Bolt Circle Calculator uses BCD, hole count, and start angle to calculate chord distance, angle step, pitch radius, and X/Y coordinates using C = BCD × sin(π/N) for circular hole layout checks in CNC.
| Hole # | Angle | X Coord (in) | Y Coord (in) |
|---|---|---|---|
| 1 | 0.000° | 2.0000 | 0.0000 |
| 2 | 72.000° | 0.6180 | 1.9021 |
| 3 | 144.000° | -1.6180 | 1.1756 |
| 4 | 216.000° | -1.6180 | -1.1756 |
| 5 | 288.000° | 0.6180 | -1.9021 |
This Bolt Circle Calculator generates the full set of X/Y Cartesian coordinates, adjacent hole chord distance, angle step, and pitch radius for any equally-spaced bolt hole pattern — from three inputs: number of holes, bolt circle diameter (BCD), and starting angle. Enter your parameters and the calculator immediately returns every hole position in a coordinate table ready for use at the machine, on the drawing, or in a DRO.
What the Bolt Circle Calculator Finds
Each result the calculator produces serves a specific layout or machining purpose. The cards below explain every output in the same order it appears in the tool.
The straight-line chord distance between two neighbouring hole centres — the distance you would measure with calipers across adjacent holes on the finished part. Useful for a quick dimensional check before committing to final machining, and for scribing or punch layout on flat plate.
The angular increment between consecutive holes — 360° divided equally by the hole count. For a 5-hole pattern this is 72.000°. The Hole 2 Angle is the absolute angular position of the second hole, measured from the 3 o'clock position (0°) counterclockwise unless a starting angle offset is entered. Use the angle step to index a rotary table, set a dividing head, or verify angular spacing from a drawing callout.
The radius of the bolt circle — exactly half the BCD. When a drawing specifies a Pitch Circle Diameter (PCD) or BCD, the pitch radius is the dimension you set on a rotary table or use to define the tool path radius in CNC. It is the distance from the centre of the part to the centre of each hole.
The absolute X/Y coordinate offsets from the bolt circle centre (origin 0,0) for holes 1 and 2. These are the values you enter into a DRO or CNC controller to position the spindle over each hole. Hole 1 sits at the starting angle; Hole 2 is one angle step further around the circle.
Confirms the total hole count and shows the angular position and X/Y coordinates of the last hole in the sequence. Cross-check this against the first hole to verify rotational closure of the pattern before drilling.
A complete table listing hole number, angle, X coordinate, and Y coordinate for every hole in the pattern. Copy this directly into a job card, a DRO sequence list, or a CNC program comment block. All coordinates reference the same centre origin (0,0) so they can be entered in any order without accumulated error.
Bolt Circle Formulas
All calculations are trigonometric functions applied to the pitch radius and the hole angles. No approximations are used — the full floating-point results are computed before being rounded for display.
R = BCD ÷ 2
The radius of the bolt circle. All X and Y coordinates are computed from this value.
θ_step = 360° ÷ N
The equal angular increment between any two consecutive holes. Produces whole-number degree steps for common bolt patterns (e.g. 4-hole = 90°, 6-hole = 60°, 8-hole = 45°).
C = BCD × sin( π ÷ N )
The chord length — straight-line distance between two adjacent hole centres — derived from the inscribed polygon relationship. For N = 5 and BCD = 4.000 in: C = 4.000 × sin(π/5) = 4.000 × 0.5878 = 2.351 in.
θ_i = θ_start + ( i − 1 ) × θ_step
The absolute angular position for each hole, counted from the starting angle. i = 1 for the first hole, i = N for the last. All angles are in degrees, measured counterclockwise from the 3 o'clock (positive X-axis) direction.
X_i = R × cos( θ_i ) Y_i = R × sin( θ_i )
Standard Cartesian trigonometry applied to the pitch radius and each hole angle. Angles are converted to radians internally (radians = degrees × π / 180) before applying cos and sin. Results are signed — negative values indicate holes in the left (X) or lower (Y) half of the circle.
Worked Example
Using the calculator's default values — 5 holes on a 4.000 in bolt circle starting at 0.0° — the following results are produced step by step.
| Hole # | Angle | X Coord (in) | Y Coord (in) |
|---|---|---|---|
| 1 | 0.000° | 2.0000 | 0.0000 |
| 2 | 72.000° | 0.6180 | 1.9021 |
| 3 | 144.000° | −1.6180 | 1.1756 |
| 4 | 216.000° | −1.6180 | −1.1756 |
| 5 | 288.000° | 0.6180 | −1.9021 |
How to Use the Results
Each output value serves a specific purpose at the machine or on the drawing. The guide below matches each result to its most common application.
After scribing or rough-drilling, use the chord distance to verify spacing between adjacent hole centres with a set of calipers. This is the fastest manual check for a bolt pattern before committing to finish drilling or reaming. On a flange or hub, it also confirms the pattern did not index incorrectly between holes.
Set the angle step directly on a rotary table or manual indexing head to advance between holes. In a CNC environment, use the angle step in a drilling cycle loop or verify it against the angular dimension shown on the engineering drawing. For a 5-hole pattern at 72.000°, any deviation from this value in the drawing or setup indicates an error to resolve before drilling.
Enter each hole's X and Y values directly as absolute position offsets from the part centre into your DRO or CNC controller. All coordinates in the table reference the same centre origin (0,0), so they can be entered in any sequence — no incremental chaining or accumulated offset error. For CNC use, the coordinate table from this calculator maps directly to absolute G90 mode position calls.
When setting up a rotary table offset or defining a bolt circle tool path in CAM software, use the pitch radius rather than the full BCD. Some DRO systems and legacy manual setups ask for the circle radius rather than the diameter — the pitch radius output eliminates the mental divide-by-two step and the risk of entering the wrong value.
By default, starting angle 0° places Hole 1 at the 3 o'clock position (positive X-axis). Enter a different starting angle to rotate the entire pattern to align Hole 1 with a keyway, datum surface, or existing feature on the part. All other hole coordinates update automatically — the relative spacing between holes does not change.
⚠ Assumptions and Limitations
The Bolt Circle Calculator produces mathematically exact results for equally-spaced circular patterns from the entered parameters. Before using any coordinate in a machining operation or inspection decision, note the following:
- Equal spacing only: All holes are assumed to be equally spaced at the same angular interval. The calculator does not support unequally spaced or asymmetric bolt patterns.
- Coordinates reference the circle centre at origin (0,0): All X and Y values are offsets from the geometric centre of the bolt circle. If your machine datum, workpiece zero, or drawing origin is at a different location, you must apply the appropriate offset to shift the coordinate set.
- Sign convention follows standard mathematics: Positive X is to the right, positive Y is upward, angles are measured counterclockwise from the positive X-axis. Some machine tools or drawings use different conventions — confirm your machine's coordinate orientation before entering values.
- Whole number of holes, minimum 2: Hole count (N) must be a positive integer of at least 2. Decimal entries are not accepted.
- BCD must be a positive value: Zero or negative BCD inputs are rejected. There is no minimum BCD enforced beyond positive value — ensure the BCD matches your drawing and is expressed in the selected unit system.
- No hole geometry calculations: This calculator does not compute hole diameter, clearance fit, fastener size, thread engagement, torque, bolt load, or any tolerance stack-up. These require separate calculations based on your applicable engineering drawing and fastener standard.
- Always verify against the engineering drawing: Coordinate values from this calculator should be cross-checked against the dimensioned engineering drawing, tolerances, and machine setup before drilling, punching, or milling. Final acceptance of the machined part depends on the drawing requirements and applicable dimensional tolerances, not this calculator alone.
References
The trigonometric methods, coordinate conventions, and unit relationships used in this calculator are consistent with the following authoritative sources. Consult them for dimensioning standards, tolerance requirements, and machining practice guidance applicable to your work.