Bolt Circle Layout: How to Calculate Hole Pattern Coordinates for Mill Work and DROs

The Bolt Circle Formula

The math for a bolt circle is basic trigonometry. If you have N holes equally spaced on a circle of diameter D (radius R = D/2), the angle between adjacent holes is 360/N degrees. The X and Y coordinates of each hole, measured from the center of the bolt circle, are:

X = R × cos(θ), Y = R × sin(θ), where θ is the angular position of each hole. For N equally spaced holes, the angles are: θ_1 = start_angle, θ_2 = start_angle + 360/N, θ_3 = start_angle + 2 × 360/N, and so on.

The start angle defines where the first hole sits. A start angle of 0 degrees puts the first hole directly to the right of center (on the positive X axis). A start angle of 90 degrees puts it directly above center. Many engineering drawings specify the start angle, either explicitly or by dimensioning the first hole's position relative to a datum.

For example, a 4-hole bolt circle with a 6-inch bolt circle diameter and a start angle of 45 degrees: R = 3.000", angular spacing = 90°. Hole 1: X = 3.000 × cos(45) = 2.121", Y = 3.000 × sin(45) = 2.121". Hole 2: X = 3.000 × cos(135) = -2.121", Y = 3.000 × sin(135) = 2.121". Hole 3: X = 3.000 × cos(225) = -2.121", Y = 3.000 × sin(225) = -2.121". Hole 4: X = 3.000 × cos(315) = 2.121", Y = 3.000 × sin(315) = -2.121".

These coordinates are relative to the center of the bolt circle. To get the machine coordinates, add the center's position. If the bolt circle center is at X4.500, Y3.000 on the workpiece, then Hole 1 is at machine X = 4.500 + 2.121 = 6.621", Y = 3.000 + 2.121 = 5.121".

Setting Up the DRO for Bolt Circle Work

Most modern DROs (Digital Read-Outs) on manual mills have a built-in bolt circle function. You enter the number of holes, the bolt circle diameter, the start angle, and the center position, and the DRO calculates all the hole positions for you. You then use the DRO readout to position the table for each hole.

Setting the work zero: Before using the bolt circle function, you need to establish a work coordinate origin. Typically, you edge-find or indicate the part datum (a corner, a bore center, or a reference surface) and zero the DRO at that point. All bolt circle center coordinates are then relative to this origin.

Using the bolt circle function: On most DROs (Newall, Acu-Rite, Mitutoyo), you press the bolt circle key, enter the parameters (number of holes, diameter, start angle, center X, center Y), and the DRO switches to a mode that shows you the X and Y distances to the next hole. Move the table until both X and Y read zero, and you're on the hole center. Drill, then advance to the next hole.

Without a bolt circle function: If your DRO doesn't have bolt circle mode, pre-calculate all the hole coordinates on paper (or use a bolt circle calculator tool), write them down, and position the table to each X, Y coordinate manually. This is the old-school method and works fine — it's just slower.

Edge finding the center of the bolt circle: If the bolt circle is centered on an existing bore, use an indicator in the spindle to pick up the bore. Sweep the indicator around the bore, adjusting X and Y until the indicator reads the same at all four quadrants (north, south, east, west). This locates the bore center. Zero the DRO at this point and your bolt circle will be concentric with the existing bore.

Absolute vs. Incremental Positioning

Bolt circle coordinates can be expressed in absolute or incremental form, and confusing the two is a reliable way to put holes in wrong places.

Absolute coordinates: Every hole position is measured from the same origin (work zero). Hole 1 is at X2.121, Y2.121. Hole 2 is at X-2.121, Y2.121. Each coordinate is independent — if you make an error on one hole, it doesn't propagate to the next. This is the preferred method for bolt circles.

Incremental coordinates: Each hole position is measured as a distance from the previous hole. From Hole 1, move X-4.243, Y0.000 to reach Hole 2. From Hole 2, move X0.000, Y-4.243 to reach Hole 3. The problem with incremental positioning for bolt circles is error accumulation. If you over-travel on the move to Hole 2 by 0.002", that error carries to Hole 3, Hole 4, and every subsequent hole. By the last hole, accumulated error can be significant.

When to use each: For bolt circles, always use absolute coordinates from a common origin. Incremental positioning is useful for evenly spaced linear patterns (row of holes at 1-inch spacing) but is risky for circular patterns because the X and Y increments are different for each hole and rounding errors accumulate.

CNC note: In CNC programming, G90 sets absolute mode and G91 sets incremental mode. Many bolt circle canned cycles (G70 on Haas, for example) automatically use absolute coordinates internally even if the program is in incremental mode. But if you're programming bolt circle holes as individual G81 (drill cycle) lines, make sure you're in G90 mode.

G-Code Canned Cycles for Bolt Circles

Most CNC controllers have built-in bolt circle canned cycles that calculate hole positions automatically. You provide the center, diameter, number of holes, and start angle, and the controller generates all the positions internally.

Haas (G70): G70 is the bolt hole circle command. Example: G81 Z-0.750 R0.100 F8.0 (set up drill cycle), then G70 I3.000 J0.000 K0.000 L4 (I = BC radius, J = start angle, K = center X [in some formats], L = number of holes). The exact syntax varies by control software version — always check the operator's manual for your specific machine.

Fanuc: Fanuc controls don't have a native bolt circle cycle in the standard G-code set. You program each hole position explicitly or use a macro (G65 with a custom macro) or parametric programming. Most CAM software generates individual hole positions automatically, making this a non-issue for CAM-programmed parts.

Manual programming approach: If your control lacks a bolt circle cycle, pre-calculate the coordinates and program each hole as a separate line. For a 6-hole pattern: G81 X1.500 Y2.598 Z-0.500 R0.100 F8.0 (Hole 1), X-1.500 Y2.598 (Hole 2), X-3.000 Y0.000 (Hole 3), X-1.500 Y-2.598 (Hole 4), X1.500 Y-2.598 (Hole 5), X3.000 Y0.000 (Hole 6), G80 (cancel cycle).

CAM software approach: Modern CAM programs (Fusion 360, Mastercam, SolidCAM) recognize bolt circle patterns in the solid model and automatically generate the hole positions. You pick the holes, select the drill cycle type, and the CAM handles the math. This is the fastest and most error-proof method for CNC work.

Common Bolt Circle Sizes in Industry

Certain bolt circle patterns repeat across industries because they're defined by standards. Knowing these saves time because you can verify your calculation against the expected pattern.

ANSI pipe flanges (150# class, common sizes): 2" flange: 4 holes on a 4.75" BC. 3" flange: 4 holes on a 6.00" BC. 4" flange: 8 holes on a 7.50" BC. 6" flange: 8 holes on a 9.50" BC. 8" flange: 8 holes on a 11.75" BC. Bolt hole sizes are typically 3/4" for 150# flanges up to 4 inches.

Bearing pillow blocks: Standard pillow block mounting patterns are defined by the bearing manufacturer. A UCP205 (1" bore pillow block) typically has a 2-bolt pattern with 5-1/4" center-to-center. Larger bearings use 4-bolt patterns. These are linear patterns, not bolt circles, but are worth mentioning because they're so common.

Motor mounting (NEMA frames): NEMA 56 frame: 4 holes on a bolt pattern defined by 2.75" × 3.00" (not a circle — it's a rectangle). NEMA 143/145: 5.875" × 4.375". NEMA 182/184: 6.625" × 4.875". Motor mounting patterns are rectangular, not circular, but the math is simpler (just X and Y coordinates).

Automotive wheel bolt patterns: 4 × 100mm (common Honda/Toyota), 5 × 4.5" (common Ford/Jeep), 5 × 114.3mm (common Toyota/Honda), 6 × 5.5" (common GM truck), 8 × 6.5" (HD truck). These are true bolt circles and are specified as "number of lugs × bolt circle diameter."

SAE flange sizes (hydraulic): SAE 4-bolt flanges are specified by code: Code 61 (3000 PSI) and Code 62 (6000 PSI). A 1" Code 61 flange has 4 holes on a 2.375" bolt circle. A 2" Code 61 flange has 4 holes on a 3.625" bolt circle. These are critical in hydraulic system assembly.

Mistakes to Avoid

Confusing diameter and radius: The bolt circle specification on a drawing is always the DIAMETER. The formula uses the RADIUS. If a drawing calls for a 6.000" bolt circle and you use 6.000 as the radius, your holes will be at twice the correct distance from center. This mistake happens every week in shops everywhere. Always divide the bolt circle diameter by 2 before plugging into the trig formula.

Wrong start angle: A start angle of 0° puts the first hole at the 3 o'clock position. Many drawings define the first hole at the 12 o'clock position (90°) or at some other specific angle. If the drawing shows the first hole at 45° from vertical, that's 90° - 45° = 45° from horizontal, so your start angle is 45°. Read the drawing carefully to determine the angular reference.

Calculator in wrong mode: If your calculator is in radians and you enter 45 degrees, cos(45 radians) = 0.5253, not 0.7071. The resulting hole positions will be wildly wrong. Always verify your calculator is in degree mode before computing bolt circle coordinates.

Not verifying the pattern: After drilling, measure the distance between adjacent holes and compare to the calculated value. For a 4-hole pattern on a 6" BC, the chord length between adjacent holes should be 6.000 × sin(45°) × 2 = 4.243". If your measured distance is significantly different, something went wrong.

Drilling without spotting: On a manual mill, a twist drill can walk on the surface if you don't center-drill or spot-drill first. On angled or curved surfaces, this is even more critical. Always spot-drill every hole in the bolt circle before switching to the full-size drill. This also applies to CNC — if the part surface isn't flat and perpendicular to the spindle, a spot drill establishes a reliable starting point.