construction

Bolt Circle Calculator

Bolt circle layout is essential for manufacturing flanges, brackets, and structural connections. This calculator maps the exact position of each hole in a circular pattern by computing Cartesian coordinates from your specified radius, hole count, starting angle, and centerpoint offset. Machinists, fabricators, and CAD technicians use it to generate coordinate lists for CNC mills, drilling robots, and design software without manual trigonometry.

Last updated: May 1, 2026

Creators Maciej Kowalski, Civil Engineer

Reviewers Tom Wright and Joanna Andrzejewska

2,863 people find this calculator helpful

Understanding Bolt Circles

A bolt circle is the imaginary circumference passing through the center of all holes in a circular array. When you need to fasten components—such as pump flanges, motor mounts, or pipe connections—the holes must align precisely on this circle.

Key parameters defining your bolt circle are:

Radius (R): Distance from the bolt circle's center to each hole's center
Number of holes (n): Count of fastener positions
Starting angle (A): Angular position of the first hole, measured from the horizontal (0° to 360°)
Angular spacing (B): Gap between consecutive holes, calculated as 360° ÷ n
Centerpoint offset: X and Y coordinates locating the bolt circle's center relative to your origin (often 0,0)

These parameters let you generate a complete coordinate table suitable for machine programming, drilling templates, or fabrication drawings.

Calculating Hole Positions

Each hole's position is computed using polar-to-Cartesian conversion. The formulas account for angular spacing, your chosen starting angle, and the offset of the circle's center.

B = 360° ÷ n

x_i = R × cos((i − 1) × B + A) + x_c

y_i = R × sin((i − 1) × B + A) + y_c

B — Angular spacing between consecutive holes (degrees)
n — Total number of holes in the circle
R — Radius of the bolt circle (distance from center to hole center)
i — Hole number (1, 2, 3, … n)
A — Starting angle of the first hole (degrees from horizontal)
x_c, y_c — Coordinates of the bolt circle's center relative to your reference origin
x_i, y_i — Calculated Cartesian coordinates of hole i

Step-by-Step Workflow

Enter your bolt circle parameters in this order:

Number of holes: Count the fastener positions needed. Common patterns include 4, 6, 8, and 12.
Radius: Measure or specify the distance from the center to any hole center in millimeters or your preferred unit.
First hole angle: Set where the numbering begins—0° points right (positive X direction), 90° points up (positive Y).
Center offset (x, y): If your bolt circle doesn't align with the origin, enter its actual position. Leave as (0, 0) if centered.

The calculator returns a table with each hole number, its angle, and X–Y coordinates. Export this data directly to your CNC control, CAM software, or drilling jig design.

Common Pitfalls and Best Practices

Avoid costly errors when translating bolt circle data into production.

Verify the starting angle convention — Different CAD and CNC systems measure angles differently—some use 0° at 3 o'clock, others at 12 o'clock. Always confirm your machine's angle reference before drilling or programming. A single 90° misalignment can ruin your part.
Check your radius measurement twice — An error of 1 mm in radius compounds across all holes, creating an off-center bolt circle. Measure from the flange mounting face or drawing datum plane, not from an arbitrary edge.
Account for tool clearance and material thickness — The bolt circle defines nominal hole positions. In practice, ensure your drill bit diameter, hole tolerance, and the thickness of material don't cause binding. Larger-diameter bolts may need wider clearance holes.
Test with a small sample first — For critical parts, drill or machine a few holes on one prototype and check them with calipers or a coordinate measuring machine (CMM) before committing the full array. Catching an offset or angular error early saves time and material.

CNC and CAM Integration

Most CNC machines accept coordinates in plain-text or proprietary formats. Common approaches:

G-code format: Convert your hole list to machine code. Example: N10 X50 Y0 Z−5 G01 moves to coordinates (50, 0) and plunges 5 mm deep.
CAM software import: Many programs accept CSV or spreadsheet data. Paste your X–Y table directly into the coordinate input field.
Drilling templates: Print the hole layout at full scale, mount it on your workpiece, and use it as a visual guide for manual drilling.

Always verify units (mm vs. inches) match between your calculator output and your machine's control system. A unit mismatch can result in holes placed at 25.4× the intended distance.

Frequently Asked Questions

What is the relationship between bolt circle radius and hole spacing?

Holes on a smaller-radius bolt circle are closer together; on a larger radius, they spread farther apart. The straight-line distance between adjacent holes increases with radius and depends on the number of holes. For example, on a 50 mm radius circle with 4 holes, the angular spacing is 90°, so adjacent holes are separated by about 70.7 mm. On the same circle with 6 holes, angular spacing is 60°, and adjacent holes are roughly 51.8 mm apart. You can calculate linear spacing using the chord length formula: 2R × sin(B/2), where B is the angular spacing in radians.

Can I start numbering my bolt circle at an angle other than 0°?

Yes—this is the starting angle parameter. Setting it to 90° rotates your entire pattern 90° counterclockwise. This is useful when you need to align a hole with a specific feature on your part, such as a mounting lug or a cutout. Once you set the angle, all subsequent hole positions rotate by the same amount, preserving the pattern's integrity.

How do I convert hole coordinates into a drilling template for manual work?

Print the coordinate table at full scale (1:1 ratio, no shrinkage). Use a drill press with an adjustable table or an XY vise. Set each coordinate using the machine's digital readout or vernier calipers. Alternatively, create a physical template: mark the hole centers on a flat sheet using the coordinates, then use the sheet as a guide. For high precision, transfer-punch the locations first and inspect with a depth gauge before drilling.

Why do my actual hole positions not match the calculated coordinates?

Check these common sources of error: incorrect centerpoint offset entry, wrong radius measurement, misaligned machine axes or work-holding, drill bit runout (wobble), or tool deflection in thin material. Always verify the machine's axis origins, use sharp drill bits, apply consistent coolant, and clamp parts rigidly. For tolerances tighter than ±0.5 mm, consider using reaming after drilling to ensure accuracy.

What's the difference between bolt circle diameter and radius?

Bolt circle diameter is exactly twice the radius. If your drawing specifies "BCD 100 mm" (bolt circle diameter), divide by 2 to get the radius (50 mm) for this calculator. Some older drawings use "BC" or "PCD" (pitch circle diameter) as equivalent terms. Always double-check your source document to avoid a factor-of-two error.

Can this calculator handle non-equally-spaced hole patterns?

This calculator assumes equal angular spacing (360° ÷ n). For non-uniform patterns—such as asymmetric flanges or custom mounting brackets—you'll need to calculate hole positions individually using the given formulas, adjusting the angle for each hole manually, or use specialized CAM software. Some advanced programs allow you to input custom angles for each position.

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