all five crossing options for your exact inputs.
When Is Each Crossing Pattern Appropriate?
Radial lacing (0-cross) is appropriate only for front wheels on road or gravel bikes without disc brakes. It gives a stiff, slightly lighter wheel with a clean visual look and is popular on aerodynamic front wheels where the reduced spoke angle minimizes drag. It is not appropriate for rear wheels under any circumstances because the torque from pedaling and braking creates lateral stress at the hub flange holes that radial lacing cannot distribute. It is also prohibited by most reputable hub manufacturers for disc brake fronts.
One-cross lacing is occasionally used on front wheels where the builder wants a bit more tangential spoke angle than radial allows without the length penalty of two or three cross. Two-cross is a good choice for lightweight rear wheels on road bikes where the rider is lighter and the spoke count is high (28 or more), as the reduced angle still provides adequate torque resistance with slightly shorter spokes than the standard three-cross. Three-cross is the universal default for a reason: it works well for virtually every application, distributes stress evenly, and is widely validated across decades of professional wheel building. Four-cross is used for heavy-duty builds including cargo bikes, tandems, and some e-bike hubs where maximum torque handling is the priority.
Three Real American Build Stories for Road, Trail, and Urban Riding
These three build scenarios walk through the complete measurement and calculation process for different American cycling contexts. Each one highlights a different challenge that riders commonly encounter when using spoke length calculators for the first time.
Jake is building a road wheelset for the Boulder Roubaix and Front Range race series. His Enve SES 4.5AR rims have a published ERD of 570 mm (he confirms this with the two-spoke method and gets 571 mm, so he uses 571). His DT Swiss 240 rear hub has a drive-side PCD of 44.5 mm and a drive-side CTF of 17.4 mm. The non-drive side PCD is the same at 44.5 mm but the CTF is 34.1 mm. He is lacing 24 spokes total in a 2-cross pattern on both sides using Sapim CX-Ray spokes with a 2.0 mm hole diameter. The calculator gives him a drive-side length of 267.8 mm (order 268.0 mm) and a non-drive side length of 276.4 mm (order 276.5 mm). The tension balance is 51 percent, which his wheel builder notes is on the low side for a road race build and suggests a wider-flange hub or more aggressive geometry for better balance.
Dani is rebuilding a rear wheel after a crash broke three spokes and bent the rim flange slightly. She is using an Industry Nine 1/1 Hydra rear hub (PCD 46.0 mm, DS offset 17.5 mm, NDS offset 33.5 mm) with a new Stan’s MK4 29er rim that has an ERD of 583 mm. She wants 32 spokes in 3-cross using standard J-bend Sapim Race spokes with a 2.4 mm hole diameter. The calculator gives her a drive-side length of 279.6 mm (order 280.0 mm) and a non-drive side of 284.2 mm (order 284.5 mm). She also uses the warning indicator to confirm that her chosen 3-cross pattern is appropriate for this disc brake hub, and notes the tension balance of 52 percent, typical for a modern asymmetric MTB hub with Boost spacing.
Marcus snapped a spoke on his daily commuter during a particularly aggressive sprint off a red light. His Shimano Nexus 8-speed rear hub has symmetric flange measurements because internal gear hubs have a different asymmetry than cassette hubs. He measured a PCD of 88 mm (large flange hub) and a CTF of 18.5 mm on both sides. His Alex R390 rim has an ERD of 546 mm. He wants 36 spokes in 3-cross using standard 2.4 mm DT Champion spokes. The calculator gives him symmetric results: 256.4 mm on both sides (order 256.5 mm). Because both sides measure the same, he only needs to order one length, simplifying his trip to the bike shop. He notes that the large flange PCD of this hub (88 mm versus the typical 44 to 48 mm of a derailleur hub) produces notably shorter spokes than he expected.
What Happens When Your Measurement Is Two Millimeters Off?
Two millimeters sounds trivial. In a world of 700c wheels and 29-inch rims, two millimeters is less than half a percent of the diameter. But in wheel building, two millimeters is the difference between a wheel that passes inspection and one that goes straight back to the truing stand, and potentially the difference between a wheel that holds up under load and one that fails catastrophically.
When a spoke is two millimeters too long, the spoke tip protrudes past the top of the nipple slot after tensioning. On a rimmed wheel with inner tube, this spike punctures the rim tape and then the tube every time the wheel flexes, typically on the first ride. On a tubeless rim the same protrusion can compromise the internal sealant layer. The fix is to grind the spoke tip flush, but this weakens the spoke threads and typically leads to spoke breakage within a few thousand miles. The correct fix is to use the next length shorter.
When a spoke is two millimeters too short, the nipple threads do not engage the spoke threads far enough to achieve proper tension. Under load, the nipple head is more likely to pull through the rim nipple hole or strip the thread engagement entirely. The CPSC 16 CFR Part 1512.17 wheel side-load requirement of 2000 N (450 lbf) assumes that all spokes are present and properly tensioned. A wheel with under-engaged nipples cannot meet this structural requirement, which is why professional mechanics reject wheels where spokes bottom out in the nipple before reaching target tension. The correct fix is to use the next length longer.
The 0.5 mm Round-Up Convention
This calculator outputs two numbers: the exact calculated length and the order length, which rounds up to the nearest 0.5 mm. Spokes are manufactured and sold in 0.5 mm increments (for example 262.0, 262.5, 263.0 mm). The convention of always rounding up rather than to the nearest 0.5 mm comes from experience: the exact calculated value assumes perfect component geometry, perfectly centered nipple seats, and zero build-in tolerances. In practice, ERD measurements can be 0.3 to 0.5 mm low if the measurement spoke tips did not fully bottom out in the nipple seats. Rounding up compensates for this systematic measurement error and ensures adequate thread engagement. Most professional wheel builders add a further 1 to 2 mm in their mental model, then verify the first spoke before cutting or ordering the full set.
Why Do Drive-Side and Non-Drive Spokes Measure Differently?
If you have ever built or trued a rear wheel, you know that the rim does not sit in the center of the hub axle when viewed from behind. It is offset to the left, toward the non-drive side. This offset is called dish, and it exists because the cassette body on the drive side occupies space that would otherwise be available for a symmetrically positioned flange. The cassette forces the drive-side flange closer to the center of the axle, which means the drive-side spokes pull the rim from a position closer to center while the non-drive spokes pull from further out. To keep the rim running true in the center of the dropout spacing, the wheel builder has to pull harder on the non-drive side, which means tensioning those spokes higher or accepting a lower tension balance ratio.
How Boost and Super-Boost Spacing Changed the Math
The introduction of Boost hub spacing (148 mm rear over-locknut distance versus the previous 142 mm) was partly motivated by wheel building geometry. By widening the hub slightly, Boost spacing allows both flanges to move outward, improving the tension balance ratio on the drive side specifically. A standard 135 mm rear hub might deliver a tension balance ratio of 42 to 48 percent. A Boost 148 mm hub on the same frame with an equivalent cassette body moves that ratio closer to 50 to 56 percent. Super-Boost (157 mm OLN) pushes it even higher. Higher balance ratios mean the non-drive spokes do not need to be run at extreme over-tension relative to the drive side, which extends spoke and rim life significantly on trail and enduro mountain bikes that see heavy braking loads on the rear wheel.
For front wheels with symmetric hubs (equal CTF on both sides), both the drive-side and non-drive-side calculations return the same spoke length. The calculator still outputs separate fields for front wheels so that the user can verify the symmetry and catch any hub that has an off-center drilling or incorrect preset value. Front hub symmetry is never guaranteed, especially on budget hubs with less precise manufacturing tolerances. Use the calculator as a check even when you expect both sides to be equal.
Six Pro Tips from Certified Bicycle Mechanics
Measure ERD Three Times with Different Spoke Pairs
Rim drilling is never perfectly uniform. Spoke holes around the rim can vary in position by up to 0.3 mm from the theoretical ERD, which is why professional builders measure ERD using three different pairs of opposing holes and average the results. If any single measurement is more than 0.5 mm from the average, the rim has a quality control defect that will make truing difficult regardless of how accurate your spoke lengths are. Most production rims from Mavic, DT Swiss, and Stan’s fall within this tolerance. No-name rims sometimes do not.
Use Spoke Prep on Every Thread Before Assembly
Spoke prep (also called thread compound or spoke butter) is a slightly sticky paste that goes on the spoke threads before you thread the nipple. It has two functions: it prevents the nipple from backing off under vibration and cyclic loads, and it prevents aluminum nipples from galling on stainless steel spoke threads. Without spoke prep, an aluminum nipple on a stainless spoke can seize within a few hundred miles of riding, making future truing adjustments impossible without breaking the nipple. Wheelsmith Spoke Prep is the American market standard. DT Swiss recommends their own compound. Boeshield T-9 is an acceptable substitute.
Stress Relieve Before Final Tension
After initial lacing and truing to roughly correct tension, stand the wheel up and press down firmly on pairs of crossed spokes around the entire wheel. You will hear and feel pops and creaks as the spokes shift and bed into their seats at the hub flange and rim. This stress relief is not optional: it releases trapped stress in the spoke elbows and at the nipple seats that would otherwise release progressively over the first few hundred miles of riding, causing the wheel to go out of true. Do two complete circuits of the wheel at approximately 60 pounds of force on each spoke pair, then retrue and retension to final specification. The USA Cycling mechanic certification curriculum covers this procedure as a mandatory step in any wheel build.
Check Tension with a Gauge, Not Your Fingers
Experienced mechanics can estimate spoke tension by plucking the spoke and listening to the pitch, but this method has a margin of error of plus or minus 20 percent in practiced hands and plus or minus 50 percent for beginners. A Park Tool TM-1 or Wheelsmith tensiometer costs between $60 and $90 and pays for itself on the first wheel by preventing either under-tensioned failures or over-tensioned rim cracking. Target tensions for most road wheels are 100 to 130 kgf on the drive side and proportionally lower on the non-drive side based on your tension balance ratio. MTB wheels typically run 80 to 110 kgf. Always check the rim manufacturer’s maximum tension specification before exceeding 120 kgf.
Recheck After the First 100 Miles
New wheels lose tension over the first 100 miles of riding as the spokes rotate slightly in their elbow seats, the nipples compress into the rim eyelets, and the rim tape beds in. This is normal and expected. Plan for a retensioning and retruing session after the break-in period. Skipping this step is the main reason DIY wheel builds develop spokes that rattle loose, unwind under load, or break prematurely at the elbow. Schedule the follow-up session before you use the wheel for any serious riding, especially if the wheel is for a high-load application like a loaded tour, a race, or daily urban commuting.
Record Your Component Specs in a Permanent Build Log
Write down your verified ERD, hub PCD values, CTF offsets, spoke count, crossing pattern, and final spoke lengths somewhere you will actually find them again: a note in your phone’s app, a label on the inside of the saddle rail, or a shared document. The next time you replace a broken spoke, get a flat from a pinhole puncture through rim tape, or rebuild the wheel entirely, you will have all the inputs ready for the calculator without remeasuring. Professional shops keep build logs for every wheel they sell. Home builders who keep these records spend far less time with calipers and far more time actually riding.
Quick Reference: Hub Flange Specs and ERD Data by Discipline
These ranges represent the majority of production components available in the US market as of 2025 and 2026. Use them to sanity-check any calculator output: if your result falls far outside these typical ranges, verify your measurements before placing a spoke order.
- Road 700c (23-30mm section): 565 to 604 mm
- Road 700c (35-50mm aero deep): 550 to 580 mm
- Gravel 700c (wide, 40-60mm): 555 to 598 mm
- MTB 29er (standard): 558 to 590 mm
- MTB 27.5 / 650b: 528 to 570 mm
- MTB 26 inch: 503 to 535 mm
- Fat bike (26 x 4.0): 480 to 510 mm
- 700c track / velodrome: 563 to 595 mm
- Modern road rear (cassette): 40 to 50 mm
- Modern road front: 42 to 52 mm
- Large-flange road / track: 60 to 100 mm
- MTB Boost rear: 40 to 52 mm
- MTB standard front: 44 to 52 mm
- IGH (internal gear hub): 68 to 100 mm
- Cargo / e-bike rear: 44 to 60 mm
- Tandem: 40 to 55 mm per side
- Road front (3-cross, 24h): 275 to 298 mm
- Road rear DS (3-cross, 28h): 264 to 285 mm
- Road rear NDS (3-cross, 28h): 270 to 295 mm
- MTB 29er rear DS (3-cross, 32h): 272 to 290 mm
- MTB 29er front (3-cross, 32h): 282 to 300 mm
- Track front (radial, 16h): 256 to 270 mm
- Commuter / IGH rear (3-cross, 36h): 250 to 270 mm
- Road race drive side: 110 to 130 kgf
- Road race non-drive: proportional to balance ratio
- Endurance road both sides: 100 to 120 kgf
- MTB XC both sides: 90 to 115 kgf
- MTB trail and enduro: 80 to 110 kgf
- Commuter / touring: 80 to 100 kgf
- Cargo / tandem: 100 to 125 kgf
- Never exceed rim maker’s published maximum
Frequently Asked Questions About Hub and Rim Measurements
More Tools for the Active American Cyclist
Round out your workshop toolkit with these related calculators, all free and built for US riders.