How to Calculate Bolt Circle Diameter (BCD) for Chainrings and Bash Guards

Updated on November 14, 2018
eugbug profile image

Eugene is a qualified control/instrumentation engineer Bsc (Eng) and has worked as a developer of electronics & software for SCADA systems.

Bolt circle diameter (BCD)
Bolt circle diameter (BCD) | Source

What's a Bolt Circle Diameter (BCD) or Pitch Circle Diameter (PCD)?

As you may be aware aware if you've found this guide, a bolt circle is an imaginary circle that passes through the centre of the bolt or screw holes in a round pattern. This is typically a wheel hub on a vehicle, chain ring on a bicycle or flange on a pipe. The diameter of this circle is known as the bolt circle diameter (BCD) or pitch circle diameter (PCD). Typically BCD is quoted for bash guards covering the chain wheels on bikes and you can calculate it by measuring the distance between the fixing holes. If you need to make a ring or other shape out of card or metal, or order a part for a bicycle, you may need to know this dimension.

Imaginary bolt circle
Imaginary bolt circle | Source

Some Revision: Sine and Cosine for a Right Angled Triangle

A right-angled triangle has one of angle that measures 90 degrees. The longest side opposite this angle is called the hypotenuse. Sine and cosine are trigonometric functions of an angle and are the ratios of the lengths of the other two sides to the hypotenuse of a right-angled triangle.

Let's represent one of the angles by the Greek letter θ (theta).

Side a is called the "opposite" side and side b is called the "adjacent" side to the angle θ.

"|" around the words below means "length of"

Then:

sine θ = |opposite side| / |hypotenuse|

cosine θ = |adjacent side| / |hypotenuse|

Sine and cosine are sometimes abbreviated to sin and cos

Sine and cosine
Sine and cosine | Source

Angle Subtended by the Arc

Since there are 360 degrees in a full circle, then if there are N equally spaced holes, the angle subtended by an arc (produced by joining the ends of the arc to the centre) on an imaginary circle passing through the bolt holes is:

θ = 360 / N

Angle subtended by arc
Angle subtended by arc | Source

Use Sine and Cosine to Work Out the Radius

We can draw triangles and use sine and cosine to solve the triangles and find the length of the radius R, and therefore the diameter D.

Working out bolt circle diameter (BCD)
Working out bolt circle diameter (BCD) | Source

Working Out the Formula for Bolt Circle Diameter

The simplest case is when holes are equally spaced around in a circle.

If we can find the radius R of the bolt circle, then this gives us the diameter D

We calculated that:

θ = 360 / N

Also A is the spacing between holes.

A triangle can be drawn between the two ends of an arc on the bolt circle and the centre of the circle. This can be split up into two equal right angled triangles. The length of the chord or line joining the two ends of the arc is A.

(For more info on circles see this guide :
How to Calculate Arc Length of a Circle Segment and Sector Area)

The sine of an angle in a right angled triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

So Sin (θ/2) = |opposite| / |hypotenuse| = (A/2) / R

Rearranging:

R = (A/2) / Sin (θ/2)

But D = 2R

So D = (A/2) / Sin (θ/2) x 2 = A/Sin (θ/2)

But we worked out θ = 360 / N

So substituting for θ gives

D = A/Sin (θ/2) = A/Sin ((360 / N)/2) = A/Sin (180 / N)


D = A/Sin (180 / N)

Equation for Bolt Circle Diameter

BCD equation. D is it BCD, N is the number of holes and A is the hole spacing
BCD equation. D is it BCD, N is the number of holes and A is the hole spacing | Source

Working Out the BCD for a Chainring or Bash Guard

All you need to do to calculate the BCD is measure the hole spacing A between adjacent holes, count the number of holes N and plug them into the equation above to calculate the BCD.

A bicycle chainring
A bicycle chainring | Source

Tables of Bolt Circle Diameters

The tables below gives the BCD for hole spacings from 10 to 200 mm, 1 to 12 inches and 3 to 8 holes.

Table 1 - Bolt Circle Diameters for Hole Spacings From 10 to 200 mm

 
 
 
Number of Holes
 
 
 
Hole Spacing A (mm)
3
4
5
6
7
8
10
11.5
14.1
17.0
20
23.0
26.1
11
12.7
15.6
18.7
22
25.4
28.7
12
13.9
17.0
20.4
24
27.7
31.4
13
15.0
18.4
22.1
26
30.0
34.0
14
16.2
19.8
23.8
28
32.3
36.6
15
17.3
21.2
25.5
30
34.6
39.2
16
18.5
22.6
27.2
32
36.9
41.8
17
19.6
24.0
28.9
34
39.2
44.4
18
20.8
25.5
30.6
36
41.5
47.0
19
21.9
26.9
32.3
38
43.8
49.6
20
23.1
28.3
34.0
40
46.1
52.3
21
24.2
29.7
35.7
42
48.4
54.9
22
25.4
31.1
37.4
44
50.7
57.5
23
26.6
32.5
39.1
46
53.0
60.1
24
27.7
33.9
40.8
48
55.3
62.7
25
28.9
35.4
42.5
50
57.6
65.3
26
30.0
36.8
44.2
52
59.9
67.9
27
31.2
38.2
45.9
54
62.2
70.6
28
32.3
39.6
47.6
56
64.5
73.2
29
33.5
41.0
49.3
58
66.8
75.8
30
34.6
42.4
51.0
60
69.1
78.4
31
35.8
43.8
52.7
62
71.4
81.0
32
37.0
45.3
54.4
64
73.8
83.6
33
38.1
46.7
56.1
66
76.1
86.2
34
39.3
48.1
57.8
68
78.4
88.8
35
40.4
49.5
59.5
70
80.7
91.5
36
41.6
50.9
61.2
72
83.0
94.1
37
42.7
52.3
62.9
74
85.3
96.7
38
43.9
53.7
64.6
76
87.6
99.3
39
45.0
55.2
66.4
78
89.9
101.9
40
46.2
56.6
68.1
80
92.2
104.5
41
47.3
58.0
69.8
82
94.5
107.1
42
48.5
59.4
71.5
84
96.8
109.8
43
49.7
60.8
73.2
86
99.1
112.4
44
50.8
62.2
74.9
88
101.4
115.0
45
52.0
63.6
76.6
90
103.7
117.6
46
53.1
65.1
78.3
92
106.0
120.2
47
54.3
66.5
80.0
94
108.3
122.8
48
55.4
67.9
81.7
96
110.6
125.4
49
56.6
69.3
83.4
98
112.9
128.0
50
57.7
70.7
85.1
100
115.2
130.7
51
58.9
72.1
86.8
102
117.5
133.3
52
60.0
73.5
88.5
104
119.8
135.9
53
61.2
75.0
90.2
106
122.2
138.5
54
62.4
76.4
91.9
108
124.5
141.1
55
63.5
77.8
93.6
110
126.8
143.7
56
64.7
79.2
95.3
112
129.1
146.3
57
65.8
80.6
97.0
114
131.4
148.9
58
67.0
82.0
98.7
116
133.7
151.6
59
68.1
83.4
100.4
118
136.0
154.2
60
69.3
84.9
102.1
120
138.3
156.8
61
70.4
86.3
103.8
122
140.6
159.4
62
71.6
87.7
105.5
124
142.9
162.0
63
72.7
89.1
107.2
126
145.2
164.6
64
73.9
90.5
108.9
128
147.5
167.2
65
75.1
91.9
110.6
130
149.8
169.9
66
76.2
93.3
112.3
132
152.1
172.5
67
77.4
94.8
114.0
134
154.4
175.1
68
78.5
96.2
115.7
136
156.7
177.7
69
79.7
97.6
117.4
138
159.0
180.3
70
80.8
99.0
119.1
140
161.3
182.9
71
82.0
100.4
120.8
142
163.6
185.5
72
83.1
101.8
122.5
144
165.9
188.1
73
84.3
103.2
124.2
146
168.2
190.8
74
85.4
104.7
125.9
148
170.6
193.4
75
86.6
106.1
127.6
150
172.9
196.0
76
87.8
107.5
129.3
152
175.2
198.6
77
88.9
108.9
131.0
154
177.5
201.2
78
90.1
110.3
132.7
156
179.8
203.8
79
91.2
111.7
134.4
158
182.1
206.4
80
92.4
113.1
136.1
160
184.4
209.1
81
93.5
114.6
137.8
162
186.7
211.7
82
94.7
116.0
139.5
164
189.0
214.3
83
95.8
117.4
141.2
166
191.3
216.9
84
97.0
118.8
142.9
168
193.6
219.5
85
98.1
120.2
144.6
170
195.9
222.1
86
99.3
121.6
146.3
172
198.2
224.7
87
100.5
123.0
148.0
174
200.5
227.3
88
101.6
124.5
149.7
176
202.8
230.0
89
102.8
125.9
151.4
178
205.1
232.6
90
103.9
127.3
153.1
180
207.4
235.2
91
105.1
128.7
154.8
182
209.7
237.8
92
106.2
130.1
156.5
184
212.0
240.4
93
107.4
131.5
158.2
186
214.3
243.0
94
108.5
132.9
159.9
188
216.6
245.6
95
109.7
134.4
161.6
190
219.0
248.2
96
110.9
135.8
163.3
192
221.3
250.9
97
112.0
137.2
165.0
194
223.6
253.5
98
113.2
138.6
166.7
196
225.9
256.1
99
114.3
140.0
168.4
198
228.2
258.7
100
115.5
141.4
170.1
200
230.5
261.3
101
116.6
142.8
171.8
202
232.8
263.9
102
117.8
144.2
173.5
204
235.1
266.5
103
118.9
145.7
175.2
206
237.4
269.2
104
120.1
147.1
176.9
208
239.7
271.8
105
121.2
148.5
178.6
210
242.0
274.4
106
122.4
149.9
180.3
212
244.3
277.0
107
123.6
151.3
182.0
214
246.6
279.6
108
124.7
152.7
183.7
216
248.9
282.2
109
125.9
154.1
185.4
218
251.2
284.8
110
127.0
155.6
187.1
220
253.5
287.4
111
128.2
157.0
188.8
222
255.8
290.1
112
129.3
158.4
190.5
224
258.1
292.7
113
130.5
159.8
192.2
226
260.4
295.3
114
131.6
161.2
193.9
228
262.7
297.9
115
132.8
162.6
195.6
230
265.0
300.5
116
133.9
164.0
197.4
232
267.4
303.1
117
135.1
165.5
199.1
234
269.7
305.7
118
136.3
166.9
200.8
236
272.0
308.3
119
137.4
168.3
202.5
238
274.3
311.0
120
138.6
169.7
204.2
240
276.6
313.6
121
139.7
171.1
205.9
242
278.9
316.2
122
140.9
172.5
207.6
244
281.2
318.8
123
142.0
173.9
209.3
246
283.5
321.4
124
143.2
175.4
211.0
248
285.8
324.0
125
144.3
176.8
212.7
250
288.1
326.6
126
145.5
178.2
214.4
252
290.4
329.3
127
146.6
179.6
216.1
254
292.7
331.9
128
147.8
181.0
217.8
256
295.0
334.5
129
149.0
182.4
219.5
258
297.3
337.1
130
150.1
183.8
221.2
260
299.6
339.7
131
151.3
185.3
222.9
262
301.9
342.3
132
152.4
186.7
224.6
264
304.2
344.9
133
153.6
188.1
226.3
266
306.5
347.5
134
154.7
189.5
228.0
268
308.8
350.2
135
155.9
190.9
229.7
270
311.1
352.8
136
157.0
192.3
231.4
272
313.4
355.4
137
158.2
193.7
233.1
274
315.8
358.0
138
159.3
195.2
234.8
276
318.1
360.6
139
160.5
196.6
236.5
278
320.4
363.2
140
161.7
198.0
238.2
280
322.7
365.8
141
162.8
199.4
239.9
282
325.0
368.5
142
164.0
200.8
241.6
284
327.3
371.1
143
165.1
202.2
243.3
286
329.6
373.7
144
166.3
203.6
245.0
288
331.9
376.3
145
167.4
205.1
246.7
290
334.2
378.9
146
168.6
206.5
248.4
292
336.5
381.5
147
169.7
207.9
250.1
294
338.8
384.1
148
170.9
209.3
251.8
296
341.1
386.7
149
172.1
210.7
253.5
298
343.4
389.4
150
173.2
212.1
255.2
300
345.7
392.0
151
174.4
213.5
256.9
302
348.0
394.6
152
175.5
215.0
258.6
304
350.3
397.2
153
176.7
216.4
260.3
306
352.6
399.8
154
177.8
217.8
262.0
308
354.9
402.4
155
179.0
219.2
263.7
310
357.2
405.0
156
180.1
220.6
265.4
312
359.5
407.6
157
181.3
222.0
267.1
314
361.8
410.3
158
182.4
223.4
268.8
316
364.2
412.9
159
183.6
224.9
270.5
318
366.5
415.5
160
184.8
226.3
272.2
320
368.8
418.1
161
185.9
227.7
273.9
322
371.1
420.7
162
187.1
229.1
275.6
324
373.4
423.3
163
188.2
230.5
277.3
326
375.7
425.9
164
189.4
231.9
279.0
328
378.0
428.6
165
190.5
233.3
280.7
330
380.3
431.2
166
191.7
234.8
282.4
332
382.6
433.8
167
192.8
236.2
284.1
334
384.9
436.4
168
194.0
237.6
285.8
336
387.2
439.0
169
195.1
239.0
287.5
338
389.5
441.6
170
196.3
240.4
289.2
340
391.8
444.2
171
197.5
241.8
290.9
342
394.1
446.8
172
198.6
243.2
292.6
344
396.4
449.5
173
199.8
244.7
294.3
346
398.7
452.1
174
200.9
246.1
296.0
348
401.0
454.7
175
202.1
247.5
297.7
350
403.3
457.3
176
203.2
248.9
299.4
352
405.6
459.9
177
204.4
250.3
301.1
354
407.9
462.5
178
205.5
251.7
302.8
356
410.2
465.1
179
206.7
253.1
304.5
358
412.6
467.7
180
207.8
254.6
306.2
360
414.9
470.4
181
209.0
256.0
307.9
362
417.2
473.0
182
210.2
257.4
309.6
364
419.5
475.6
183
211.3
258.8
311.3
366
421.8
478.2
184
212.5
260.2
313.0
368
424.1
480.8
185
213.6
261.6
314.7
370
426.4
483.4
186
214.8
263.0
316.4
372
428.7
486.0
187
215.9
264.5
318.1
374
431.0
488.7
188
217.1
265.9
319.8
376
433.3
491.3
189
218.2
267.3
321.5
378
435.6
493.9
190
219.4
268.7
323.2
380
437.9
496.5
191
220.5
270.1
324.9
382
440.2
499.1
192
221.7
271.5
326.6
384
442.5
501.7
193
222.9
272.9
328.4
386
444.8
504.3
194
224.0
274.4
330.1
388
447.1
506.9
195
225.2
275.8
331.8
390
449.4
509.6
196
226.3
277.2
333.5
392
451.7
512.2
197
227.5
278.6
335.2
394
454.0
514.8
198
228.6
280.0
336.9
396
456.3
517.4
199
229.8
281.4
338.6
398
458.6
520.0
200
230.9
282.8
340.3
400
461.0
522.6

Table 2 - Bolt Circle Diameters for Hole Spacings From 1 to 12 Inches

Bolt circle diameter. Value in brackets is to nearest 1/16"
Bolt circle diameter. Value in brackets is to nearest 1/16"

© 2018 Eugene Brennan

Comments

    0 of 8192 characters used
    Post Comment

    No comments yet.

    working

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, owlcation.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://owlcation.com/privacy-policy#gdpr

    Show Details
    Necessary
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Features
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Marketing
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Statistics
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)