Bolt Circle Calculator

Calculate bolt circle diameter (PCD), adjacent hole spacing, and first-hole coordinates for any bolt pattern.

Practical Guide

Bolt Circle Calculator

Bolt circles (also called pitch circle diameter or PCD patterns) show up everywhere—flanges, couplings, wheel hubs, baseplates, sprockets, covers, and jigs. This guide explains the geometry behind bolt circles, how to use the calculator correctly, and how to interpret spacing and coordinates so your parts assemble cleanly the first time.

6–8 min read Updated 2025

Quick Start

Use these steps to get a correct bolt pattern quickly. The calculator is built around standard equal-spacing bolt circle geometry.

  1. 1 Choose your Solve For mode: Adjacent Spacing & First-Hole Coordinates (when the bolt circle diameter is known) or Bolt Circle Diameter (PCD) (when adjacent spacing is known).
  2. 2 Enter the number of holes \(N\). This must be an integer ≥ 2. Odd counts are fine.
  3. 3 If solving spacing/coordinates, enter the bolt circle diameter \(D\) and its units.
  4. 4 If solving PCD, enter the adjacent hole spacing (chord) \(S\) and its units.
  5. 5 Set a start angle \( \alpha \) if you want the first hole rotated from the +X axis. Use \(0^\circ\) for a hole on the right. (Hidden automatically in PCD mode.)
  6. 6 Pick output units (mm, cm, m, in, ft). Results and quick stats will display in these units.
  7. 7 Read the result, then sanity-check with the quick stats (radius and angle between holes).

Tip: The calculator uses equally spaced holes. If your pattern is asymmetric, you’ll need custom coordinates.

Common mistake: Adjacent spacing is a straight-line chord, not arc length along the circle.

Choosing Your Method

Bolt circles can be defined a few different ways in drawings and standards. Pick the approach that matches your input data.

Method A — Known Bolt Circle Diameter (PCD)

Most machine drawings and flange standards specify the bolt circle diameter directly.

  • Fastest when PCD is in the spec.
  • Directly gives radius, adjacent spacing, and coordinates.
  • Best for layout on CNC, drilling jigs, or CAD sketches.
  • Requires a reliable PCD value—don’t guess from OD without checking.
You enter \(N\) and \(D\). The calculator outputs \(S\) and \((x_0,y_0)\).

Method B — Known Adjacent Hole Spacing (Chord)

Sometimes you measure an existing part and only know the spacing between neighboring holes.

  • Perfect for reverse-engineering or field verification.
  • Uses just a caliper measurement and hole count.
  • Small measurement errors propagate into the calculated PCD.
  • Harder to measure accurately when holes are large or angled.
You enter \(N\) and \(S\). The calculator outputs \(D\).

Method C — Two-Hole Across Measurement

A common shop trick is measuring between two holes separated by one or more pitches.

  • Reduces error on small circles by spanning more distance.
  • Useful if adjacent holes are hard to access.
  • You must know how many pitches are between the holes measured.
  • Not directly supported—convert to \(S\) first.
Convert to chord using \(S_k = D\sin(k\pi/N)\), then use Method B.

What Moves the Number

Bolt circle outputs are driven by a few dominant variables. Understanding these “levers” helps you catch bad inputs early.

Number of holes \(N\)

Determines the pitch angle \( \theta = 360^\circ/N \). More holes means smaller pitch angles and shorter adjacent spacing for the same PCD.

Bolt circle diameter \(D\)

Sets the pattern’s scale. Adjacent spacing grows linearly with \(D\) through \( S = D\sin(\pi/N) \).

Adjacent spacing (chord) \(S\)

This is the straight-line distance between neighboring hole centers. If you confuse chord with arc length, the resulting PCD will be too large.

Start angle \( \alpha \)

Rotates the pattern. It doesn’t change spacing or PCD, only the coordinate orientation. Use it to match an existing datum or keyway.

Units and rounding

The geometry is unit-agnostic, but mixing mm and inches will wreck the result. Round only at the final output, not during measurement.

Tolerances & hole size

The calculator assumes hole centers on the PCD. Large holes, slots, or clearance can hide true center error—measure carefully.

Worked Examples

Below are two realistic bolt-circle problems walked through with the same equations used in the calculator.

Example 1 — Find Adjacent Spacing and First-Hole Coordinates

  • Given: \(N = 6\) holes
  • PCD: \(D = 200\ \text{mm}\)
  • Start angle: \(\alpha = 30^\circ\)
1
Radius: \[ R=\frac{D}{2}=\frac{200}{2}=100\ \text{mm} \]
2
Pitch angle: \[ \theta = \frac{360^\circ}{N}=\frac{360^\circ}{6}=60^\circ \]
3
Adjacent spacing (chord): \[ S=D\sin\!\left(\frac{\pi}{N}\right) =200\sin\!\left(\frac{\pi}{6}\right) =200(0.5)=100\ \text{mm} \]
4
First-hole coordinates: \[ x_0=R\cos\alpha=100\cos 30^\circ=86.60\ \text{mm} \] \[ y_0=R\sin\alpha=100\sin 30^\circ=50.00\ \text{mm} \]

The calculator will show \(S=100\ \text{mm}\), the radius \(R\), and the first-hole coordinate \((86.6, 50.0)\ \text{mm}\). To get any other hole, add \(i\theta\) to the angle in the coordinate formula.

Example 2 — Back-Calculate PCD from Measured Adjacent Spacing

  • Given: \(N = 5\) holes
  • Measured chord between adjacent holes: \(S = 3.25\ \text{in}\)
1
Compute sine term: \[ \sin\!\left(\frac{\pi}{N}\right) =\sin\!\left(\frac{\pi}{5}\right) =\sin(36^\circ)\approx 0.5878 \]
2
Solve for PCD: \[ D=\frac{S}{\sin(\pi/N)} =\frac{3.25}{0.5878} \approx 5.53\ \text{in} \]
3
Radius: \[ R=\frac{D}{2}\approx 2.765\ \text{in} \]
4
Quick check: \[ S=D\sin(36^\circ)\approx 5.53(0.5878)\approx 3.25\ \text{in} \]

If your measured spacing varies around the circle by more than your tolerance, the holes may not be equally spaced, or the part may be distorted. Re-measure across multiple adjacent pairs and average before using this mode.

Common Layouts & Variations

Bolt circles show up in many applications. The underlying geometry is the same, but practical choices (materials, fasteners, and standards) affect how you lay out and verify the pattern.

ApplicationTypical Spec GivenNotes / ProsWatch-Outs
ANSI / ASME flangesPCD \(D\) + \(N\)Standard tables list bolt circle directly; easy to check.Don’t confuse bolt circle with flange OD.
Automotive wheels / hubsPCD (e.g., 5×114.3)PCD format is “holes × diameter”; calculator matches this well.Offset datums vary by manufacturer—set your \(\alpha\) carefully in CAD.
Couplings & gearboxesPCD or measured chordOften reverse-engineered from existing parts.Measure center-to-center, not edge-to-edge.
Baseplates / anchorsCoordinates or PCDCoordinates help set drill templates and embeds.Confirm clearance to edges and weld zones.
Sheet-metal patternsPCD + start angleLaser/CNC likes coordinate layouts.Thin parts can warp—verify after forming.
  • Confirm if the standard uses diameter or radius notation.
  • Check whether angles are referenced from a keyway, flat, or slot.
  • If holes are slotted, layout is still based on slot centerlines.
  • For tapped holes, check minimum edge distance and thread engagement.

Specs, Logistics & Sanity Checks

Before finalizing a bolt circle, verify the geometry against real constraints: fastener size, tooling reach, edge distance, and tolerance stack-ups.

Drawing & CAD Checks

  • Annotate the PCD and hole count on the drawing, even if you also show coordinates.
  • Lock your datum: the calculator’s 0° is the +X direction in a standard Cartesian plane.
  • Round displayed dimensions to your manufacturing tolerance, not earlier.

Fabrication Notes

  • For drilling jigs, mark the center first, then rotate by \( \theta \) increments.
  • Use a rotary table / indexing head when hole spacing tolerance is tight.
  • If you’re flame-cutting or plasma-cutting, expect larger positional drift and plan clearance accordingly.

Sanity Tests

  • Does \(S\) seem plausible vs. the circle size? If \(S \approx D\), you likely entered the wrong \(N\).
  • Recompute \(S\) from the output \(D\) (Example 2) to verify consistency.
  • Measure multiple adjacent chords and average if reverse-engineering.

Tip: For very small patterns, measure across two holes separated by multiple pitches to reduce percent error.

Limitation: The calculator assumes perfect equal spacing. Real parts may deviate; treat outputs as nominal.

Frequently Asked Questions

What is a bolt circle (PCD)?
A bolt circle is the circle passing through all hole centers in a pattern. The pitch circle diameter (PCD) is its diameter \(D\). It’s a standard way to define equally spaced bolt patterns for flanges, wheels, and couplings.
Is adjacent hole spacing the same as arc length?
No. Adjacent spacing \(S\) is a straight-line chord between hole centers. Arc length would be \(L = R\theta\) (with \(\theta\) in radians), which is longer than the chord. Using arc length will overestimate PCD.
How do I measure adjacent spacing on an existing part?
Measure center-to-center with calipers. If holes are large, measure edge-to-edge and add one hole diameter. Take several adjacent measurements around the circle and average to reduce error.
How do I get coordinates for all holes?
The calculator shows the first-hole coordinate and pitch angle. For hole \(i\): \[ x_i=R\cos(\alpha+i\theta),\quad y_i=R\sin(\alpha+i\theta) \] Use \(i=0,1,2,\dots,N-1\). This is easy to plug into a CNC drilling routine or CAD sketch.
What start angle should I use?
Use \(0^\circ\) if you want the first hole on the +X axis (to the right). If the pattern needs to align with a keyway, flat, or slot, set \(\alpha\) to match that datum in your coordinate system.
Can this calculator handle unevenly spaced holes or slots?
Not directly. It assumes equal spacing. For uneven patterns, you need individual angles or coordinates from the drawing. For slots, you can still use this tool for the nominal slot centerline circle.
Why doesn’t my measured spacing give a “nice” PCD?
Small measurement error gets amplified, especially for low \(N\) (like 3 or 4 holes). Re-measure across more than one pitch, average several readings, and ensure you’re measuring true center-to-center.
Scroll to Top