# Spoke length calculator review

`By Roger Musson, 20 July 2018`

I'm going to look at some of the popular online spoke length calculators, and check the method they use to calculate the spoke lengths.

If you know that a calculator has been changed since this review date, then please let me know and I'll update the review.

# The spoke length formula

If you understand the geometry of a cycle wheel, you can easily derive the spoke length formula using basic trigonometry. Here is the standard spoke length formula which is used by all the calculators under review.

Where:

 R = Rim radius (half the ERD) H = Hub flange radius F = Hub flange offset X = Cross pattern h = Number of spokes in the wheel d = Diameter of the spoke hole in the hub

This formula uses angles in radians, which is the default for spreadsheets and programming languages.

# Wheel data

The data is for one side of the wheel. If you want to put the data into one of the calculators, then use the same hub data for both left and right sides.

 Hub diameter 50 35 2.6 600 28 2

# Effective Rim Diameter ERD

This is the diameter of the rim at the spoke ends in the finished wheel, and the calculator will calculate a spoke length that reaches this point. For example, if I were using standard 12mm nipples, then I'd want the spoke ends to finish somewhere between the top surface of the nipple and the bottom of the nipple slot, and for 12mm nipples, my ERD measurement would be taken at the bottom of the nipple slot.

# The standard calculation

Using the wheel data, the formula gives a spoke length of 285.9240

This length is purely theoretical, it doesn't mean that spokes cut to 285.924 will be the perfect length, because spokes are elastic, and in a tensioned wheel the spokes will stretch (this is elastic stretch, once the tension is removed, they will return to their original length). Longer spokes will stretch more, thinner spokes will stretch more, higher tensioned spokes will stretch more, and a spoke can stretch up to 1mm. So you need to use your wheelbuilding experience to determine the correct length to build with, taking into consideration the intended spoke type, and their location. For example a rear wheel with tighter drive side spokes (more stretch), and not so tight non drive (not as much stretch), and type of spoke being used, for example, a Sapim CX-Ray will stretch more than a Sapim Race, etc.

There is some leeway when selecting a suitable spoke length, and a spoke length +/- 1mm from this standard calculation is usually okay. Some calculators will specifically advise how to round the fractional spoke lengths, for example the Wheelpro calculator.

Two of the calculators reviewed here will refine the output from the formula by taking into account the spoke elasticity, and produce a more accurate spoke length.

# Standard calculators

The following calculators use the basic spoke length formula shown above, and do not modify the output.

They all calculate a spoke length of 285.9

## Edd

`www.leonard.io/edd/`

## Pro Wheel Builder

`www.prowheelbuilder.com/spokelengthcalculator/`

## United Bicycle Institute

`www.bikeschool.com/index.php/resources/spoke-calculator`

## FreeSpoke

kstoerz.com/freespoke/fullcalc

## Spocalc

`www.sheldonbrown.com/rinard/spocalc.htm`

These calculators do something different...

# The Sapim calculator

`www.sapim.be/spoke-calculator`

The formula used by the Sapim calculator does not include the spoke hole diameter in the hub, so will produce spoke lengths 1.3mm longer. However, for the Sapim calculator, you need to specify the rim erd the Sapim way, which is measured at the internal diameter of the rim, then specify the rim thickness, which puts the erd at the nipple seat diameter. Their calculation method is :

1. Calculate the spoke length using the standard formula, but do not include the hub spoke hole parameter.
2. Round the result to the nearest whole number.
3. Add on the rim thickness.

The additional 1.3mm from missing out the hub spoke hole diameter in the formula will give an approximately correct spoke length when using standard nipples.

The test data erd of 600 is measured the standard way, and it's not possible to show you a test calculation with the Sapim calculator, because it requires the rim internal diameter and rim thickness. They also specify the hub flange offsets in a non standard way.

# DT Swiss calculator

`spokes-calculator.dtswiss.com/en/calculator`

This calculator will compensate for spoke stretch, and also modifies the length based on the selected DT nipple.

1. Calculate the spoke length using the standard formula.
2. Use correction values based on the selected DT spoke and DT nipple.
3. Round to the nearest whole number.

For this test, I'll specify DT Competition 2.0/1.8 spokes, and DT 12mm nipples.

Two spoke lengths are shown : 285.9 (accurate) 286 (recommended)

The accurate length is the standard length given by the formula (not strictly accurate, it's just the standard calculation). The recommended length uses correction factors shown in the tables below.

285.9 - 0 (DT Competition correction) - 0 (DT 12mm nipple correction) = 285.9
Rounded to the nearest whole number gives 286

An example, using DT Revolution 2.0/1.5 spokes and DT 14mm nipples.

285.9 - 0.5 (DT Rev correction) - 1 (DT 14mm nipple correction) = 284.4
Rounded to the nearest whole number gives 284

## DT correction values (17 July 2018)

The correction value for the spoke does not take into account spoke tension (tighter spokes will stretch more), so on a rear wheel with 50% less tension on the left side, the compensation value will be the same.

The correction value for the nipple is only for DT nipples. In particular, DT 14 and 16mm nipples will affect the spoke length (longer nipples from other manufacturers generally, do not).

The correction tables are shown below. The values were conveniently stored as a javascript object in the calculator source code, so it was easy to take a copy of it, and write a few lines of code to format these tables (which means I didn't have to type every entry, and there are no transcription errors). There seems to be a lot of inconsistencies in the correction values.

These are the nipple corrections that DT use, when a straight pull hub is selected.

# The Wheelpro calculator

`www.wheelpro.co.uk/spokecalc/`

This calculator will compensate for spoke stretch.

1. Calculate the spoke length using the standard formula.
2. Modify the standard length by calculating the spoke stretch using engineering equations, taking into account the spoke type, and spoke tension.

DT Competition 2.0/1.8 spokes. Calculated spoke length : 285.3

DT Revolution 2.0/1.5 spokes. Calculated length : 285.0

If you calculate a spoke length, then check the Log, you will see the standard length and how it is then refined for spoke stretch. If you calculate for a dished wheel (and check the Log), you will see that tension ratio is also taken into account, with the lower tensioned side stretching less.

# Conclusion

It's easy to test whether your chosen calculator is using a basic calculation, just put the test data into it and see if the result is 285.9

This review is only to show how each calculator works. Obviously I have my opinion on which calculator is the best, but I'm biased, because I designed and wrote one of them! Choose whatever you like.