Bolt Circle Calculator

Bolt Circle Calculator for X/Y hole positions, hole spacing, BCD from a caliper reading, partial arcs and ASME B16.5 pipe flange patterns, with G81 drill code and a layout diagram.

(8 HOLES ON 6.0000 IN BOLT CIRCLE)
(CENTER X0.0000 Y0.0000, HOLE 1 AT 0 DEG CCW)
G20 G17 G90 G80
G0 X3.0000 Y0.0000
G98 G81 X3.0000 Y0.0000 Z-0.2500 R0.1000 F5.0
X2.1213 Y2.1213
X0.0000 Y3.0000
X-2.1213 Y2.1213
X-3.0000 Y0.0000
X-2.1213 Y-2.1213
X0.0000 Y-3.0000
X2.1213 Y-2.1213
G80

How a Bolt Circle Calculator Places Each Hole

A bolt circle calculator turns three numbers into a drilling plan: the bolt circle diameter (BCD), the hole count and the angle of hole 1. Every hole sits on one circle, one equal angle step from the last, so plain trigonometry gives each X and Y position.

The angle step for a full circle is 360° divided by the hole count. Hole 1 sits at the start angle, measured counterclockwise from the +X axis (3 o'clock), and each next hole adds one step.

$$X_i=X_0+R\cos (A+(i-1)\cdot 360^{\circ }/N)$$

$$Y_i=Y_0+R\sin (A+(i-1)\cdot 360^{\circ }/N)$$

R is half the BCD, A is the hole 1 angle, N is the hole count and i is the hole number. X₀ and Y₀ shift the whole pattern when the circle center is not the part origin, such as a hub that sits 3 in from the left edge of a plate.

For clockwise numbering, a bolt circle calculator subtracts the step instead of adding it. The holes land in the same places; only their order changes, which matters for drilling sequence and for matching a print that numbers holes clockwise.

Worked Example: 5 Holes on a 4.5 in Circle

Take a 5-hole pattern on a 4.5 in BCD with hole 1 at 12 o'clock (90°) and the circle center at X 3.000, Y 2.000 from the plate corner. The radius is 2.25 in and the step is 72°.

Holes 3 and 4 share a Y value, and holes 2 and 5 mirror each other about X 3.000. That symmetry is a fast check on any bolt circle calculator output for an odd-count pattern with hole 1 on a centerline.

Which Start Angle to Use

A bolt circle calculator with angle input lets you rotate the whole pattern. Use 0° when the print has no orientation, or 90° to put hole 1 at the top, which is common on wheel hubs. Pipe flanges use half a step, 180° ÷ N, so no hole sits on the vertical or horizontal centerline.

When a mating part already exists, match its orientation instead of picking a convenient number. A 4-hole plate drilled at 0° will not bolt to a 4-hole flange drilled at 45°, even with the same BCD.

Bolt Circle Formula for Hole Spacing

The straight-line distance between two neighboring holes is the chord of the circle between them. That chord is what you check with calipers, and it is the number most bolt circle chart tables print.

$$S=BCD\times \sin (180^{\circ }/N)$$

S is the center-to-center spacing between adjacent holes. The term sin(180° ÷ N) is the chord factor; multiply it by any BCD to get the spacing for that hole count.

For holes k steps apart, replace 180° ÷ N with k × 180° ÷ N. On an even count, the holes N ÷ 2 steps apart sit straight across the center, and their spacing equals the BCD itself.

Spacing from the inside edges of two holes is S minus one hole diameter, and from the outside edges it is S plus one hole diameter. Those two numbers are what a caliper reads directly when the jaws sit in or across the holes.

Bolt Circle Chart: Chord Factors by Hole Count

The chord factors below come straight from the formula a bolt circle calculator uses for distance between holes. The last two columns show the adjacent spacing on a 6 in and a 100 mm bolt circle.

The 6-hole row is worth remembering. Adjacent holes on a 6-hole circle are exactly one radius apart, so a 4 in BCD puts neighboring holes 2.000 in apart.

Arc length is a different number from chord spacing, and a bolt circle calculator that reports both saves confusion. The curved distance hole to hole is the radius times the step angle in radians, so 8 holes on a 6 in circle are 2.3562 in apart along the arc but only 2.2961 in apart in a straight line.

Find the Bolt Circle Diameter From Hole Spacing

To get the BCD of an existing part, measure two holes and divide their center distance by the chord factor. This is the bolt circle diameter formula run backward, the same math a bolt circle calculator uses to find the BCD, and it is how sprockets, brake rotors, hubs and old flanges get identified.

$$BCD=\frac{C}{\sin (k\times 180^{\circ }/N)}$$

C is the center-to-center distance you measured and k is how many steps apart the two holes are: 1 for neighbors, N ÷ 2 for holes straight across on an even count.

Converting Edge-to-Edge Readings

Calipers rarely land on hole centers, so convert the reading first, or let the bolt circle calculator do it from the hole diameter. Add one hole diameter to an inside-edge reading, or subtract one hole diameter from an outside-edge reading, and the result is C.

Example: a 6-hole sprocket with 0.375 in holes reads 1.625 in between the inside edges of two neighbors. C is 1.625 + 0.375 = 2.000 in, and the BCD is 2.000 ÷ 0.5 = 4.000 in.

A second example: a 5-lug hub reads 2.645 in center to center between neighboring studs. Divide by 0.587785 and the BCD is 4.4999 in, which is the 5 × 4.5 in (5 × 114.3 mm) pattern.

Measure the Farthest Pair When You Can

Which two holes you measure changes how much a caliper error moves the answer. The error in the BCD equals the reading error divided by the chord factor, so a short chord multiplies your mistake.

Each row assumes a 0.001 in caliper error. On a 24-hole flange, measuring neighbors makes that error nearly eight times worse, so measure straight across whenever a hub or axle is not in the way.

On a 5-hole pattern there is no hole straight across. The farthest pair is two steps apart, with a chord factor of sin 72° = 0.951057, so a 4.5 in circle reads 4.2798 in between those centers, not 4.5 in.

Bolt Pattern Calculator for Wheels and Hubs

A wheel bolt pattern is a bolt circle written as lug count × BCD, such as 5 × 114.3 mm or 6 × 139.7 mm. The same chord math applies, so any bolt circle calculator doubles as a bolt pattern calculator once you know the lug count.

Even-count patterns (4, 6, 8 lugs) can be measured center to center straight across. Five-lug patterns cannot, so measure two neighbors and use the 0.587785 factor, or measure the farthest pair and use 0.951057.

Matching the bolt pattern alone does not make a wheel fit. Center bore, offset, stud thread and lug seat type must also match the vehicle, and a 5 × 4.5 in wheel will not seat on a hub with a larger center pilot.

ASME B16.5 Flange Bolt Circle Chart

Standard pipe flanges use fixed bolt circles, hole counts and hole sizes set by ASME B16.5. Bolt counts are always a multiple of four, and the holes straddle both centerlines, so hole 1 sits half a step off the X axis.

Any bolt circle calculator needs the right BCD and hole count first, and for flanges those come from the standard. The figures below match the Class 150 and Class 300 bolting tables in the Ferguson Industrial ASME B16.5 flange data sheet, which prints them rounded to two decimals. Bolt diameter is the hole size minus 1/8 in, and the spacing columns are computed from the chord formula.

Class 150 Flange Bolt Circles

Class 150 is the lightest standard pressure class and the most common pattern on water, air and low-pressure process lines.

Class 300 Flange Bolt Circles

Class 300 flanges are thicker and use a larger, non-interchangeable bolt circle for the same pipe size, so a Class 150 flange cannot bolt to a Class 300 flange.

The same data sheet lists a drilling tolerance of ±0.06 in on the bolt circle and ±0.03 in center to center between adjacent holes. Check the adjacent spacing against the column above after drilling; a reading outside ±0.03 in means the pattern will fight the mating flange.

A rotated flange, such as a valve flange that must clock its handle, keeps the same BCD but shifts hole 1 by the rotation. Drill the mating flange with the identical rotation, or the bolts will not line up.

Bolt Circle Calculator Output for CNC G-Code

To drill a bolt circle on a CNC mill, list every hole as an absolute X/Y position and drill each one with a canned cycle. G81 is the plain drilling cycle: rapid to the hole, feed to depth Z, rapid back out.

Here is bolt circle calculator output for a 6-hole pattern on a 4.000 in BCD, hole 1 at 30°, drilled 0.500 in deep with the part zero at the circle center:

(6 HOLES ON 4.0000 IN BOLT CIRCLE)
G20 G17 G90 G80
G0 X1.7321 Y1.0000
G98 G81 X1.7321 Y1.0000 Z-0.5000 R0.1000 F6.0
X0.0000 Y2.0000
X-1.7321 Y1.0000
X-1.7321 Y-1.0000
X0.0000 Y-2.0000
X1.7321 Y-1.0000
G80

R is the retract plane the drill rapids down to before feeding, and Z is the hole bottom. Under G98 the drill returns to its starting height between holes; under G99 it returns only to R, which saves time when nothing sticks up between holes. The LinuxCNC G-code reference spells out both retract modes and the full G81 sequence.

Once G81 is active, each later line with a new X and Y drills another hole at the same Z and R. G80 cancels the cycle so the next move does not drill. For holes deeper than about three drill diameters, a common shop rule, G83 peck drilling clears chips between pecks.

Fanuc, Haas and LinuxCNC read this format as written. Siemens, Heidenhain, Mazak and Okuma conversational controls use their own cycle syntax, so keep the X/Y list and rewrite only the cycle lines. Set the feed with the Spindle Speed Calculator before running it.

Bolt Circle Calculator in Excel

A bolt circle calculator in Excel works the same way. With X₀ in B1, Y₀ in B2, BCD in B3, N in B4, start angle in B5 and hole numbers 1 to N down column A from row 8, enter these in B8 and C8 and fill down:

=$B$1+($B$3/2)*COS(RADIANS($B$5+(A8-1)*360/$B$4))
=$B$2+($B$3/2)*SIN(RADIANS($B$5+(A8-1)*360/$B$4))

Excel's COS and SIN expect radians, which is why RADIANS wraps the angle. Leaving it out is the most common reason a homemade sheet gives nonsense coordinates.

Holes on a Partial Arc

When holes span only part of a circle, the step is the arc span divided by one less than the hole count. Five holes from 0° to 120° need four gaps, so each step is 30°, not 24°.

$$\Delta \theta =\frac{\text{span}}{N-1}$$

On an 8 in BCD, that 30° step puts neighbors 2.0706 in apart center to center and 2.0944 in apart along the arc. The holes land at X 4.0000 Y 0.0000, X 3.4641 Y 2.0000, X 2.0000 Y 3.4641, X 0.0000 Y 4.0000 and X -2.0000 Y 3.4641.

Partial arcs show up on semicircular brackets, segmented flanges, clamp rings and index plates. Using 360° ÷ N by mistake leaves the last hole short of the arc end, so pick a bolt circle calculator that takes the arc span directly.

How Many Holes Fit on a Bolt Circle

Holes start to touch when the adjacent spacing shrinks to one hole diameter. Setting S equal to d and solving gives the most holes of that size a circle can carry.

$$N_{max}=\lfloor \frac{\pi }{\arcsin (d/BCD)}\rfloor$$

Half-inch holes fit 37 times on a 6 in BCD and 25 times on a 4 in BCD before their edges meet. Real parts need a wall between holes for strength, so stay well under that limit; the edge gap a bolt circle calculator reports shows how much wall is left.

The same check runs the other way. For a set hole count and size, the BCD must exceed d ÷ sin(180° ÷ N); for 12 holes of 0.5 in, that is 1.932 in.

Laying Out a Bolt Circle on a Manual Mill

On a mill with a DRO, bolt circle calculator coordinates go straight to the readout. Zero both axes at the circle center, then move to each X/Y position in turn. Absolute positions avoid stacking errors, because each hole is measured from the same zero rather than from the last hole.

Incremental moves (ΔX, ΔY from the previous hole) suit a mill with only dials, which is why a machinist bolt circle calculator lists both. Rounding on each move adds up around the circle, so check the last hole against its absolute position before drilling it.

Spot every hole with a center drill first, then measure the spacing between spots with calipers. Fixing a spot is cheap; fixing a drilled hole is not. For hole location callouts with GD&T, the True Position Calculator compares measured hole centers to these theoretical positions.

With a rotary table or dividing head, skip X/Y entirely. Center the part, then index 360° ÷ N between holes; on a standard 40:1 dividing head, that is 40 ÷ N crank turns per hole, or 5 turns for 8 holes.

Bolt Size, PCD and Bolt Circle Basics

Hole positions are only half the job. The bolts still need the right size, thread, area and joint, and the same terms (PCD, BCD, bolt pattern) mean different things to different shops.

What is a bolt circle calculator?

A bolt circle calculator finds where each hole goes on a circular pattern from the BCD, hole count and start angle. It returns X/Y positions, the spacing between neighboring holes, and often the reverse: the BCD from a measured spacing.

What is a bolt circle diameter (BCD)?

The BCD is the diameter of the imaginary circle running through the center of every hole in the pattern. It is never measured to hole edges, and it is smaller than the flange or plate outside diameter.

Is PCD the same as BCD?

Yes, PCD (pitch circle diameter) and BCD name the same dimension. PCD is common on metric drawings and wheel specs, while BCD and "bolt circle" are the usual US shop terms. A bolt circle calculator in mm mode gives the same geometry in metric units.

How do you calculate a bolt circle in CNC?

Set the part zero at the circle center, compute each hole with X = R cos θ and Y = R sin θ, then drill them with a G81 or G83 canned cycle in absolute mode (G90). A bolt circle calculator online or as a phone app speeds up the list. Many controls also offer a built-in bolt hole circle cycle, but the explicit X/Y list runs on any machine.

How do I determine the BCD of an existing bolt pattern?

On an even hole count, measure center to center between two holes straight across; that reading is the BCD. On an odd count, measure two neighbors and divide by sin(180° ÷ N), such as 0.587785 for 5 holes or 0.866025 for 3 holes.

How do I calculate bolt area?

Bolt area for strength is the tensile stress area, not the shank area. For a 1/2-13 UNC bolt it is 0.1419 in², and for an M12 × 1.75 bolt it is about 84.3 mm². The Bolt Area Calculator finds it for any size and pitch.

How do you calculate the diameter of a bolt?

Measure across the thread crests with calipers to get the major diameter, then read the pitch with a thread gauge. A reading of 0.495 in with 13 threads per inch is a 1/2-13 bolt. The Thread Calculator and Pitch Diameter Calculator cover the rest of the thread geometry.

How do I size a bolt for a bolt circle?

Size the bolt for the load first, then fit the circle around it. Bolt holes are usually drilled a set clearance over the bolt, such as 1/8 in over on B16.5 flanges; the Clearance Hole Calculator gives close and free fits. Clamp force comes from the Bolt Preload Calculator and tightening torque from the Bolt Torque Calculator.

What size is a 12 mm bolt in inches?

A 12 mm bolt is 0.472 in across, just under 1/2 in (0.500 in). The two are not interchangeable: M12 coarse thread is 1.75 mm pitch, while 1/2-13 UNC has a 1.954 mm pitch, so an M12 nut will not run onto a 1/2-13 bolt.

How do you calculate circle diameter from circumference?

Divide the circumference by π, the same step a bolt circle calculator runs in reverse. A bolt circle with a 14.137 in circumference has a 4.5 in diameter, and a 6 in BCD has an 18.850 in circumference.

Can a bolt circle calculator handle rectangular bolt patterns?

No, rectangular and grid patterns need no trigonometry. Each hole is the corner offset plus whole multiples of the row and column spacing. A square 4-hole pattern does sit on a circle, though, with a BCD equal to the side length times 1.414.

How do I join two pieces of material?

Bolts give a joint you can take apart, rivets give a permanent mechanical joint, and welds fuse the parts. For riveted joints, the Solid Rivet Length Calculator sizes the rivet; for welded ones, the Welding Calculator estimates weld size and filler. Bolt length through the stack comes from the Bolt Length Calculator.