Bolt Circle (PCD
Pitch Circle Diameter (PCD) is the diameter of the circle passing through the centers of all bolt holes on a pipe flange, wheel rim, or engine flywheel.
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📐 Formula
💡 Practical Example
6-hole bolt circle on a 6.0-inch PCD (starting at 0°): Step Angle = 360° / 6 = 60°. Center-to-Center Chord Distance = 6.0 × sin(30°) = 3.000 inches. Hole 1: (3.000, 0.000) | Hole 2: (1.500, 2.598) | Hole 3: (-1.500, 2.598).
📖 About Bolt Circle (PCD
Pitch Circle Diameter (PCD) is the diameter of the circle passing through the centers of all bolt holes on a pipe flange, wheel rim, or engine flywheel. Machinists use PCD calculators to generate G-code coordinates for CNC drilling.
To use the Bolt Circle (PCD) & Flange Hole Coordinate Calculator, enter your Pitch Circle Diameter (PCD), Number of Holes (N), Start Angle (First Hole). The calculator instantly computes Center-to-Center Hole Distance (Chord), Angle Between Holes and more. Results update in real time as you change any input — no submit button needed.
How to Use This Calculator
Enter your Pitch Circle Diameter (PCD) (e.g. 6.0 in in / mm), Number of Holes (N) (e.g. 6 in holes), and Start Angle (First Hole) (e.g. 0 in degrees). Results update instantly as you type — adjust any value to compare scenarios.
The Formula
Pitch Radius R = PCD ÷ 2
Adjacent Hole Chord C = PCD × sin(180° ÷ N)
Hole Coordinates: X_i = R × cos(θ_i), Y_i = R × sin(θ_i)
Worked Example
6-hole bolt circle on a 6.0-inch PCD (starting at 0°):
Step Angle = 360° / 6 = 60°.
Center-to-Center Chord Distance = 6.0 × sin(30°) = 3.000 inches.
Hole 1: (3.000, 0.000) | Hole 2: (1.500, 2.598) | Hole 3: (-1.500, 2.598).
Understanding Your Result
Geometric calculations assume ideal shapes — real-world measurements should include a 5–15% tolerance for irregular shapes, cutting waste, and installation overlap. For construction applications: always verify calculated areas match your physical measurements before ordering materials. Standard practice is to measure the same dimension twice from different reference points and use the average. Express results in the units required by your supplier or building permit — conversions between cubic yards, cubic feet, and cubic meters must be precise for material orders.
💡 Mathematical Rigor & Applied Context
- This calculator applies exact mathematical definitions following conventions established by NIST and international standards bodies.
- Rounding errors accumulate across multi-step calculations. For precision-critical work, maintain extra significant figures through all intermediate steps.
- Many mathematical concepts have multiple valid formulations — if a result seems unexpected, verify which convention or definition applies to your context.
- Dimensional analysis (unit tracking) is the fastest way to catch formula errors. Every term in an equation must have consistent, compatible units.
- Numerical methods used in digital calculators introduce floating-point precision limits (~15 significant digits for IEEE 754 double precision).
- For statistical and probabilistic calculations, always specify whether you are working with population parameters or sample statistics — formulas differ.
- Visualizing a problem geometrically or testing with known boundary values (zero, infinity, negative) reveals hidden errors faster than algebraic checking.
- When in doubt, validate your result against a simplified hand calculation or a published worked example from a textbook or standards document.
Results are for informational and educational purposes only. Always verify critical decisions with a qualified professional.