Bolt Circle Calculator

Free Online Bolt Circle Calculator

This bolt circle calculator finds the exact position of every hole evenly spaced around a bolt circle, also called a bolt hole circle, pitch circle, or PCD (pitch circle diameter). Just enter the number of holes and the bolt circle diameter, and the calculator instantly gives you the angle between holes, the straight-line spacing, the curved arc spacing, and the precise X and Y coordinate of every single hole — plus a labeled, to-scale diagram and a full step-by-step solution.

Whether you're machining a flange, drilling a wheel, laying out a motor mount, designing a pipe fitting, or just checking a mechanical drawing, this tool gives you exact, ready-to-use numbers in seconds — no CAD software, protractor, or manual trigonometry required.

What Is a Bolt Circle?

A bolt circle is an imaginary circle that passes through the center of every bolt hole in a circular pattern, such as the lug holes on a car wheel, the bolt holes on a pipe flange, or the mounting holes on a motor face plate. The diameter of that imaginary circle is called the bolt circle diameter (BCD) or pitch circle diameter (PCD) — you'll see both terms used interchangeably across engineering drawings, automotive parts catalogs, and machine shop manuals.

Because the holes are always spaced perfectly evenly around this circle, the whole layout can be described with just two numbers: how many holes there are, and how big the bolt circle is. Everything else — the angle between each hole, their exact coordinates, and the distance between them — follows directly from simple trigonometry.

Bolt Circle Formula

Every bolt circle layout is built from a handful of core formulas. Here's what this calculator uses:

• Radius: radius = diameter ÷ 2
• Angle between holes: angle = 360° ÷ number of holes
• Chord (straight-line) spacing: chord = 2 × radius × sin(angle ÷ 2)
• Arc (curved) spacing: arc = (π × diameter) ÷ number of holes
• Hole coordinates: X = radius × cos(θ), Y = radius × sin(θ), where θ is that hole's angle around the circle

How to Use This Bolt Circle Calculator — Step by Step

Getting your hole layout takes just a few seconds:

• Enter the number of holes you need spaced evenly around the circle (for example, 4, 5, 6, or 8).
• Enter the bolt circle diameter (BCD/PCD) — the diameter of the circle that passes through the center of every hole.
• Set the starting angle for hole 1. Use 90° to place the first hole at the top (12 o'clock), or 0° to place it at the right (3 o'clock) — whatever matches your drawing or fixture.
• Choose millimeters or inches to match your measurements.
• Instantly read the angle between holes, the chord spacing, the arc spacing, and the full X/Y coordinate table for every hole in the results.
• Check the diagram to see the holes plotted to scale exactly where they'll sit on the real part, and scroll to the step-by-step solution to see every formula used.

Worked Example 1 — A Standard 5-Lug Wheel

A common car wheel uses a 5-lug bolt pattern with a bolt circle diameter of 114.3 mm (a very common metric PCD, often written 5x114.3). The radius is 114.3 ÷ 2 = 57.15 mm. The angle between holes is 360° ÷ 5 = 72°. The chord spacing between any two adjacent lug holes is 2 × 57.15 × sin(36°) = 2 × 57.15 × 0.5878 ≈ 67.18 mm — this is the number you'd actually measure with calipers between two neighboring lug holes to confirm the pattern.

Worked Example 2 — A 6-Hole Flange

An industrial pipe flange has 6 bolt holes on a 200 mm bolt circle. The radius is 100 mm, and the angle between holes is 360° ÷ 6 = 60°. The chord spacing is 2 × 100 × sin(30°) = 2 × 100 × 0.5 = 100 mm. With a starting angle of 90° (first hole at the top), hole 1 sits at (0, 100), hole 2 at 30° further around, and so on — every subsequent hole's coordinates follow the same X = r·cos(θ), Y = r·sin(θ) pattern.

Bolt Circle vs. Bolt Pattern: What's the Difference?

The bolt circle is the imaginary circle itself; the bolt pattern is the shorthand way of describing it, written as (number of holes) x (bolt circle diameter) — for example, 5x114.3 mm means 5 holes evenly spaced on a 114.3 mm bolt circle. You'll see this notation everywhere from wheel and tire shops to industrial parts catalogs, and this calculator works with either way of thinking about the layout: give it the hole count and the diameter, and it fills in every other detail.

Common Real-World Bolt Circle Patterns

Certain bolt patterns come up constantly across automotive, industrial, and plumbing work:

• 4-lug car wheel — 4x100 mm (common on small/compact cars)
• 5-lug car wheel — 5x114.3 mm (common on sedans, SUVs, and trucks)
• 6-lug truck wheel — 6x139.7 mm (common on pickup trucks and vans)
• 8-lug heavy truck wheel — 8x165.1 mm (common on heavy-duty and dually trucks)
• 4-hole pipe flange — 4 holes on a bolt circle (standard ANSI/ASME flange pattern)
• 6-hole motor mount — 6 holes on a bolt circle (common industrial motor face pattern)

Understanding the Diagram: Reading the Layout Directly

The diagram above the step-by-step solution plots every hole exactly where it belongs on the bolt circle, drawn to scale and numbered in order starting from your chosen starting angle. The dashed lines from the center to the first two holes, connected by a solid green line, show the exact chord spacing between adjacent holes — this is the real, straight-line distance you'd use to double-check your layout with a ruler or calipers before drilling or machining.

Real-World Applications of Bolt Circle Calculations

Bolt circle math isn't just for wheels — it shows up throughout mechanical design and fabrication:

• Automotive: laying out wheel lug patterns and checking wheel/hub compatibility.
• Piping and plumbing: positioning bolt holes on flanges to match ANSI, DIN, or JIS standards.
• Machine design: placing mounting holes evenly around motor faces, pump housings, and gearboxes.
• CNC machining: programming a bolt-hole circle (BHC) canned cycle using the exact X/Y coordinates.
• Woodworking and fabrication: marking out evenly spaced holes for round tabletops, lazy Susans, or decorative patterns.

How to Measure a Bolt Circle by Hand

If you're working from a real part instead of a drawing, measuring the bolt circle diameter depends on how many holes it has. For an even number of holes, you can measure straight across the circle from the center of one hole to the center of the hole directly opposite it — that distance is exactly the bolt circle diameter. For an odd number of holes, like 5, there's no hole exactly opposite another one, so the usual trick is to measure the chord distance between two adjacent holes with calipers, then enter that value along with the hole count into this calculator's related right triangle or trigonometry tools to back-calculate the diameter, or simply try a few standard diameters (like 100, 108, 112, 114.3, or 120 mm for wheels) until the calculated chord spacing matches your measurement.

A quicker shop-floor method for odd-hole patterns is measuring from the center of one hole, across the center of the bolt circle, to the outer edge of the hole that sits roughly opposite it, then adding half a hole diameter — though this is less precise than working from a known or catalog diameter whenever one is available.

Why Even Spacing Matters

Evenly spacing every hole around the bolt circle isn't just a matter of appearance — it directly affects how evenly clamping force is distributed once bolts are tightened. On a flange or wheel, uneven hole spacing can create weak points where the joint isn't pulled together as tightly, leading to leaks on pressurized pipe connections, or uneven load distribution on a wheel that can accelerate wear on the hub or bearings. Because the math behind even spacing is simple but easy to get wrong by hand — especially for patterns with 5, 7, or 9 holes where the angles don't divide into round numbers — using a calculator that outputs exact coordinates and angles removes the guesswork from the layout stage, before a single hole is drilled.

Common Mistakes to Avoid

It's also worth double-checking the number of holes you enter before drilling anything — a pattern of 5 holes and a pattern of 6 holes can look surprisingly similar at a glance on a small part, but the angle between holes is 72° for one and only 60° for the other, which throws off every downstream measurement.

The most common mix-up is confusing radius with diameter — always double-check whether your source (a drawing, a parts catalog, or a measurement) is giving you the full bolt circle diameter or just the radius, since using the wrong one doubles or halves every calculated coordinate. Another frequent error is confusing chord spacing with arc spacing: the chord is the straight-line distance you'd measure with a ruler, while the arc is the curved distance along the circle itself, and the two are only equal for very small angles between holes. Finally, remember that the starting angle only rotates the whole pattern — it never changes the spacing between holes, so pick whichever starting angle makes the diagram match your actual part or drawing.

Tips for Getting Accurate Results

Always measure or confirm the bolt circle diameter carefully — it's easy to accidentally measure between two opposite holes on a pattern with an odd number of holes, which does not give you the true diameter unless the holes sit exactly 180° apart. When double-checking a manufactured part with calipers, the chord spacing between physically adjacent holes is the number to compare against, not the arc spacing. If you're programming a CNC bolt-hole circle cycle, most controllers expect the same X = r·cos(θ), Y = r·sin(θ) coordinates this calculator produces, so you can copy the table directly into your program.