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HOLE DIVIDING CALCULATION

How to Drill Perfectly Spaced Holes
Bolt Circles Formulas Real Examples
"Precision starts with the pitch circle."
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Definition

What Is Hole Dividing?

Hole dividing is the process of locating equally spaced holes on a circular pitch circle.
⚙️ Pipe flanges
🔩 Gear mounting
🏭 Machine components
⚙️ Pump & valve bodies
🏗️ Structural connections
The key inputs: number of holes (N) and pitch circle diameter (D).
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Why It Matters

Precision Matters

✓ Accurate assembly
✓ Uniform load distribution
✓ Interchangeable components
✓ Less manufacturing waste
✓ Reliable hole positioning
Even small positioning errors can affect assembly accuracy and joint integrity.
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Methods

4 Ways to Divide a Circle

1. Angular Method
Divide 360° equally by index angle
2. Coordinate Method
Calculate X-Y positions for each hole
3. Chord Method
Measure the straight-line distance between adjacent holes
4. Polar Method
Specify radius and angle for each hole
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Step 1

Calculate Angular Spacing

θ = 360° / N
Angle between adjacent holes
θ
Angular increment
N
Total holes
6 HOLES → θ = 360° / 6 = 60°
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Step 2

Find the Chord Length

C = D × sin(180° / N)
Chord length (mm or in)
C = 2 × R × sin(θ / 2)
Equivalent using radius
The chord is the straight-line distance between adjacent hole centres — not the arc distance.
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Coordinate Method

Find Every Hole Position

Xk = R × cos(α + kθ)
X coordinate
Yk = R × sin(α + kθ)
Y coordinate
R
Radius
α
Start angle
θ
360°/N
k
0 to N−1
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Worked Example

6 Holes on 100 mm PCD

N 6
D 100 mm
α 0°
θ
60°
C = 100 × sin(30°)
50 mm
Hole
X (mm)
Y (mm)
1
50
0
2
25
43.30
3
−25
43.30
4
−50
0
5
−25
−43.30
6
25
−43.30
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Worked Example

8 Holes on 200 mm PCD

N 8
D 200 mm
α 45°
θ
45°
C = 200 × sin(22.5°)
76.54 mm
FIRST HOLE (70.71, 70.71) MM
The starting angle shifts the entire pattern's orientation without changing its spacing.
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Manual Method

Divide 5 Holes With a Chord

N 5
D 150 mm
θ = 360° / 5 = 72°
Angular increment
C = 150 × sin(36°)
Chord length
C = 88.17 MM
Set dividers to 88.17 mm and step around the pitch circle five times. Check that the final step returns to the start.
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Setup & Safety

Accurate Setup = Better Results

✓ Locate the centre accurately
✓ Confirm the correct PCD
✓ Clamp the workpiece securely
✓ Use dividing head or rotary table
✓ Centre-punch or spot-drill locations
✓ Verify coordinates and dimensions
✓ Use guards and eye protection
For CNC operations, simulate the toolpath before machining.
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Calculate Your Bolt Circle Now

Enter the hole count. Enter the PCD. Get accurate hole coordinates.
Angular θ Chord C X-Y Coords mm / in
OPEN HOLE DIVIDING CALCULATOR READ THE FULL GUIDE →
Simple Indexing Differential Indexing Gear Train Bearing Decoder
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