# Bolt Circle Calculator (Hole Coordinates, Pitch and Chord)

> Source: https://netray.co/tools/bolt-circle-hole-coordinates-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Enter the pitch circle diameter, hole count and start angle to get the X and Y position of any hole plus the chord between neighbours.

## Category

engineering-plm

## Industry

Discrete Manufacturing

## Audience

- CNC programmer
- Machinist
- Design engineer

## Tool

**Kind:** calculator

**Inputs:**

#### Pitch circle diameter

**Key:** pcd

**Type:** number

**Default:** 100

**Min:** 1

**Step:** 0.5

**Unit:** mm

#### Number of holes

**Key:** n

**Type:** number

**Default:** 6

**Min:** 3

**Max:** 48

**Step:** 1

#### Hole number to locate

**Key:** k

**Type:** number

**Default:** 2

**Min:** 1

**Max:** 48

**Step:** 1

**Help:** Hole 1 is at the start angle. Counting runs counterclockwise.

#### Start angle of hole 1

**Key:** start

**Type:** number

**Default:** 0

**Min:** -360

**Max:** 360

**Step:** 1

**Unit:** deg

**Help:** Measured counterclockwise from the positive X axis.

**Outputs:**

#### Pitch circle radius

**Key:** radius

**Expr:** pcd / 2

**Format:** decimal

#### Angular pitch

**Key:** pitch

**Expr:** 360 / n

**Format:** decimal

**Description:** Degrees between adjacent holes.

#### Chord between adjacent holes

**Key:** chord

**Expr:** pcd*(pi/n)*(1 - (pi*pi/(n*n))/6*(1 - (pi*pi/(n*n))/20*(1 - (pi*pi/(n*n))/42*(1 - (pi*pi/(n*n))/72*(1 - (pi*pi/(n*n))/110*(1 - (pi*pi/(n*n))/156*(1 - (pi*pi/(n*n))/210*(1 - (pi*pi/(n*n))/272*(1)))))))))

**Format:** decimal

**Primary:** true

**Description:** Straight-line spacing, equal to PCD times sin(180/n).

#### Hole angle (radians, reduced)

**Key:** theta

**Expr:** (start + 360 * (k - 1) / n - 360 * round((start + 360 * (k - 1) / n) / 360)) * pi / 180

**Format:** decimal

#### Sine of hole angle

**Key:** sin_t

**Expr:** theta*(1 - theta*theta/6*(1 - theta*theta/20*(1 - theta*theta/42*(1 - theta*theta/72*(1 - theta*theta/110*(1 - theta*theta/156*(1 - theta*theta/210*(1 - theta*theta/272*(1)))))))))

**Format:** decimal

#### Cosine of hole angle

**Key:** cos_t

**Expr:** 1 - theta*theta/2*(1 - theta*theta/12*(1 - theta*theta/30*(1 - theta*theta/56*(1 - theta*theta/90*(1 - theta*theta/132*(1 - theta*theta/182*(1 - theta*theta/240*(1))))))))

**Format:** decimal

#### Hole X coordinate

**Key:** x

**Expr:** radius * cos_t

**Format:** decimal

**Primary:** true

#### Hole Y coordinate

**Key:** y

**Expr:** radius * sin_t

**Format:** decimal

**Primary:** true

**Disclaimer:** Coordinates are relative to the centre of the pattern. Sine and cosine use a series accurate to well below 0.001 mm for normal sizes. Verify the first program run on scrap.

## Content

**Intro:** A bolt circle, also called a pitch circle diameter or PCD pattern, is a set of equally spaced holes on a circle. This calculator gives the X and Y position of any hole in the pattern, the angular pitch, and the chord distance between adjacent holes for layout or inspection.

**Sections:**

#### How to use it

**Body:** Enter the PCD, the number of holes and the start angle of hole 1, measured counterclockwise from the positive X axis. Then enter the number of the hole you want to locate. Step through hole numbers to get a full coordinate list for a CNC program or CMM routine, and read the centre of the pattern as the origin. If your pattern is offset, add the offset to every X and Y value. For a six-hole pattern at 100 mm PCD starting at zero degrees, hole 2 is at X 25.000 and Y 43.301.

#### The formulas

**Body:** Hole k is at angle theta equal to the start angle plus 360 times k minus 1 over n. Its coordinates are X equals radius times cosine theta and Y equals radius times sine theta, where radius is half the PCD. The chord between adjacent holes is PCD times the sine of 180 degrees over n. For the default six holes this is 100 times 0.5, or 50 mm, since a hexagon has sides equal to its circumradius. The tool evaluates sine and cosine with a convergent series, as the formula engine has no trig functions.

#### Using the results

**Body:** Chord spacing is what you check with calipers or a hole-to-hole CMM measurement. For an even number of holes, opposite holes sit exactly one PCD apart. For an odd number, the farthest pair is PCD times the sine of (90 degrees times (n minus 1) over n), or simply use coordinates. Allow for the tolerance on the PCD in your drawing, usually a position callout of a few hundredths of a millimetre for flange work.

**Bullets:**

- Cross-check the last hole against the first by rotating through a full circle
- Use a bolt hole circle cycle or macro if your control has one
- For imperial parts, enter inches and read inches

#### Common mistakes

**Body:** Typical mistakes are mixing up PCD with radius, forgetting that hole 1 starts at the start angle rather than at 90 degrees, counting clockwise on a drawing that counts counterclockwise, and rounding every coordinate to two decimals so the error accumulates around the circle. Also watch odd hole counts, where holes are not diametrically opposite, so a direct across-the-pattern measurement is not simply the PCD.

**Cta:** If you generate CNC programs or inspection plans from item and routing data in your ERP, we can help connect those so geometry like this is not retyped.

**Faq:**

#### How do you calculate bolt circle hole coordinates?

**Answer:** Compute each hole angle as start angle plus 360 times hole number minus 1 over the number of holes, then X equals half the PCD times cosine of the angle and Y equals half the PCD times sine. Add any pattern centre offset afterwards.

#### What is the chord distance between bolt holes?

**Answer:** It is the straight-line distance between adjacent hole centres, equal to the pitch circle diameter times the sine of 180 degrees divided by the number of holes. For six holes the chord equals the radius.

#### What does PCD mean?

**Answer:** PCD stands for pitch circle diameter, the diameter of the circle passing through the centres of all holes in the pattern. It is the main dimension on flange and wheel drawings, often written with the hole count, such as 6 holes on 100 PCD.

#### How do I measure a bolt circle with an odd number of holes?

**Answer:** Opposite holes do not exist, so you cannot measure the PCD directly. Measure the chord between adjacent holes or between two nonadjacent holes and compare with the calculated value, or use a CMM to fit a circle through all the hole centres.

## Search terms

bolt circle calculator, bolt hole circle coordinates, pcd calculator, pitch circle diameter hole coordinates, bolt circle chord length, bolt pattern calculator, hole circle x y calculator, cnc bolt circle program

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