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
Choose what to solve for
Select the mode that matches the dimension you already know.
Enter the known values
Fill in the visible fields. Hidden fields are ignored for the current solve mode.
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.
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
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.
On this page
Calculator Guide
How to Use the Bolt Circle Calculator
The Bolt Circle Calculator above helps calculate bolt circle diameter, pitch circle diameter, adjacent spacing, skipped-hole chord spacing, wheel bolt patterns, and X/Y hole coordinates. Use it when you know a bolt pattern dimension and need a layout, machining coordinate table, wheel pattern check, or quick geometry verification.
A bolt circle is the imaginary circle that passes through the centers of equally spaced holes, studs, or lugs. In practical layout work, PCD, BCD, and bolt circle diameter usually describe the same diameter through those hole centers.
Quick Answer
To calculate a bolt circle, choose the solve mode that matches what you know. If you know the PCD or BCD, the calculator can generate hole coordinates. If you know adjacent or skipped-hole spacing, it can solve for PCD using chord geometry. For equally spaced holes, the adjacent spacing formula is \(S = D\sin(\pi/N)\), and the rearranged PCD formula is \(D = S/\sin(\pi/N)\).
When not to rely on geometry alone
Do not treat a matching bolt circle as final design approval. Bolt circle geometry does not verify fastener strength, thread engagement, flange capacity, wheel offset, hub bore, brake clearance, material tolerances, or manufacturer fitment requirements.
Inputs and Outputs Used by the Bolt Circle Calculator
The calculator uses different inputs depending on the selected solve mode. Coordinate mode starts with a known PCD or BCD, while measurement modes start with hole spacing and calculate the diameter of the bolt circle.
| Type | Value | What It Means | Common Unit |
|---|---|---|---|
| Input | Number of holes or lugs | Total equally spaced holes around the bolt circle. | count |
| Input | PCD / BCD | Diameter through the centers of the holes or studs. | mm, in |
| Input | Measured spacing | Center-to-center, inside-to-inside, outside-to-outside, or center-to-outer spacing between selected holes. | mm, in |
| Input | Hole or stud diameter | Used to convert edge-based measurements back to center-to-center chord spacing. | mm, in |
| Input | Chord span | How many hole intervals the measurement crosses. Adjacent holes use \(k=1\). | step |
| Input | Start angle and direction | Controls where the first hole is placed and whether the pattern rotates clockwise or counterclockwise. | degrees, radians |
| Output | PCD / BCD | The calculated bolt circle diameter from the measured chord or spacing. | mm, in |
| Output | X/Y coordinates | Hole center locations for drawing, layout, manual machining, or CNC-style point lists. | mm, in |
If your workflow includes rotating parts, fasteners, shafts, or tool loads, the Torque Calculator can help with a separate force-and-distance check after the hole pattern geometry is known.
Bolt Circle Formula Used by the Calculator
Bolt circle calculations are based on circle radius, central angle, and chord length. The chord is the straight-line distance between two hole centers on the same bolt circle.
Radius from PCD or BCD
Use this when the bolt circle diameter \(D\) is already known and you need the radius for coordinates.
Adjacent Hole Spacing from PCD
This gives the center-to-center distance between neighboring holes when the bolt circle diameter and hole count are known.
PCD from Adjacent Hole Spacing
This is the most useful rearranged formula when you measure adjacent hole centers and need the bolt circle diameter.
Skipped-Hole Chord Formula
Use \(k=1\) for adjacent holes. Use \(k=2\) for a two-apart measurement, such as a common 5-lug wheel measurement.
Edge Measurement Conversion Formulas
Many real parts are easier to measure from edges instead of exact centers. Convert the measured value \(M\) into a center-to-center chord \(C\) before solving for PCD.
Here \(d\) is the hole or stud diameter. These conversions are only correct when the measured holes or studs have the same diameter and the measurement is taken along the straight chord between the selected holes.
Hole Coordinate Formula
Use this to generate the X/Y center point for each bolt hole. The calculator applies start angle, direction, center offset, and output units for layout use.
Geometry source note
The skipped-hole formula comes from the standard circle chord relationship \(a=2r\sin(\theta/2)\). For a direct reference on the chord length equation, see the Wolfram Formula Repository circle chord length formula.
What the Variables Mean
Every bolt circle formula depends on using the right diameter, hole count, chord span, measurement type, and angle. A small measurement mistake can move every coordinate or produce the wrong wheel pattern.
\(D\)
Bolt circle diameter, pitch circle diameter, or bolt center diameter. This is the full diameter through the hole centers, not the radius.
\(R\)
Bolt circle radius. This equals \(D/2\) and is used for X/Y coordinate calculations.
\(N\)
Number of holes, bolts, or wheel lugs equally spaced around the circle.
\(S\)
Adjacent center-to-center spacing between neighboring holes. This is a chord, not an arc length.
\(C\)
Center-to-center chord distance between selected holes after any edge-measurement conversion is applied.
\(M\)
The raw measured distance taken from the part, such as outside-to-outside, inside-to-inside, center-to-center, or center-to-outer.
\(d\)
Hole diameter or stud diameter used to convert edge-based measurements into center spacing.
\(k\)
Chord span measured in hole intervals. Adjacent holes use \(k=1\), two-apart holes use \(k=2\), and opposite holes on an even pattern use \(k=N/2\).
How to Use the Bolt Circle Calculator
Use the calculator by matching the solve mode to the measurement you actually have. Do not enter an edge-to-edge measurement as center-to-center unless you first account for the hole or stud diameter.
Select the solve mode
Choose known PCD/BCD for coordinates, adjacent spacing for a simple measured pattern, skipped/opposite chord for non-adjacent measurements, or wheel pattern mode for lug pattern identification.
Enter hole count and measurement
Enter the total number of equally spaced holes. Then enter the known PCD, adjacent spacing, chord spacing, or wheel measurement depending on the solve mode.
Choose the measurement type
Center-to-center is the cleanest input. For outside-to-outside, inside-to-inside, or center-to-outer measurements, enter the hole or stud diameter so the calculator can convert back to center spacing.
Review coordinates and checks
Check the calculated PCD, radius, angle between holes, adjacent spacing, edge-to-edge gap, and coordinate table before using the result for layout or fabrication.
What measurement should you enter?
If you measured from hole center to hole center, enter the measurement directly. If you measured outside edges, inside edges, or center-to-outer, select that measurement type and enter the hole or stud diameter so the calculator can correct the chord spacing.
How to Interpret Bolt Circle Results
A good bolt circle result should match the physical pattern you measured. If a wheel pattern is close to a common value, the nearest standard pattern may be more useful than the raw rounded measurement.
What to do with the result
Use the PCD or BCD to identify the bolt pattern, create a drawing, lay out holes on a plate, compare wheel patterns, or generate coordinate points for machining.
What changes the result most?
The measurement method controls the result most. A two-apart chord, adjacent spacing, and edge-to-edge measurement are not interchangeable.
Sanity check
For any pattern, adjacent spacing must be less than the PCD. If adjacent spacing is equal to or larger than the calculated PCD, the input mode or units are probably wrong.
Wheel pattern interpretation
A result like \(5 \times 114.3\text{ mm}\) means 5 lugs on a 114.3 mm pitch circle diameter. It does not confirm final wheel fitment by itself.
Input Checklist Before You Trust the Answer
Most bolt circle errors come from measuring the wrong chord, mixing edge measurements with center measurements, or confusing diameter with radius.
Confirm hole count
Count every equally spaced hole or lug on the circle. Do not include extra slots, drain holes, or non-pattern holes.
Match the measurement type
Use center-to-center, inside-to-inside, outside-to-outside, or center-to-outer exactly as measured.
Use the correct chord span
Adjacent holes use one step. A 5-lug two-apart measurement uses two steps. Opposite holes on a 6-lug pattern use three steps.
Check units
Wheel patterns are often named in millimeters even when measured in inches. Convert carefully before comparing to common patterns.
Worked Example: Find PCD from Adjacent Hole Spacing
This example shows how the calculator finds bolt circle diameter from a measured adjacent center-to-center spacing.
Formula
Substitution
Final answer
The bolt circle diameter is 100 mm. This is reasonable because a 6-hole pattern has 60° between adjacent holes, and on a 100 mm PCD the adjacent chord is exactly 50 mm.
Reverse check
Use \(S=D\sin(\pi/N)\). Substituting \(D=100\text{ mm}\) and \(N=6\) gives \(S=100\sin(30^\circ)=50\text{ mm}\), which matches the measured input.
5-Lug Mini Example
For a 5-lug pattern measured two lugs apart, use \(N=5\) and \(k=2\). The PCD formula becomes:
If the two-apart center-to-center chord is \(108.7\text{ mm}\), then \(D\approx108.7/0.9511=114.3\text{ mm}\), which matches a common \(5\times114.3\text{ mm}\) wheel pattern.
How to Visualize the Bolt Circle Calculation
The bolt circle is easier to understand if you picture all hole centers sitting on one circle. The PCD is the full diameter of that circle, and the measured spacing is a straight chord between selected hole centers.
The orange line is adjacent center spacing, which is a straight chord between hole centers, not the curved arc length. The blue dimension line represents the full PCD / BCD across the bolt circle.
Reference Checks for Common Bolt Patterns
Bolt circle calculators do not need one universal reference table because patterns vary by part, manufacturer, and application. However, common wheel and mechanical patterns are often recognizable after converting between inches and millimeters.
| Pattern | What It Means | Useful Check |
|---|---|---|
| \(4 \times 100\text{ mm}\) | Four holes on a 100 mm PCD. | Opposite-hole center spacing equals 100 mm. |
| \(5 \times 114.3\text{ mm}\) | Five lugs on a 114.3 mm PCD, also commonly written as 5 × 4.5 in. | Two-apart center spacing is about 108.7 mm. |
| \(6 \times 139.7\text{ mm}\) | Six lugs on a 139.7 mm PCD, also commonly written as 6 × 5.5 in. | Opposite-hole center spacing equals the PCD for even lug counts. |
| \(8 \times 165.1\text{ mm}\) | Eight lugs on a 165.1 mm PCD, also commonly written as 8 × 6.5 in. | Small rounding differences are common when converting between inch and metric names. |
For area-based layout or material checks around a circular plate, the Square Footage Calculator can help estimate circular or rectangular surface area separately from the bolt pattern geometry.
Design Notes and Practical Ranges
For simple layout work, the bolt circle result is a geometric answer. For real parts, the final pattern must also make sense for hole diameter, material thickness, fastener size, edge distance, tolerances, and assembly clearances.
Hole clearance matters
If adjacent center spacing is close to the hole diameter, the edge-to-edge gap may be too small or negative. That can indicate overlap or an impractical pattern.
Start angle matters
The same PCD and hole count can produce different coordinates if the first hole starts at 0°, 30°, 45°, or another reference angle.
Wheel fitment is more than PCD
Wheel bolt pattern checks do not replace hub bore, offset, brake clearance, thread size, lug nut seat, or manufacturer fitment verification.
Machining needs tolerances
The coordinate table gives ideal center points. Final drawings should still specify tolerances, hole sizes, datums, and inspection requirements.
Units and Conversions
Use one length unit consistently for the bolt circle, spacing, hole diameter, and center offsets. The most common bolt circle units are millimeters and inches.
Inch to Millimeter Conversion
Degree to Radian Conversion
Hidden unit trap
A wheel pattern written as 5 × 4.5 in is the same nominal PCD as 5 × 114.3 mm because \(4.5 \times 25.4 = 114.3\). Do not round too aggressively for machining coordinates.
PCD vs BCD vs Bolt Pattern
These terms are closely related, but users often apply them in different contexts. PCD and BCD describe the circle diameter, while bolt pattern usually combines the number of holes with that diameter.
PCD
Pitch circle diameter. Common in machining, mechanical design, wheels, pulleys, chainrings, and circular hole patterns.
BCD
Bolt circle diameter. Common in fabrication, flanges, hubs, adapter plates, and layout drawings.
Bolt pattern
Usually written as hole count × PCD, such as \(5 \times 114.3\text{ mm}\).
Common Bolt Circle Mistakes
The formula is simple, but the measurement setup is easy to get wrong. Use the correct solve mode and measurement type before trusting the result.
Do
- Measure from center to center when possible.
- Enter hole or stud diameter for edge-based measurements.
- Use the correct skipped-hole span.
- Check whether the output is diameter or radius.
- Compare wheel results to nearby common patterns.
Don’t
- Do not enter outside-to-outside spacing as center spacing.
- Do not confuse arc length with chord length.
- Do not assume all holes on a part belong to one bolt circle.
- Do not use bolt pattern alone to approve wheel fitment.
- Do not round coordinates too early in the layout process.
Troubleshooting Unrealistic Bolt Circle Results
If the result looks wrong, check the measurement type before changing the formula. A mathematically valid PCD can still be wrong if the measured chord or hole span was entered incorrectly.
PCD is too large
You may have entered a skipped-hole or opposite-hole measurement as adjacent spacing. Check the chord span value.
PCD is too small
You may have subtracted hole diameter when you should have added it, or selected inside-to-inside instead of center-to-center.
Coordinates look rotated
Change the start angle or direction. A 0° start usually places the first hole on the positive X-axis.
Hole gap is negative
The hole diameter is larger than the adjacent center spacing. Recheck hole size, PCD, hole count, and units.
Assumptions and Limitations
The Bolt Circle Calculator is a geometric calculator. It assumes the holes are equally spaced and their centers lie on one circular pattern.
Equal spacing
The formulas assume every hole is separated by the same central angle of \(360^\circ/N\).
Single circle
The calculator assumes all selected holes are on one PCD or BCD. It does not solve mixed or irregular patterns.
Ideal coordinates
The coordinate table gives theoretical center locations. It does not include tolerance stack-up, tooling runout, or inspection limits.
No strength check
The result does not check bolt shear, bearing, preload, fatigue, flange strength, or material capacity.
Final-use warning
For manufactured parts, pressure flanges, structural connections, rotating equipment, vehicles, or safety-related assemblies, verify the final design with the applicable standard, drawing requirements, manufacturer data, and qualified review.
Key Bolt Circle Terms
These terms help connect the calculator inputs, formulas, and result table.
PCD
Pitch circle diameter, the diameter through the centers of the holes, bolts, studs, or lugs.
BCD
Bolt circle diameter, another common name for the same hole-center diameter.
Chord
A straight-line distance between two points on a circle. Hole spacing is a chord, not the curved arc length.
Chord span
The number of hole intervals crossed by the measurement. Adjacent holes use one span.
Start angle
The angle used to locate the first hole before stepping around the circle.
Center offset
The X/Y location of the bolt circle center relative to the drawing, part, or machine coordinate origin.
FAQ
What is a bolt circle calculator used for?
A bolt circle calculator is used to calculate pitch circle diameter, bolt circle diameter, adjacent hole spacing, skipped-hole chord spacing, wheel bolt patterns, and X/Y coordinates for equally spaced holes around a circle.
Is PCD the same as BCD?
In most practical bolt circle calculations, yes. PCD means pitch circle diameter and BCD means bolt circle diameter. Both usually refer to the diameter through the centers of the bolt holes.
How do you calculate PCD from adjacent hole spacing?
Use \(D = S/\sin(\pi/N)\), where \(D\) is the pitch circle diameter, \(S\) is the adjacent center-to-center spacing, and \(N\) is the number of equally spaced holes.
How do you convert edge-to-edge bolt measurements?
For outside-to-outside measurements, subtract one hole or stud diameter to get center spacing. For inside-to-inside measurements, add one hole diameter. For center-to-outer measurements, subtract half the hole or stud diameter.
How do you calculate bolt hole coordinates?
Use \(x=x_0+R\cos(\theta)\) and \(y=y_0+R\sin(\theta)\). The angle for each hole is found by starting at the chosen start angle and adding \(360^\circ/N\) for each next hole.
How do you measure a 5-lug bolt pattern?
A 5-lug pattern has no directly opposite lug, so use a two-apart center-to-center measurement or a center-to-outer measurement method. Make sure the calculator mode matches the way you measured the pattern.
Does matching a wheel bolt pattern guarantee fitment?
No. A matching bolt pattern only confirms lug count and pitch circle diameter. Hub bore, offset, brake clearance, thread size, load rating, and lug seat type must also be checked.