Bolt Circle Calculator
Calculate precise bolt hole coordinates for circular patterns in construction and manufacturing
Bolt Pattern Parameters
Total number of bolt holes in the pattern
Radius from center to bolt hole centers
Angle of first hole from horizontal (positive x-axis)
X coordinate of bolt circle center
Y coordinate of bolt circle center
Bolt Pattern Summary
Bolt Pattern Equations:
• x_i = cos((i × 360/n) + A) × R + x_c
• y_i = sin((i × 360/n) + A) × R + y_c
• Chord length = 2 × R × sin(θ/2), where θ = 360°/n
Bolt Hole Coordinates
| Hole # | Angle (°) | X (mm) | Y (mm) |
|---|---|---|---|
| 1 | 0.00 | 50.000000 | 0.000000 |
| 2 | 90.00 | 0.000000 | 50.000000 |
| 3 | 180.00 | -50.000000 | 0.000000 |
| 4 | 270.00 | -0.000000 | -50.000000 |
Note: Coordinates are given from the center of the bolt circle. Use these values for CNC programming, CAD design, or manual drilling operations.
Example Calculation
5-Hole Flange Pattern
Application: Pipe flange with 5 bolt holes
Number of holes: n = 5
Bolt circle radius: R = 50 mm
First hole angle: A = 0° (horizontal)
Center offset: (0, 0) mm
Step-by-step Calculation
1. Angle between holes: B = 360°/5 = 72°
2. Hole 1: θ = 0° + 0° = 0°, x = cos(0°) × 50 = 50.00, y = sin(0°) × 50 = 0.00
3. Hole 2: θ = 72° + 0° = 72°, x = cos(72°) × 50 = 15.45, y = sin(72°) × 50 = 47.55
4. Hole 3: θ = 144° + 0° = 144°, x = cos(144°) × 50 = -40.45, y = sin(144°) × 50 = 29.39
5. Continue for remaining holes...
Result: 5 precisely positioned holes for secure flange connection
Common Applications
Flanges
Pipe connection patterns
ANSI, DIN, JIS standards
Wheel Rims
Automotive lug patterns
4, 5, 6, 8 bolt patterns
Machine Parts
Gears, pulleys, couplings
Precision manufacturing
Common Patterns
Manufacturing Tips
Use coordinates for CNC programming
Verify measurements with precision tools
Mark center punch before drilling
Export CSV for CAD import
Double-check hole spacing
Understanding Bolt Circle Calculations
What is a Bolt Circle?
A bolt circle (also called bolt pattern or PCD - Pitch Circle Diameter) is an imaginary circle that passes through the centers of all bolt holes in a circular pattern. It's fundamental for creating precise, evenly-spaced bolt patterns in manufacturing and construction.
Key Parameters
- •n: Number of holes in the pattern
- •R: Radius of the bolt circle
- •A: Angle of first hole from horizontal
- •(x_c, y_c): Center coordinates of bolt circle
Mathematical Formulas
Bolt Pattern Equations
x_i = cos((i × 360°/n) + A) × R + x_c
y_i = sin((i × 360°/n) + A) × R + y_c
Where i = 0, 1, 2, ..., n-1
Angle Between Holes
B = 360° / n
Equal spacing formula
Chord Length
L = 2 × R × sin(B/2)
Distance between adjacent holes
Applications in Industry
Automotive
Wheel bolt patterns, brake disc mounting, engine block attachments, transmission cases, and differential housings.
Construction
Structural steel connections, pipe flanges, tower foundations, bridge components, and crane mounting plates.
Manufacturing
Machine tool fixtures, gear mounting, pump casings, motor mounts, and precision instrument assemblies.