What is a bolt circle?

A virtual circle passing through the centers of a group of evenly spaced holes, studs or rivets. Its diameter is called the stud pitch or bolt circle diameter and this value determines whether two parts can be joined by bolts.

How can you determine the diameter of a bolt circle from measured values?

Measure the straight line distance between the centers of two holes, count how many "step" distances the line spans and divide that result by the sine of the value "(number of steps multiplied by 180 divided by number of holes)". For a hexagonal pattern of fasteners, the measurement for adjacent holes is 50 mm. Divide 50 by sin(30), and the result is 100 mm.

Are PCD and BCD the same?

Yes, they are the same in this type of mounting pattern. Both the Pitch Circle Diameter (PCD) and Bolt Circle Diameter (BCD) refer to the diameter that runs through the center points of the holes. The two terms come from different industries and have no differing geometric definitions.

How do you measure a five hole wheel pattern?

Since a five hole pattern does not have holes directly opposite each other, measure two holes separated by one hole and set the number of "step" spacings to 2. If the spacing between any two adjacent holes is about 108.7mm this corresponds to a typical 5x114.3 mm bolt circle.

How are measurement values converted from one side to another?

To determine the diameter of a hole, subtract the value equal to the hole diameter when measuring from outside edge to outside edge and add that amount when measuring inside edge to inside edge. When measuring from center of one side to outside edge of opposite side, subtract half of the hole diameter. These corrections are only valid if both holes are the same size.

If the bolt pattern matches can the wheel be mounted?

No. This just means that the bolts will fit through the holes. The hub bore, wheel offset, brake caliper clearance, bolt thread size and contact surface shape all have to match as well.

Bolt Circle Calculator

Bolt pattern

What do you already know?

I know the bolt circle diameter

I measured the distance between holes

Enter the diameter through the hole centres and the hole count, and the calculator lays out every hole position for you.

Number of holes or lugs

Bolt circle diameter (PCD or BCD)

Hole or stud diameter

Angle of the first hole

Numbering direction

Counterclockwise

Clockwise

Offset the bolt circle centre

Move the pattern away from the origin when the drawing datum is not the circle centre.

Edge to edge gap between holes

More layout numbers

Adjacent hole spacing

Bolt circle diameter (PCD): mm
Bolt circle radius: mm
Angle between holes: deg (°)

Adjacent hole spacing: mm
Edge to edge gap: mm

Pattern outside diameter: mm
Pattern inside diameter: mm

The nearest common wheel bolt pattern is 6 by 114.3 mm, which is 14.3 mm away from this result. A gap that size usually means a different pattern or a measurement that slipped.

Hole coordinates

Show the hole coordinate table

A row per hole with the angle, X and Y in millimetres and inches, plus a G-code style point.

Hole centres measured from the bolt circle centre, or from your offset when one is set.
Hole	Angle (deg)	X (mm)	Y (mm)	X (in)	Y (in)	G-code point (mm)
1	0	50	0	1.969	0	X50.0000 Y0.0000
2	60	25	43.301	0.984	1.705	X25.0000 Y43.3013
3	120	-25	43.301	-0.984	1.705	X-25.0000 Y43.3013
4	180	-50	0	-1.969	0	X-50.0000 Y0.0000
5	240	-25	-43.301	-0.984	-1.705	X-25.0000 Y-43.3013
6	300	25	-43.301	0.984	-1.705	X25.0000 Y-43.3013

Layout charts

Show the layout charts

Plot the hole coordinates and compare spacing and clearance across hole counts.

A bolt circle is a virtual circle that passes through the centers of evenly spaced holes. This arrangement is used for example on flange faces, hubs, sprockets, adapter plates and street light bases.

This calculation tool supports bidirectional calculations. If you enter a diameter, the positions of individual holes will be listed. If you enter the distance between two measured holes on an existing part, then you can calculate the diameter.

The bolt circle, PCD (pitch circle diameter), and BCD (bolt circle diameter) are the same.

In manufacturing often referred to as the "pitch circle diameter", in production as the "bolt circle diameter" and simply as the "pattern" for wheels. In fact each term refers to the diameter of a circle passing through the center points of holes.

A pattern of fasteners is usually specified by the number of holes and their diameter. A wheel marked "5x114.3" has five fastener points arranged on a circle with a diameter of 114.3 millimeters.

It is especially important to note the difference between diameter and radius. Sometimes drawings will give you a hole center radius. If this is interpreted as a diameter all coordinates are halved.

The geometric principles behind it are as follows:

To determine the circumference of bolt holes you only need three values: diameter, number of holes and position of first hole. Everything else follows from this.

The holes are arranged with equal central angles. The angle for a full turn is divided by the number of holes to obtain the step angle between adjacent holes.

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

The line connecting the centers of two holes is a chord and not an arc along the circumference. Confusion between these two concepts is the most common cause for miscalculation. For a hole that is k steps away from another hole on a circle with diameter D:

C_{k} = D \times \sin\!\left(\frac{k \times 180^\circ}{N}\right)

For adjacent holes, k=1, so that the measuring distance can be determined with a caliper.

S = D \times \sin\!\left(\frac{180^\circ}{N}\right)

Conversely, this provides a formula for using this calculation tool for already milled parts.

D = \frac{C_{k}}{\sin\!\left(\dfrac{k \times 180^\circ}{N}\right)}

Position of each hole:

Once the diameter is determined, the radius is half of that and each hole is at a specific angle around the circumference. The coordinates for the ith hole, starting with zero, are as follows:

x_{i} = x_{0} + R \times \cos\!\left(A + i\,\theta\right) \qquad y_{i} = y_{0} + R \times \sin\!\left(A + i\,\theta\right)

where R is the radius, A is the angle of the first hole and (x0,y0) is the center point of the circle of holes. The coordinate system used is determined by the drawing or machine tool. If the angle is 0 then the first hole is directly to the right on the positive X axis. Positive angles are counter clockwise.

Example for calculating diameter based on measurements:

Assume there is a six hole flange without drawing. A caliper measures the distance between the centers of two adjacent holes and gets a value of 50mm.

Since the two holes are separated by one step, k = 1 and there are six holes.

D = \frac{50}{\sin\!\left(\dfrac{180^\circ}{6}\right)} = \frac{50}{\sin 30^\circ} = \frac{50}{0.5} = 100 \text{ mm}

We check the results backwards. For a screw circle with a diameter of 100 mm and six holes, the length of adjacent chords is 50 mm, which corresponds to the product of 100 and sin(30) degrees. As this matches the measured values, we know that the answer is correct.

The full arrangement resulting from this is as follows:

Quantity	Value
Bolt circle diameter	100 mm
Radius	50 mm
Angle between holes	60 degrees
Adjacent hole spacing	50 mm
Edge to edge gap with 12 mm holes	38 mm
First hole at 0 degrees	X 50, Y 0
Second hole at 60 degrees	X 25, Y 43.301

For five bolt patterns, there are no corresponding holes on the opposite side.

If the number of holes is even, measurements are easier because there is a hole opposite each one and the distance between them forms the diameter. However, with an odd number of holes this is not true which can make the wheel confusing to work on when it has five bolts.

It is important to measure not the adjacent carpets but those that are two positions apart from each other. Therefore, k = 2 and N = 5.

D = \frac{C_{2}}{\sin\!\left(\dfrac{2 \times 180^\circ}{5}\right)} = \frac{C_{2}}{\sin 72^\circ} \approx \frac{C_{2}}{0.9511}

The measured distance between two holes separated by two positions is 108.7 mm, which leads to a calculated diameter of the pitch circle of about 114.3 mm. This corresponds to a common bolt pattern of 5x114.3, also referred to as 5x4.5 inches.

Measure from outside, not center.

While it is difficult to reach the center of a hole with a caliper, the edges are more accessible. So many people first measure from edge to edge and then correct for that amount. Regardless of method, the reading will be off by the known diameter of the hole (d).

How you measured	Correction to centre chord	Example with 12 mm holes
Centre to centre	No change	50 mm stays 50 mm
Outside edge to outside edge	Subtract one hole diameter	62 mm becomes 50 mm
Inside edge to inside edge	Add one hole diameter	38 mm becomes 50 mm
Centre of one hole to the far outside edge	Subtract half a hole diameter	56 mm becomes 50 mm

These corrections only apply if the two holes are equal size and measured along a straight line not diagonally. Entering the value read from the edge into the center to center distance field will move the diameter by the amount of one hole diameter, and is thus the fastest method for correction.

Common bolt patterns for comparison:

The pin patterns vary from manufacturer to manufacturer but there are some very common patterns and if the result is no more than a few hundredths of a millimetre away from one of these patterns you can probably be sure that it is.

Pattern	Also written as	Useful check
4 by 100 mm	4 by 3.937 in	Opposite hole centres measure 100 mm
5 by 114.3 mm	5 by 4.5 in	Two lugs apart measures about 108.7 mm
5 by 120 mm	5 by 4.724 in	Two lugs apart measures about 114.1 mm
6 by 139.7 mm	6 by 5.5 in	Opposite hole centres measure 139.7 mm
8 by 165.1 mm	8 by 6.5 in	Opposite hole centres measure 165.1 mm

A matching bolt pattern only indicates that the holes are aligned. To ensure a secure fit, the hub hole, wheel offset, brake clearance, screw thread and seat type must also match.

Distance between holes

The nominal gap refers to the value between centers, so it is not known how much metal actually remains between two holes. Subtracting the hole diameter gives the actual gap.

g = S - d = D \times \sin\!\left(\frac{180^\circ}{N}\right) - d

If the distance is zero or negative, then the holes overlap and it will not be possible to drill the holes according to the drawing. Even a small positive distance is a warning sign. The thin connection between the holes can easily break under stress. Also many construction standards require a minimum distance of two-and-a-half to three times the diameter of the fasteners.

Units and conversions that are easy to confuse

If diameter, distance, hole diameter and offset have the same unit then any arbitrary unit can be used. Even if inches are entered in one column and millimeters in another, the calculation tools will process this correctly. This is because all values are first converted to a common base unit before trigonometric calculations are performed.

The only conversion you should memorize is that one inch equals exactly 25.4 mm. This explains why 5x4.5 inches and 5x114.3 mm are the same bolt pattern for a rim. Also, rounding off inch values to two decimal places before converting them sometimes results in coordinates that are outside of manufacturing tolerances.

1\ \text{in} = 25.4\ \text{mm} \qquad \theta_{\text{rad}} = \theta_{\text{deg}} \times \frac{\pi}{180}

Symbols used in this article.

Symbol	Meaning	Example
$D$	Bolt circle diameter through the hole centres	100 mm
$R$	Bolt circle radius, half of D	50 mm
$N$	Number of equally spaced holes	6
$\theta$	Angle between neighbouring holes	60 degrees
$S$	Adjacent centre to centre spacing	50 mm
$C_{k}$	Chord across k hole steps	86.6 mm at k = 2
$d$	Hole or stud diameter	12 mm
$A$	Angle of the first hole from the X axis	0 degrees

Applications of the hole circle for screws.

Processing and CNC layout.

The coordinate table is the part most machinists need most urgently. Each row contains the X and Y coordinates of a hole center point and can be entered directly into the control, inserted into a CAD sketch or integrated into a drilling operation.

Flanges and pressure pipeline fittings.

Flanges are defined by their nominal size, pressure rating and bolt circle. When reverse engineering old flanges the distance between two bolts is usually measured before calculating the diameter. This is the method of measurement we use here.

Rims and hubs

When measuring rims, the circumference is important. For a stud pattern with five fastening points, the distance between two adjacent fastening points must be measured. With other stud patterns, measurement can be done directly.

Lantern poles and foundation plates

For light poles, a square anchor hole pattern with four attachment points is common, but often the pole itself obscures the diagonal. Measure the distance between two adjacent anchor bolts and enter that as the value for all four holes. The diameter can be calculated using this formula:

D = \frac{S}{\sin 45^\circ} = S\sqrt{2} \approx 1.4142\,S

Common sources of error

If the result does not seem correct, most likely the problem is not with the formula itself. Check your measurement procedure first.

If the diameter becomes significantly larger, you will usually enter the measurement with the continuous hole as a distance between adjacent holes. Set the number of steps over which the measuring line runs to the actual number of steps.

If the diameter is only slightly smaller, either enter the measurement on the inner edge without correction or mistakenly subtract the hole diameter twice from the measurement on the outer edge.

The apparent rotation of the coordinates is due to the starting angle. If this is set to zero, then the first hole will be on the positive X axis, while it normally starts at the top or a 45 degree angle in drawings.

Frequently asked questions

What is a bolt circle?: A virtual circle passing through the centers of a group of evenly spaced holes, studs or rivets. Its diameter is called the stud pitch or bolt circle diameter and this value determines whether two parts can be joined by bolts.
How can you determine the diameter of a bolt circle from measured values?: Measure the straight line distance between the centers of two holes, count how many "step" distances the line spans and divide that result by the sine of the value "(number of steps multiplied by 180 divided by number of holes)". For a hexagonal pattern of fasteners, the measurement for adjacent holes is 50 mm. Divide 50 by sin(30), and the result is 100 mm.
Are PCD and BCD the same?: Yes, they are the same in this type of mounting pattern. Both the Pitch Circle Diameter (PCD) and Bolt Circle Diameter (BCD) refer to the diameter that runs through the center points of the holes. The two terms come from different industries and have no differing geometric definitions.
How do you measure a five hole wheel pattern?: Since a five hole pattern does not have holes directly opposite each other, measure two holes separated by one hole and set the number of "step" spacings to 2. If the spacing between any two adjacent holes is about 108.7mm this corresponds to a typical 5x114.3 mm bolt circle.
How are measurement values converted from one side to another?: To determine the diameter of a hole, subtract the value equal to the hole diameter when measuring from outside edge to outside edge and add that amount when measuring inside edge to inside edge. When measuring from center of one side to outside edge of opposite side, subtract half of the hole diameter. These corrections are only valid if both holes are the same size.
If the bolt pattern matches can the wheel be mounted?: No. This just means that the bolts will fit through the holes. The hub bore, wheel offset, brake caliper clearance, bolt thread size and contact surface shape all have to match as well.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Wikipedia: Chord (geometry)
The chord length relation a = 2R sin(theta/2) that every bolt circle spacing formula is derived from.
Wolfram MathWorld: Circular Segment
Chord, central angle and radius relationships for a circle.
Wikipedia: Regular polygon
Equally spaced points on a circle form a regular polygon, which is where the side length and circumradius relation comes from.
Wikipedia: Wheel sizing
Bolt pattern notation, pitch circle diameter and the other fitment dimensions a matching pattern does not cover.
NIST: Units outside the SI and conversion factors
Guide for the use of the International System of Units, the reference for the exact 1 inch = 25.4 mm conversion.