BIZOMAT MAKEOS · Engineering
Bolt Circle Coordinates
Where are the centres of equally spaced holes?
Generate a coordinate table for an equally spaced bolt circle with a defined origin, start angle and direction.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Pitch circle diameter | mm | Hole-centre circle diameter from the drawing. |
| Hole count | holes | Equally spaced hole count. |
| Start angle from +X | ° | First hole angle; positive angles are anticlockwise. |
| Centre X | mm | Circle centre relative to the drawing or setup origin. |
| Centre Y | mm | Circle centre relative to the drawing or setup origin. |
| Numbering direction | choice | Direction in which successive hole numbers increase. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Pitch circle diameter
- What it is
- The diameter of the circle that passes through the centres of all the holes, often called the PCD.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All hole offsets from the centre and the chord between holes are directly proportional to it.
- Get it right
- Do not use the radius or the outside diameter of the flange; hole positions use half this value.
What this means: Hole count
- What it is
- The number of holes equally spaced around the bolt circle.
- Units and format
- Enter a number in holes: holes. The form accepts 2 holes to 100 holes. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 holes as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More holes give a smaller angular spacing and shorter chord.
- Get it right
- The tool assumes equal spacing; unequal patterns need coordinates worked out separately.
What this means: Start angle from +X
- What it is
- The angle of hole 1, measured from the positive X axis around the circle centre. Positive angles run anticlockwise.
- Units and format
- Enter a number in °: degrees of angle. The form accepts -360° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It rotates the whole pattern without changing spacing.
- Get it right
- Check whether your drawing measures from X or from Y; 90° here means hole 1 is straight up.
What this means: Centre X
- What it is
- The X coordinate of the bolt circle centre relative to the drawing or machine setup origin.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It shifts every X coordinate by the same amount.
- Get it right
- Use the same origin and units as your program; leave 0 if the centre is the origin.
What this means: Centre Y
- What it is
- The Y coordinate of the bolt circle centre relative to the drawing or machine setup origin.
- Units and format
- Enter a number in mm: millimetres. The form accepts -1000000 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It shifts every Y coordinate by the same amount.
- Get it right
- Check the Y direction for your view: some setups have Y positive away from the operator.
What this means: Numbering direction
- What it is
- Whether hole numbers 1, 2, 3 and so on increase anticlockwise or clockwise around the circle, as seen in the drawing view.
- Units and format
- Choose one of 2 options from the list: Anticlockwise; Clockwise.
- Example
- The form opens with “Anticlockwise” selected as a worked example. Choose the option that matches your case.
- Get it right
- Viewing from the back of the part reverses the direction; confirm the view matches the setup.
Method and formulas
- Angular step = 360° ÷ hole count.
- X = centre X + radius × cos(angle); Y = centre Y + radius × sin(angle).
- Adjacent chord = 2 × radius × sin(π ÷ hole count). Example: four holes on a 100 mm circle centred at zero give (50,0), (0,50), (−50,0), (0,−50).
Limitations
- Coordinates are geometry only, not a CNC program.
- The drawing’s datum, view direction and tolerance system must be resolved separately.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- PCD
- hole coordinates
- bolt pattern
Who it is for
- Designers
- Toolmakers
- CNC programmers
What you get
- Angular spacing
- Adjacent centre chord
- Coordinate count
Interpreting the result
- Check one known hole and the coordinate origin before transferring positions to equipment.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 95–103, 692–695. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Bolt circles, polar arrays and arc slots
In Drafting Geometry by the Numbers
What it covers: Lay out holes on a pitch circle, set polar arrays without the fill-angle error, draw straight and arc slots exactly, and calculate the adjustment an arc slot really gives.
Method explained here · BIZOMAT original book
Rings, stiffeners and flanges
What it covers: Roll a 75 × 75 × 6 angle into a ring on its centroid, not its back: length, toe and heel strains, toe-out against toe-in, splices, bolt circles on the outlet flange, and a ring cut 132 mm short.
Method explained here · Library collection
Circles, arcs, chords and bolt circles: hole patterns, rolled shells, bends and radius checks
In Practical Mathematics for Engineering and Manufacturing
What it covers: How circumference, arc length, chords and sagitta solve practical problems, from bolt-circle hole coordinates and rolled cylinders to sheet metal bend allowances and finding a radius from a chord.
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