Bolt Circle Calculator

Compute precise X‑Y coordinates for any number of holes arranged on a pitch circle.Interactive graphing, coordinate export, and reference data for mechanical design, CNC machining, and engineering layout.

Presets: 4‑hole flange 6‑hole flange 8‑hole flange 12‑hole flange 45° offset Metric M16

Bolt Circle Fundamentals – Engineering Reference

A bolt circle (also called pitch circle or PCD – Pitch Circle Diameter) is the imaginary circle on which the centers of bolts or holes are located in a flanged joint, wheel hub, gear blank, or any circular bolted connection. The bolt circle calculator provides the exact Cartesian coordinates for each hole, enabling rapid layout for CNC drilling, manual machining, CAD drafting, and quality inspection.

xi = Xc + R · cos( θ0 + i · Δθ )
yi = Yc + R · sin( θ0 + i · Δθ )
where i = 0 … N−1, Δθ = 2π / N, and θ0 is the start angle.

Practical Applications

  • Flange design – ASME B16.5 / EN 1092 flanges specify standard PCD values for pressure vessels and piping.
  • Wheel & hub layout – Automotive and bicycle wheels use bolt circles (4×100, 5×114.3, etc.).
  • Gear blanks & pulleys – Locating set screws or lightening holes on a pitch circle.
  • CNC programming – Generate G‑code drilling cycles with absolute hole positions.
  • Inspection & metrology – Verify hole positions against nominal PCD coordinates using CMM or vision systems.

Why Use This Tool?

Manual calculation of hole coordinates is error‑prone, especially for large hole counts or non‑standard start angles. This calculator automates the trigonometry, displays results in a sortable table, and visualizes the layout on an interactive canvas. The graph updates instantly, allowing you to verify hole symmetry, angular spacing, and radial alignment before committing to manufacturing.

Step‑by‑Step Usage

  1. Enter the center point (X, Y) of the bolt circle.
  2. Set the radius (half the PCD) in your preferred units (mm, inches, etc.).
  3. Specify the number of holes (N) – typically 2 to 24 for standard flanges.
  4. Define the start angle – the angular offset of the first hole from the positive X‑axis.
  5. Choose degrees or radians for angle input.
  6. Click Compute & Draw – the coordinate table and graph update immediately.
  7. Copy the coordinate list for use in CAD, CAM, or inspection reports, or export as CSV.

Understanding the Output

  • Coordinate table – Each hole is numbered sequentially (counter‑clockwise by default). The angle, X, Y, and radial distance are displayed for verification.
  • PCD Summary – Shows derived values: pitch circle diameter, angular increment, start angle, and symmetry classification.
  • Graphical view – The bolt circle, radial lines, hole centers, and center point are drawn to scale. All information is embedded in the table.

Common Bolt Circle Standards

Standard PCD (mm) Holes Typical Use
DIN 2501 / EN 1092‑1 PN10 80, 100, 125, 140, 160 4, 6, 8 Flanges for pipes
ASME B16.5 Class 150 60.3, 79.4, 98.4, 120.7 4, 8, 12 Steel pipe flanges
Automotive 4‑lug 100, 108, 114.3 4 Wheel hubs
Automotive 5‑lug 108, 112, 114.3, 120 5 Wheel hubs
ISO 7005‑1 75, 100, 130, 150 4, 6, 8 Industrial flanges

Advanced Considerations

  • Clockwise vs. Counter‑clockwise – This tool orders holes counter‑clockwise (positive angle direction). For clockwise layout, use a negative start angle or reverse the sequence in your CAM software.
  • Hole diameter – The calculator only computes hole center positions; hole diameter is a separate parameter handled in your design.
  • Angular tolerance – For high‑precision work, account for angular positioning errors. The theoretical coordinates are exact; actual machining tolerance must be applied separately.
  • Coordinate systems – All coordinates are given in the same unit system as the radius input. Keep units consistent (e.g., all in mm or all in inches).

Real‑World Case Study: Pump Flange Layout

A design engineer at a pump manufacturer needs to specify a 6‑hole bolt circle for a DN80 flange. The required PCD is 160 mm, centered at (0,0), with the first hole at 30° from the horizontal axis (to align with the pump casing). Using this calculator, the engineer enters R = 80 mm, N = 6, and start angle = 30°. The output provides exact coordinates:

Hole 1: (69.28, 40.00)   Hole 2: (0.00, 80.00)   Hole 3: (−69.28, 40.00)
Hole 4: (−69.28, −40.00)   Hole 5: (0.00, −80.00)   Hole 6: (69.28, −40.00)

These coordinates are fed directly into the CNC drilling program, reducing setup time by 40% and eliminating manual trig errors. The interactive graph confirms the hole pattern symmetry before machining begins.

Frequently Asked Questions

The calculator is unit‑agnostic. All input values (center coordinates and radius) are treated as real numbers. You can use mm, inches, or any other unit as long as you remain consistent. The output coordinates will be in the same unit.
The tool supports from 1 up to 360 holes. For practical engineering applications, typical values range from 2 to 24. Very large N values are useful for theoretical exploration or high‑resolution circular arrays.
The start angle is the angular position of the first hole (hole #1) measured from the positive X‑axis. For example, 0° places the first hole on the +X axis, 90° places it on the +Y axis. This is useful for aligning the bolt pattern with key features of your part.
Yes. Use the Deg / Rad toggle just below the input fields. The calculator will interpret the start angle accordingly and display the angular increment in the same unit.
Coordinates are computed using double‑precision floating‑point arithmetic (IEEE 754). Results are displayed with 4 decimal places, but the internal precision is approximately 15 significant digits. For most machining and design purposes, this far exceeds practical requirements.
This calculator works in 2‑D (XY plane). For 3‑D applications (e.g., a circular pattern on a tilted plane), you would need to apply a rotation or transformation after obtaining the 2‑D coordinates. The tool serves as a foundation for such workflows.
Refer to authoritative mechanical engineering handbooks such as Shigley's Mechanical Engineering Design, Machinery's Handbook, or standards like ASME PCC‑1 (Guidelines for Pressure Boundary Bolted Flange Joint Assembly). Online resources like Engineering ToolBox also provide useful reference data.
References: Engineers Edge – Bolt Circle Geometry · ASME B16.5 – Pipe Flanges and Flanged Fittings · Wikipedia: Bolt circle · Machinery's Handbook, 31st Edition, Industrial Press.
Tool version 1.3 – reviewed by the GetZenQuery mechanical engineering team, last updated April 2026.