Pentagon (5-Hole) Bolt Circle Pattern

The Oddball

The 5-hole pattern is the weirdo. No nice round numbers here, no simple fractions. With 4, 6, or 8 holes, you get nice angles that play well with shop math. But 5 holes? That's 72° spacing (360° ÷ 5 = 72°), and 72° doesn't give you any of those clean ratios.

Understanding The Problem

For a 5-hole pattern, you're going to need:

• Sin(72°) = 0.9511
• Cos(72°) = 0.3090
• Sin(36°) = 0.5878
• Cos(36°) = 0.8090

Sorry, I don't have any mnemonic tricks to help you remember this one. Not exactly numbers you'll memorize like 0.7071 or 0.86603. Just bookmark this tutorial.

Practical Method

There is a practical method though. So here's how I do it without borking my brains.

Step 1: First Hole on the X-axis

Start simple. Put your first hole on the positive X-axis:

• Hole 1: X = +R, Y = 0

Step 2: Calculate the Other Four

For a radius R, here are your coordinates:

1. Hole 1: X = +R, Y = 0 (0°)
2. Hole 2: X = +R × 0.3090, Y = +R × 0.9511 (72°)
3. Hole 3: X = -R × 0.8090, Y = +R × 0.5878 (144°)
4. Hole 4: X = -R × 0.8090, Y = -R × 0.5878 (216°)
5. Hole 5: X = +R × 0.3090, Y = -R × 0.9511 (288°)

Example: 100mm Bolt Circle

For a 100mm diameter bolt circle (50mm radius):

1. Hole 1: X = +50.00, Y = 0
2. Hole 2: X = +15.45, Y = +47.55
3. Hole 3: X = -40.45, Y = +29.39
4. Hole 4: X = -40.45, Y = -29.39
5. Hole 5: X = +15.45, Y = -47.55

Figure 1: Complete 5-hole pattern layout with coordinates

Understanding the Math

Here's how we get from angles to coordinates:

Figure 2: The trigonometry behind the weird numbers

Shortcuts Are Nice

Method 1: The Template

Once you calculate one 5-hole pattern, make a template. Drill it in aluminum plate and keep it on your pegboard. Future you will thank present you.

Method 2: CAD Cop-Out

It's 2025 and we all have pocket sized supercomputers. Fire up a CAD app, draw your bolt circle, array 5 holes, read the coordinates. No shame in using technology.

Method 3: Grandpa's Sine Bar

Some dead guys sine bar, probably.

If you have inherited a sine bar and you're feeling saucy:

1. Set sine bar to 72°
2. Drill first hole
3. Rotate part and sine bar together
4. Repeat 4 more times

Quick Reference Table

Circle	R	H1	H2	H3
80mm	40	(40, 0)	(12.36, 38)	(-32.36, 24)

Circle	H4	H5
80mm	(-32.36, -24)	(12.36, -38)
100mm	(-40.45, -29)	(15.45, -48)
127mm	(-51.37, -37)	(19.62, -60)

Circle	R	H1	H2	H3
100mm	50	(50, 0)	(15.45, 48)	(-40.45, 29)
127mm	63.5	(63.5,0)	(19.62, 60)	(-51.37, 37)

The Constants

Instead of memorizing sines and cosines, just remember these multipliers for your radius:

• Position 1: X = R × 1.0000, Y = 0
• Position 2: X = R × 0.3090, Y = R × 0.9511
• Position 3: X = R × -0.8090, Y = R × 0.5878
• Position 4: X = R × -0.8090, Y = R × -0.5878
• Position 5: X = R × 0.3090, Y = R × -0.9511

Some old guys have these on a card taped to the mill. It works ┐( ͡° ʖ̯ ͡°)┌

Verification

The distance between adjacent holes should be:

• Chord length = R × 1.1756

This is harder to measure than diameter, but it's what you've got.

Figure 3: Measuring chord length to verify your pattern

Real Talk

5-hole patterns are rare for a reason. They're a pain in the ass. If you're designing something and thinking "hmm, 5 bolts would be perfect here"

• stop. Use 4. Use 6. Your machinist might even buy you a beer. 🍻

But when you absolutely must do a 5-hole pattern (yeah, I'm looking at you low-rider wheel adapter dudes), now you know how. Just don't expect it to be fun.

Pro Tip

If you find yourself doing a lot of 5-hole patterns, invest in a rotary table or a dividing head. Set it to 72° increments and save your sanity. The math works, and it's a cool flex, but a rotary table works better.