Bolt Circle Calculator

Calculate bolt circle diameter, PCD, BCD, adjacent hole spacing, X/Y hole coordinates, wheel bolt patterns, and layout points from the measurements you know.

Also called a PCD calculator, BCD calculator, bolt hole circle calculator, wheel bolt pattern calculator, or bolt hole coordinate calculator.

Calculator is for informational purposes only. Terms and Conditions

Bolt circle geometry

Choose what to solve for

Select the mode that matches the dimension you already know.

Unit Preset

Changing presets converts the active dimensions instead of overwriting your geometry.

Solve Mode

Use coordinate mode for drawings and CNC layout. Use PCD modes when measuring an existing part.

Enter the known values

Fill in the visible fields. Hidden fields are ignored for the current solve mode.

Number of Holes / Lugs

Total equally spaced holes or wheel lugs on the bolt circle. Common values are 3, 4, 5, 6, 8, 10, and 12.

Bolt Circle Diameter / PCD

PCD and BCD both refer to the diameter through the centers of the bolt holes.

Measured Hole Spacing

Use the measured chord distance between two bolt holes or wheel lugs. The measurement method determines whether hole diameter is added or subtracted.

Measurement Type

Center-to-center is preferred. Edge-based measurements require hole or stud diameter.

Chord Span

Use 1 for adjacent holes. Use N/2 for opposite holes on even patterns. Use 2 for a common 5-lug two-apart measurement.

Wheel Measurement Method

For 5-lug patterns, auto mode uses a two-apart chord. For 4, 6, and 8 lugs, auto mode uses the opposite-center method.

Common Pattern Preset

Use a preset to load a known wheel bolt pattern into coordinate mode or to compare measured results.

Hole or Stud Diameter Optional

Used for clearance checks and for converting inside/outside/center-to-outer measurements back to center spacing.

Start Angle

0° places the first hole on the positive X-axis. Positive angles rotate counterclockwise unless direction is reversed.

Hole Direction

Advanced Options

Center X Offset

Center Y Offset

Answer Units

Precision

Coordinate Output

First Hole Number

Bolt circle layout preview

Live diagram with the bolt circle, first hole, active measured chord, and hole numbers.

Hole size is scaled for readability. Use the numeric hole gap check for actual edge-to-edge clearance.

Solution

Live result, layout checks, coordinate table, and solution steps.

Solution

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Real-time result updates as you type.

Quick checks

PCD / BCD—
Bolt circle radius—
Angle between holes—
Adjacent center spacing—
Edge-to-edge hole gap—
Closest common wheel pattern—

Coordinate table

Hole	Angle	X	Y	G-code Style Point
Enter valid inputs to generate coordinates.

Source, standards, and assumptions

Standard geometry

Source/standard: Standard engineering geometry for equal angular bolt circle patterns. No single governing code standard is required for this simplified geometric calculation.

Uses standard unit conversion constants only.
Assumes all holes are equally spaced around one circle.
Assumes hole centers lie on the calculated PCD / BCD.
Does not check material strength, fastener capacity, tolerance stack-up, hub bore, wheel offset, or final wheel fitment.

Show solution steps See formulas, substitutions, assumptions, and interpretation

Enter values to see the full solution steps and checks.

How to Calculate a Bolt Circle Correctly

A bolt circle is the imaginary circle that passes through the centers of equally spaced bolt holes, studs, or lugs. The diameter of that circle is called the bolt circle diameter, BCD, or pitch circle diameter, often shortened to PCD.

This calculator is designed for the most common bolt circle tasks: finding PCD from measured spacing, generating X/Y hole coordinates, checking wheel bolt patterns, laying out flange holes, and exporting coordinate data for CAD, CNC, DRO, or shop layout work.

Main output PCD / BCD, radius, spacing, and coordinates

Best used for Bolt patterns, flanges, wheels, plates, hubs, and fixtures

Most important input Correct measurement method and unit selection

Quick answer

If you know the adjacent center-to-center hole spacing S and the number of holes N, the bolt circle diameter is calculated as D = S / sin(π / N). If you already know the PCD, the radius is D / 2, and each hole coordinate is found with cosine and sine based on the hole angle.

PCD vs. BCD vs. Bolt Pattern

In most practical calculator searches, PCD and BCD refer to the same dimension: the diameter of the circle through the centers of the holes. PCD is often used in wheel, chainring, and international contexts. BCD is common in machining, mechanical design, flanges, and general bolt layout work.

A bolt pattern usually combines the hole count and the bolt circle diameter. For example, 5 × 114.3 mm means five equally spaced holes or studs on a 114.3 mm pitch circle diameter.

Common bolt circle terms and what they mean
Term	Meaning	Example
PCD	Pitch circle diameter through the hole centers	PCD = 100 mm
BCD	Bolt circle diameter through the hole centers	BCD = 4.500 in
Bolt pattern	Hole count × bolt circle diameter	5 × 114.3 mm
Radius	Half of the bolt circle diameter	R = D / 2

How to Use the Bolt Circle Calculator

The calculator works best when you choose the solve mode that matches what you actually know. If you already know the PCD, use coordinate mode. If you measured an existing part, use one of the spacing-based modes.

Choose the solve mode

Use coordinates from known PCD when you already know the bolt circle diameter. Use PCD from spacing when you measured an existing part.

Enter the number of holes or lugs

Enter the total number of equally spaced holes on the circle. Common values include 3, 4, 5, 6, 8, 10, and 12.

Select the correct measurement type

Center-to-center is the cleanest input. If you measured inside-to-inside, outside-to-outside, or center-to-outer-edge, enter the hole or stud diameter so the calculator can convert the measurement back to center spacing.

Set units, start angle, and coordinate options

Use millimeters or inches as needed. For coordinate layouts, set the start angle, clockwise or counterclockwise direction, center offset, and absolute, relative, or incremental output.

Review the result and export the layout

Use the result panel to check the PCD, radius, adjacent spacing, edge gap, coordinate table, G-code-style points, CSV export, and SVG layout.

Bolt Circle Formulas

Bolt circle calculations are based on simple circular geometry. The key idea is that every hole is separated by the same central angle. Once the diameter, radius, hole count, and start angle are known, every coordinate can be calculated.

Radius from Bolt Circle Diameter

\[ R = \frac{D}{2} \]

R is the bolt circle radius and D is the bolt circle diameter, PCD, or BCD.

Angle Between Holes

\[ \theta = \frac{360^\circ}{N} \]

N is the number of holes. A 6-hole pattern has a 60° angle between adjacent holes.

PCD from Adjacent Center Spacing

\[ D = \frac{S}{\sin\left(\frac{\pi}{N}\right)} \]

S is the adjacent center-to-center spacing. This is one of the most useful formulas when measuring an existing part.

PCD from Skipped or Opposite Chord

\[ D = \frac{C_k}{\sin\left(\frac{k\pi}{N}\right)} \]

C_k is the measured chord across k hole steps. Use this for skipped-hole or opposite-hole measurements.

Bolt Hole Coordinates

\[ x_i = x_0 + R\cos(\alpha + i\theta) \] \[ y_i = y_0 + R\sin(\alpha + i\theta) \]

x₀ and y₀ are center offsets, α is the start angle, i is the hole index, and θ is the angle step.

For an additional machining-style reference on bolt circle coordinate calculations, see the GlobalSpec reference on bolt circles and hole coordinate calculations.

How to Measure a Bolt Circle

The most reliable way to measure a bolt circle is to measure from the center of one hole to the center of another hole. In real shop and wheel applications, however, the center is not always easy to access. That is why this calculator supports several measurement methods.

Center-to-center

The preferred measurement. Measure from the center of one hole to the center of another hole.

Outside-to-outside

Measure across outside edges, then subtract one hole or stud diameter to get center spacing.

Inside-to-inside

Measure between inside edges, then add one hole or stud diameter to get center spacing.

How different measurement methods convert to center spacing
Measurement Type	What You Measure	Center Spacing Conversion
Center-to-center	Hole center to hole center	Use the measurement directly
Outside-to-outside	Far outside edge to far outside edge	Center spacing = measurement − hole diameter
Inside-to-inside	Near inside edge to near inside edge	Center spacing = measurement + hole diameter
Center-to-outer-edge	Center of one hole to outside edge of another	Center spacing = measurement − half the hole diameter

Odd-number patterns need extra care

For 3-lug, 5-lug, and other odd-number patterns, there is no hole directly opposite another hole. Use the skipped-hole chord option or a known wheel measurement convention instead of assuming the measured distance is the full diameter.

Bolt Hole Coordinates for CNC, CAD, DRO, and Drill Layout

Coordinate output is one of the most valuable parts of a bolt circle calculator. Instead of manually laying out angles and chords, you can generate each X/Y coordinate from the PCD, hole count, start angle, and center offset.

This is useful for CNC drilling, manual milling with a DRO, CAD sketching, fixture plates, adapter plates, flanges, rotating equipment mounts, and shop drawings. The calculator can output absolute coordinates, relative coordinates, or incremental movement from the previous hole.

Absolute coordinates

Coordinates include the selected X/Y center offset. Use this when your part datum is not the bolt circle center.

Relative coordinates

Coordinates are measured from the bolt circle center. Use this when the center is your datum.

Incremental coordinates

Each row gives the move from the previous hole. Use carefully when converting to manual or CNC steps.

Start angle

0° places the first hole on the positive X-axis. 90° places it straight up on the positive Y-axis.

Worked Examples

The examples below show how the calculator handles common bolt circle problems. Use them to confirm whether your input method matches the real measurement you have.

Example 1: Coordinates from Known PCD

Hole count: 6 holes
PCD: 100 mm
Start angle: 0°
Center offset: 0, 0

Step 1: Find the Radius

\[ R = \frac{100}{2} = 50 \text{ mm} \]

Step 2: Find the Angle Step

\[ \theta = \frac{360^\circ}{6} = 60^\circ \]

Result

First hole coordinate: X = 50 mm, Y = 0 mm. The remaining holes are spaced every 60° around the circle.

Example 2: PCD from Adjacent Spacing

Hole count: 5 holes
Adjacent spacing: 58.78 mm
Measurement: Center-to-center

Formula

\[ D = \frac{S}{\sin(\pi/N)} \]

Substitution

\[ D = \frac{58.78}{\sin(\pi/5)} \approx 100 \text{ mm} \]

Result

PCD / BCD: approximately 100 mm.

Wheel Bolt Pattern Calculator: 4-Lug, 5-Lug, 6-Lug, and 8-Lug

Wheel bolt patterns are usually written as lug count × PCD. A wheel listed as 5 × 114.3 has five lugs on a 114.3 mm pitch circle diameter. This calculator can help identify that PCD from a measured wheel, hub, or adapter pattern.

Common wheel bolt pattern measurement approach
Pattern Type	Typical Measurement Method	Important Note
4-lug	Measure across opposite centers	The opposite-center distance is the PCD
5-lug	Use a two-apart chord or center-to-outer method	There is no directly opposite lug
6-lug	Measure across opposite centers	The opposite-center distance is the PCD
8-lug	Measure across opposite centers	The opposite-center distance is the PCD

Wheel fitment warning

Bolt pattern alone does not confirm wheel fitment. Center bore, offset, brake clearance, lug seat type, stud size, thread pitch, and load rating can also control whether a wheel is safe and compatible.

For a wheel-specific explanation of bolt pattern and center bore compatibility, see the Apex Wheels guide to bolt pattern and centerbore measurement.

Common Bolt Circle Mistakes That Cause Wrong Results

Most wrong bolt circle results come from using the right formula with the wrong measurement. Before using the result for layout, machining, or wheel comparison, check the common mistakes below.

Common Don’ts

Do not confuse radius with diameter.
Do not enter outside-to-outside spacing as center-to-center spacing.
Do not assume adjacent spacing equals PCD.
Do not treat a 5-lug skipped measurement as a full diameter.
Do not mix inch measurements with millimeter output without converting.
Do not use bolt pattern alone to confirm wheel fitment.

Better Checks

Confirm whether your measurement is center, inside, outside, or center-to-outer.
Enter the correct hole or stud diameter for edge-based measurements.
Use skipped-hole chord mode for odd-number bolt circles.
Check the coordinate table against the drawing datum.
Verify start angle and clockwise/counterclockwise direction.
Review tolerances before using the result for production work.

Limitations of a Bolt Circle Calculator

This calculator solves the geometry of an equally spaced circular bolt pattern. It does not replace a design drawing, tolerance analysis, fastener design check, or wheel fitment verification.

Geometry only

The calculator finds PCD, spacing, radius, and coordinates. It does not check bolt strength or material capacity.

Tolerances not included

Manufacturing tolerances, clearance holes, positional tolerance, runout, and datum schemes must be checked separately.

Wheel fitment not guaranteed

Wheel bolt pattern is only one part of fitment. Center bore, offset, brake clearance, and hardware details also matter.

Equal spacing assumed

The formulas assume all holes are equally spaced on one circle with one common center.

Frequently Asked Questions

What is a bolt circle?

A bolt circle is the imaginary circle passing through the centers of equally spaced bolt holes, studs, or lugs.

Is PCD the same as BCD?

For most practical bolt pattern calculations, yes. PCD means pitch circle diameter and BCD means bolt circle diameter. Both usually describe the diameter through the hole centers.

How do you calculate bolt circle diameter from adjacent spacing?

Use D = S / sin(π / N), where D is bolt circle diameter, S is adjacent center-to-center spacing, and N is the number of holes.

How do you calculate bolt hole coordinates?

Use x = x₀ + R cos(α + iθ) and y = y₀ + R sin(α + iθ), where R is radius, α is start angle, i is the hole index, and θ is 360° divided by the number of holes.

What does a 5 × 114.3 bolt pattern mean?

It means the pattern has 5 lugs or holes arranged on a 114.3 mm pitch circle diameter.

How do you measure a 5-lug bolt pattern?

A 5-lug pattern has no directly opposite hole. Use a two-apart center-to-center chord, a center-to-outer-edge method, or a calculator mode specifically built for skipped-hole measurements.

Can this calculator be used for flanges?

Yes, it can calculate equally spaced flange bolt hole coordinates and bolt circle diameter. Final flange design still requires the correct project standard, gasket, pressure class, fastener, and tolerance requirements.

Can I use the coordinate table for CNC or DRO layout?

Yes. The coordinate table is useful for CAD layout, CNC drilling, manual milling with a DRO, and shop layout. Always verify the datum, start angle, and coordinate mode before machining.

Does bolt pattern confirm wheel fitment?

No. Bolt pattern is only one fitment requirement. Center bore, offset, brake clearance, lug seat type, stud size, thread pitch, and load rating may also control compatibility.