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Category Engineering Calculators

Presets:

Pitch Circle Diameter (PCD)

Diameter of the circle through bolt hole centers

Number of Bolt HolesInteger from 1 to 360

Starting Angle Offset

Counter-clockwise from 3 o'clock (positive X-axis)

Decimal Places0 to 8 decimal places

Enter values and press Calculate to see bolt positions.

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About

Machining a bolt circle without precise coordinates risks misalignment, uneven clamping force, and gasket failure under pressure. This calculator computes exact x and y positions for each bolt hole on a given Pitch Circle Diameter (PCD) using trigonometric decomposition. Inputs are the circle diameter, the number of holes, and an optional angular offset θ₀ measured counter-clockwise from the positive x-axis. Results are suitable for DRO entry on milling machines or CNC G-code generation.

The tool assumes an ideal circle centered at the origin. For real-world work, account for stock centering error and machine backlash. Coordinates are relative to the circle center. If your datum is a workpiece corner, add the center offsets manually. All trigonometric operations use IEEE 754 double-precision arithmetic, giving positional accuracy far below any practical machining tolerance (0.0001 mm range).

Formulas

Each bolt hole position is computed by decomposing the radius vector at equal angular intervals around the circle. The angular position of hole i (zero-indexed) is:

θ_i = 2π ⋅ iN + θ₀

The Cartesian coordinates relative to the circle center are:

x_i = PCD2 ⋅ cos(θ_i)

y_i = PCD2 ⋅ sin(θ_i)

Where PCD = Pitch Circle Diameter (the diameter of the imaginary circle passing through all bolt hole centers), N = total number of bolt holes, θ₀ = starting rotation offset in degrees (converted to radians internally via θ_rad = θ_deg ⋅ π ÷ 180), and i = hole index from 0 to N − 1.

The angular spacing between consecutive holes is constant at 360°N. The chord length (center-to-center distance between adjacent holes) is C = PCD ⋅ sin(π ÷ N).

Reference Data

Standard	PCD mm	Bolts	Bolt Size	Application
ANSI B16.5 Class 150 2"	120.7	4	5/8"	Pipe flanges, low pressure
ANSI B16.5 Class 150 4"	190.5	8	5/8"	Pipe flanges, low pressure
ANSI B16.5 Class 300 6"	266.7	12	3/4"	Pipe flanges, medium pressure
ANSI B16.5 Class 150 8"	298.5	8	3/4"	Pipe flanges, low pressure
DIN 2576 PN10 DN50	125	4	M16	European pipe flanges
DIN 2576 PN10 DN100	180	8	M16	European pipe flanges
DIN 2576 PN16 DN150	240	8	M20	European pipe flanges, higher pressure
DIN 2576 PN16 DN200	295	12	M20	European pipe flanges
JIS 10K 50A	120	4	M16	Japanese standard flanges
JIS 10K 100A	175	8	M16	Japanese standard flanges
SAE 4-bolt (Group 1)	63.5	4	3/8"	Hydraulic pump/motor mount
SAE 4-bolt (Group 2)	82.6	4	7/16"	Hydraulic pump/motor mount
SAE 4-bolt (Group 3)	101.6	4	1/2"	Hydraulic pump/motor mount
4×100	100	4	M12	Automotive wheel (compact cars)
5×114.3	114.3	5	M12	Automotive wheel (sedans, SUVs)
5×120	120	5	M14	Automotive wheel (BMW, others)
6×139.7	139.7	6	M12	Automotive wheel (trucks, SUVs)
Typical CNC fixture plate	200	6	M10	Workholding fixture
Common lathe chuck (6")	130	3	M8	Lathe chuck mounting
Common lathe chuck (8")	165	3	M10	Lathe chuck mounting

Frequently Asked Questions

The rotation offset θ₀ shifts all bolt positions uniformly around the circle. A value of 0° places the first bolt on the positive X-axis (3 o'clock position). Setting it to 90° places the first bolt at the 12 o'clock position. This is critical when aligning bolt patterns to existing features, keyways, or avoiding interference with other components.

All coordinates are relative to the center of the bolt circle, which is treated as the origin (0, 0). Angles are measured counter-clockwise from the positive X-axis, following standard mathematical convention. If your machine uses a different datum (e.g., workpiece corner), you must add the X and Y offsets of the circle center to each computed coordinate.

Yes. The X/Y coordinates output by this calculator can be directly used in G81 (drill cycle) or G00/G01 positioning commands. Copy the coordinate table and convert each row to a drill point. Remember that most CNC controllers use the same mathematical convention (counter-clockwise positive angles). Verify your machine's coordinate system matches before cutting metal.

This is IEEE 754 floating-point representation. Values like cos(90°) produce numbers on the order of 10⁻¹⁶ rather than exact zero. The calculator rounds display values to 4 decimal places, so any value below 0.00005 will display as 0.0000. This rounding is well within any practical machining tolerance.

Measure the center-to-center distance between two adjacent bolt holes. This gives the chord length C. Then compute PCD = C ÷ sin(π ÷ N) where N is the number of holes. Alternatively, for an even number of holes, measure diametrically opposite holes center-to-center; that distance equals the PCD directly.

For manual milling with a DRO, 3 decimal places in millimeters (0.001 mm) or 4 in inches (0.0001 in) is standard resolution. CNC machines typically accept up to 4 decimal places in mm. This calculator provides 4 decimal places by default, which covers both use cases. Requesting higher precision is meaningless given typical machine repeatability of ±0.005 mm.