BIZOMAT MAKEOS · Geometry
Bolt Circle Layout (Coordinates, Ligament, Edge and Wrench Clearance)
Where do the holes of this bolt circle go, is there enough metal between holes and to the edges, and will a socket fit between the bolts?
Layout of equally spaced holes on a bolt circle: angular step, adjacent centre chord and the coordinates of each hole (as the bolt circle tool), the ligament between neighbouring holes, edge distances to the outside and bore of the flange, whether the socket or wrench fits between neighbouring bolts, and the most bolts the wrench clearance allows on this circle.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Bolt circle diameter | mm | Diameter of the circle through the hole centres. |
| Number of holes | Number of equally spaced holes. | |
| Angle of the first hole | ° | Angle of the first hole from the X axis, anticlockwise. |
| Hole diameter | mm | Diameter of the holes. |
| Flange outside diameter | mm | Outside diameter of the flange. |
| Flange bore (0 = solid) | mm | Diameter of the central bore (0 for a solid cover). |
| Socket or wrench clearance diameter | mm | Outside diameter of the socket or the swing clearance the wrench needs at each bolt. |
| Least ligament between holes | mm | Least metal you accept between neighbouring holes. |
| Least edge distance (hole edge to flange edge) | mm | Least metal you accept from a hole to the outside or bore edge. |
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: Bolt circle diameter
- What it is
- The diameter of the circle passing through the centres of all the bolt holes, also called the pitch circle diameter (PCD).
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 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
- The chord between holes, and so ligament and socket room, grow in proportion.
- Get it right
- A diameter, not the radius to a hole centre.
What this means: Number of holes
- What it is
- The number of holes, equally spaced around the bolt circle.
- Units and format
- Enter a plain number with no unit. The form accepts 2 to 360. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More holes shorten the chord between neighbours, reducing ligament and socket room.
What this means: Angle of the first hole
- What it is
- The angular position of the first hole, measured anticlockwise from the X axis through the circle centre. The other holes follow at equal steps.
- 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 45° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure anticlockwise from the positive X axis; a negative value goes clockwise.
What this means: Hole diameter
- What it is
- The diameter of each bolt hole as drilled, including any clearance over the bolt size.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 11 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the drilled hole size, not the bolt size.
What this means: Flange outside diameter
- What it is
- The outside diameter of the flange or cover. The edge distance from the holes to it is checked.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 140 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be larger than the bolt circle, or the tool stops.
What this means: Flange bore (0 = solid)
- What it is
- The diameter of the central bore through the flange. The edge distance from the holes to the bore is checked.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter 0 for a solid cover with no bore.
What this means: Socket or wrench clearance diameter
- What it is
- The clearance diameter needed around each bolt to turn it: the outside diameter of the socket, or the swing room for the spanner.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 24 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter 0 to skip the socket check.
What this means: Least ligament between holes
- What it is
- The least web of metal you accept between the edges of neighbouring holes, from your design rules.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Least edge distance (hole edge to flange edge)
- What it is
- The least metal you accept from the edge of a hole to the outside edge of the flange or to the bore, from your design rules.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Step = 360° ÷ n; chord = BCD sin(180° ÷ n); hole i at (BCD ÷ 2) (cos θ_i, sin θ_i) (as the bolt circle tool).
- Ligament = chord − hole diameter; outside edge = (OD − BCD) ÷ 2 − d_h ÷ 2; bore edge = (BCD − ID) ÷ 2 − d_h ÷ 2.
- Socket fits if chord ≥ socket diameter; most bolts = ⌊180° ÷ sin⁻¹(socket ÷ BCD)⌋.
- Example: 4 holes on 100 mm are 70.711 mm apart with 59.711 mm ligament; up to 12 bolts leave room for the socket.
Limitations
- Equally spaced holes; unequal patterns need individual angles.
- Coordinates from the bolt circle centre; add the part datum offsets.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Lay out a flange or cover bolt pattern
- Check a design for wrench access
- Program hole positions for drilling
Who it is for
- Design engineers
- CNC programmers
- Drafters
What you get
- Angular step, chord and coordinates
- Ligament and edge distances
- Wrench fit and the most bolts it allows
Interpreting the result
- Wrench clearance, not ligament, usually limits the number of bolts on small circles.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 686. Topic reference; no source tables or recommended settings are reproduced.
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Open the Bolt Circle Layout (Coordinates, Ligament, Edge and Wrench Clearance) calculator