Spoke Length Calculators [Long]
2Phat4Rapha
Posts: 258
Declaration of interest: I’m not making any money out of it but I’ve written my own wheel building database that includes a spoke length calculator. It’s on my site for free (http://www.dalynchi.co.uk/wbpe.html) and you are welcome to use it if you want to.
In so doing I became being interested in all things wheelie. I’ve read all the standard texts, Jobst, Gerd, Sheldon and followed the likes of Damon Rinard and Roger Musson. I also lurk and sometimes contribute to many a forum where wheel building might feature and regularly see that:
 new wheel builders usually want to use component measurements supplied by somebody else.
 they then want other people to check the resulting spoke lengths
 and then they get confused when different spoke length calculators give different answers.
The first two are understandable. When they start out novices are likely to be short of one key ingredient  confidence. But there’s plenty of advice available online on how to do the measurements yourself and that is what it is always best to do. With practice it takes only minutes. Measure several times. Average the results. Never believe someone else’s data. Believe what you own eyes tell you!
The answer to the third point is not so obvious and I’ve seen it many times on forums when a poster prefers one calculator to another because it gives “better” answers. Truth is I haven’t found a bad calculator. Some might be easier to use than others (subjective) but I’ve found them all to be accurate and fit for purpose.
Why different spoke length calculators may sometimes appear to give different answers is that sometimes they ask for slightly different things or there are assumptions built into the formula that are not obvious. So, rather like the exam advice you are given at school “answer the question in front of you, not the one you think they are asking”, it’s really important to understand the dimensions of the components you have before you and what precisely each spoke length calculator refers to. So here’s some of the “gotchas” to watch out for…
ERD
In the geometry of spoke length calculation, ERD, the Effective Rim Diameter, is the largest dimension by far and hence influences the calculated spoke length much more than any of the hub dimensions. What also distinguishes ERD is the utter confusion about what it actually means.
To begin at the beginning, Jobst Brandt wrote in the first edition of “The Bicycle Wheel” 1981, p132,
Or in English, where do you want your spoke ends to finish?
He further states in the 2003 edition p126
This is the definition adopted by early spoke length calculators such as Damon Rinard and endorsed by Roger Musson and others who advise how to determine this diameter by using two spokes cut to 200mm and nipples fixed so that the threaded end of the spokes are flush with the top of the nipple head. Some wheel builders might modify this slightly so that they calculate the spoke end to the bottom of the slot in the nipple head but that is their choice  the accepted definition of ERD is still the distance across the tops of opposing nipple heads. So unless a spoke length calculator states otherwise, that is the measurement for ERD that you must provide.
Sapim on the other hand take a slightly different approach and ask instead for two dimensions; the internal diameter of the rim and the depth of the spoke holes taking account of the thickness of any eyelets. This provides the diameter across the surface upon which the nipple heads sit and could therefore be called the “Nipple Seat Diameter”.
This is not a good point at which to land your spoke ends as it would leave the nipple head unsupported by spoke threads at a point bearing the full tension in the spoke. So Sapim’s calculator automatically adds a 2.7mm compensation for the spoke heads, hence conforming to the accepted definition of ERD. They don’t tell you this on their site but they were very prompt and helpful confirming it when I asked them.
Why do it this way? Well, it could be argued that rim manufacturers can’t provide an accurate ERD unless they know what nipples are going to be used. Mavic for example don’t supply an ERD, they give the Nipple Seat Diameter  except they’ve decided to add to the confusion by giving it their own name too, “Spoke Support Diameter”.
It is essential therefore that you are absolutely clear about what is meant by ERD  top to top of opposing nipple heads, and that you only apply it if that’s what your choice of spoke length calculator asks for. If it asks for the Nipple Seat Diameter (Spoke Support Diameter) you can either remeasure as Sapim indicate on their calculator, or convert the ERD to the NSD by subtracting twice the height if the nipple heads.
Specify the wrong dimension in either of the above calculators and you could easily introduce a 4mm to 6mm difference in “ERD” with a consequent 2mm/3mm difference in final spoke length.
Pitch Circle Diameter
DT Swiss requires the diameter to be measured centretocentre between opposite spoke holes, so do Roger Musson and Damon Rinard. But be careful with Sapim because they state outside edge to outside edge.
This is important because a couple of mm difference here can lead to a 1mm difference in a 3 cross lacing and possibly looking like 2mm when rounded up or down. So be careful that your measurement reflects which calculator you are using or, if working off printed specs, be clear about what they actually mean.
Spoke Hole Diameter
DT Swiss and Roger Musson ask for it, Sapim doesn’t so it’s making an assumption somewhere. It’ll be somewhere between 2mm and 3mm but I can’t find anything on their site to confirm it precisely. In itself the spoke hole diameter doesn’t affect the final spoke length very much but, as above, it’s influence on the PCD may be significant.
Flange Thickness
DT Swiss are not specific about from where on the flanges they measure their “flange distance”  outside surface, inside surface or centre line. Sapim’s instructions specify from the outside surfaces, Roger Musson the inside and Damon Rinard the centre line. On its own this measurement doesn’t lead to any great errors but you should still be careful about the aggregation of incremental differences.
Nipple Length.
DT Swiss state in their help text that their calculation is based upon 12mm nipples and suggest that if you use 16mm DT nipples you deduct 1mm from the calculated spoke length and for 16mm nipples you deduct 3mm. However, although the “precise” calculated value remains the same whichever nipple length you enter, the “rounded incl. corrections” value not only does the rounding but also deducts 2mm for 14mm nipples and 4mm for 16mm nipples. Confusing? You bet.
Roger Musson recognises this auto correction but has also determined through experience that these estimates are excessive. He therefore recommends deducting only 1mm for 14mm DT nipples and 2mm for 16mm.
Sapim don’t tell you but it’s very likely that their calculations are based upon 12mm nipples and it would seem reasonable to suppose that you adjust for different lengths the same way too. Roger Musson disagrees however and suggests you make no corrections for different length Sapim nipples.
Rounding
Whatever the calculated spoke length you will inevitably have to round it to the nearest millimetre and often to the nearest even number of millimetres. But do you round up or down? Unfortunately there can be as much debate about this as compact vs double so I’ll refer once again to Jobst Brandt:
Whilst this is good advice in principle, Roger Musson recognises that often you can only buy spokes in even numbered lengths so slavishly rounding down a spoke that is almost an even number would be excessive. A 265.9mm answer for example would better be rounded up to 266mm as deducting 1.9mm would be too much.
Washers
I won’t go into the whys and wherefores of using washers here but you can use them at the spoke head and at the rim hole. I can find any hard and fast rule about adjusting calculated spokes lengths for washers but it seems that some wheel builders add 1mm when using them.

To sum up then, I haven’t found any “bad” spoke length calculators, they are all accurate. You just have to be alert to the precise dimensions that your choice of calculator asks for. If you observe a difference between calculators there will be a reason, it just might not be that obvious.
In so doing I became being interested in all things wheelie. I’ve read all the standard texts, Jobst, Gerd, Sheldon and followed the likes of Damon Rinard and Roger Musson. I also lurk and sometimes contribute to many a forum where wheel building might feature and regularly see that:
 new wheel builders usually want to use component measurements supplied by somebody else.
 they then want other people to check the resulting spoke lengths
 and then they get confused when different spoke length calculators give different answers.
The first two are understandable. When they start out novices are likely to be short of one key ingredient  confidence. But there’s plenty of advice available online on how to do the measurements yourself and that is what it is always best to do. With practice it takes only minutes. Measure several times. Average the results. Never believe someone else’s data. Believe what you own eyes tell you!
The answer to the third point is not so obvious and I’ve seen it many times on forums when a poster prefers one calculator to another because it gives “better” answers. Truth is I haven’t found a bad calculator. Some might be easier to use than others (subjective) but I’ve found them all to be accurate and fit for purpose.
Why different spoke length calculators may sometimes appear to give different answers is that sometimes they ask for slightly different things or there are assumptions built into the formula that are not obvious. So, rather like the exam advice you are given at school “answer the question in front of you, not the one you think they are asking”, it’s really important to understand the dimensions of the components you have before you and what precisely each spoke length calculator refers to. So here’s some of the “gotchas” to watch out for…
ERD
In the geometry of spoke length calculation, ERD, the Effective Rim Diameter, is the largest dimension by far and hence influences the calculated spoke length much more than any of the hub dimensions. What also distinguishes ERD is the utter confusion about what it actually means.
To begin at the beginning, Jobst Brandt wrote in the first edition of “The Bicycle Wheel” 1981, p132,
To compute spoke lengths it is necessary to determine the effective rim diameter to within one millimetre. This is the diameter to which the end of the fully tensioned spokes extend.
Or in English, where do you want your spoke ends to finish?
He further states in the 2003 edition p126
The effective rim diameter is the diameter to which the ends of the fully engaged spokes will extend (flush with the end of the spoke nipple).
This is the definition adopted by early spoke length calculators such as Damon Rinard and endorsed by Roger Musson and others who advise how to determine this diameter by using two spokes cut to 200mm and nipples fixed so that the threaded end of the spokes are flush with the top of the nipple head. Some wheel builders might modify this slightly so that they calculate the spoke end to the bottom of the slot in the nipple head but that is their choice  the accepted definition of ERD is still the distance across the tops of opposing nipple heads. So unless a spoke length calculator states otherwise, that is the measurement for ERD that you must provide.
Sapim on the other hand take a slightly different approach and ask instead for two dimensions; the internal diameter of the rim and the depth of the spoke holes taking account of the thickness of any eyelets. This provides the diameter across the surface upon which the nipple heads sit and could therefore be called the “Nipple Seat Diameter”.
This is not a good point at which to land your spoke ends as it would leave the nipple head unsupported by spoke threads at a point bearing the full tension in the spoke. So Sapim’s calculator automatically adds a 2.7mm compensation for the spoke heads, hence conforming to the accepted definition of ERD. They don’t tell you this on their site but they were very prompt and helpful confirming it when I asked them.
Why do it this way? Well, it could be argued that rim manufacturers can’t provide an accurate ERD unless they know what nipples are going to be used. Mavic for example don’t supply an ERD, they give the Nipple Seat Diameter  except they’ve decided to add to the confusion by giving it their own name too, “Spoke Support Diameter”.
It is essential therefore that you are absolutely clear about what is meant by ERD  top to top of opposing nipple heads, and that you only apply it if that’s what your choice of spoke length calculator asks for. If it asks for the Nipple Seat Diameter (Spoke Support Diameter) you can either remeasure as Sapim indicate on their calculator, or convert the ERD to the NSD by subtracting twice the height if the nipple heads.
Specify the wrong dimension in either of the above calculators and you could easily introduce a 4mm to 6mm difference in “ERD” with a consequent 2mm/3mm difference in final spoke length.
Pitch Circle Diameter
DT Swiss requires the diameter to be measured centretocentre between opposite spoke holes, so do Roger Musson and Damon Rinard. But be careful with Sapim because they state outside edge to outside edge.
This is important because a couple of mm difference here can lead to a 1mm difference in a 3 cross lacing and possibly looking like 2mm when rounded up or down. So be careful that your measurement reflects which calculator you are using or, if working off printed specs, be clear about what they actually mean.
Spoke Hole Diameter
DT Swiss and Roger Musson ask for it, Sapim doesn’t so it’s making an assumption somewhere. It’ll be somewhere between 2mm and 3mm but I can’t find anything on their site to confirm it precisely. In itself the spoke hole diameter doesn’t affect the final spoke length very much but, as above, it’s influence on the PCD may be significant.
Flange Thickness
DT Swiss are not specific about from where on the flanges they measure their “flange distance”  outside surface, inside surface or centre line. Sapim’s instructions specify from the outside surfaces, Roger Musson the inside and Damon Rinard the centre line. On its own this measurement doesn’t lead to any great errors but you should still be careful about the aggregation of incremental differences.
Nipple Length.
DT Swiss state in their help text that their calculation is based upon 12mm nipples and suggest that if you use 16mm DT nipples you deduct 1mm from the calculated spoke length and for 16mm nipples you deduct 3mm. However, although the “precise” calculated value remains the same whichever nipple length you enter, the “rounded incl. corrections” value not only does the rounding but also deducts 2mm for 14mm nipples and 4mm for 16mm nipples. Confusing? You bet.
Roger Musson recognises this auto correction but has also determined through experience that these estimates are excessive. He therefore recommends deducting only 1mm for 14mm DT nipples and 2mm for 16mm.
Sapim don’t tell you but it’s very likely that their calculations are based upon 12mm nipples and it would seem reasonable to suppose that you adjust for different lengths the same way too. Roger Musson disagrees however and suggests you make no corrections for different length Sapim nipples.
Rounding
Whatever the calculated spoke length you will inevitably have to round it to the nearest millimetre and often to the nearest even number of millimetres. But do you round up or down? Unfortunately there can be as much debate about this as compact vs double so I’ll refer once again to Jobst Brandt:
Note that a spoke under full tension can stretch up to about one millimetre … The rim, depending on its strength, can also shrink in diameter as much as two millimetres. Therefore, the computed spoke length should always be rounded down rather than up.
Whilst this is good advice in principle, Roger Musson recognises that often you can only buy spokes in even numbered lengths so slavishly rounding down a spoke that is almost an even number would be excessive. A 265.9mm answer for example would better be rounded up to 266mm as deducting 1.9mm would be too much.
Washers
I won’t go into the whys and wherefores of using washers here but you can use them at the spoke head and at the rim hole. I can find any hard and fast rule about adjusting calculated spokes lengths for washers but it seems that some wheel builders add 1mm when using them.

To sum up then, I haven’t found any “bad” spoke length calculators, they are all accurate. You just have to be alert to the precise dimensions that your choice of calculator asks for. If you observe a difference between calculators there will be a reason, it just might not be that obvious.
I may be a minority of one but that doesn't prevent me from being right.
http://www.dalynchi.com
http://www.dalynchi.com
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