Bolt Hole Circle Calculator that gives X and Y coordinates for every hole, the bolt circle diameter from a measured hole spacing, G81 drill code and the matching wheel lug pattern.
Start Angle and Position
CNC software and most CAD put 0° at 3 o’clock and count counterclockwise. Some drafting systems start at 12 o’clock.
Hole Size
Used to check the metal left between holes and the smallest part the pattern fits on.
All Hole Coordinates
| Hole | Angle | X | Y | Move X | Move Y |
|---|---|---|---|---|---|
| 1 | 0° | 57.150 | 0.000 | 57.150 | 0.000 |
| 2 | 72° | 17.660 | 54.353 | -39.490 | 54.353 |
| 3 | 144° | -46.235 | 33.592 | -63.896 | -20.761 |
| 4 | 216° | -46.235 | -33.592 | 0.000 | -67.184 |
| 5 | 288° | 17.660 | -54.353 | 63.896 | -20.761 |
G-Code Drilling Block
G21 G90 G54 (SET Z DEPTH, R PLANE AND FEED FOR YOUR TOOL BEFORE RUNNING) G81 X57.150 Y0.000 Z-6.0 R2.5 F120 X17.660 Y54.353 X-46.235 Y33.592 X-46.235 Y-33.592 X17.660 Y-54.353 G80
Pattern Drawing
Bolt Hole Circle Calculator for Hubs and Flanges
The Bolt Hole Circle Calculator lays out evenly spaced holes on a circle and gives the X and Y position of each one. It also works in reverse, turning a caliper reading between two holes into the bolt circle diameter. Machinists use it to program flanges and adapter plates, and car owners use it to confirm a wheel or hub lug pattern. Every result updates as you type, and the Units menu switches between millimeters and inches at 25.4 mm per inch.
In coordinate mode you enter the number of holes and the bolt circle diameter, also called BCD or PCD. The Start Angle and Position panel sets where hole 1 sits, where the circle center lies, and whether the holes cover a full circle or only an arc.
The optional hole or stud diameter adds a wall check between holes. Results include hole-to-hole spacing, a full coordinate table, a G81 drilling block and a scaled drawing of the pattern.
How Each Hole Position Is Calculated
Every hole sits one radius from the center, at an angle that grows by the same step each time. On a full circle the step is 360° divided by the hole count, so a 5-hole pattern steps 72°. On a partial arc the span is divided by one less than the hole count, because the first and last holes sit at the two ends. The coordinates then follow from basic trigonometry.
$$X_i = X_c + \frac{D}{2}\cos\big(A + (i-1)\,\theta\big)$$
$$Y_i = Y_c + \frac{D}{2}\sin\big(A + (i-1)\,\theta\big)$$
Here D is the bolt circle diameter, A is the start angle, θ is the step, and Xc and Yc locate the circle center. These formulas assume the math convention of 0° at 3 o’clock with angles counting counterclockwise, which most CNC and CAD software uses.
Picking 12 o’clock and clockwise swaps sine and cosine, which suits drawings dimensioned from the top of the part. A 5-hole pattern on a 114.3 mm circle with a 0° start puts hole 1 at X 57.150, Y 0.000 and hole 2 at X 17.660, Y 54.353.
Hole Spacing, Wall Thickness and Part Size
The straight line between two neighboring hole centers is a chord of the bolt circle. Machinery’s Handbook tabulates these as chord lengths for spacing off a circle, and Metal Arts Press’s Machine Shop Know How uses that table to lay out a 7-hole pattern by hand. The same chord is the fastest caliper check of a finished pattern.
$$C = D \times \sin\left(\frac{180^\circ}{n}\right)$$
For 5 holes on 114.3 mm, neighboring holes sit 67.184 mm apart and holes with one between them sit 108.706 mm apart. The arc length along the circle is longer at 71.817 mm, which matters only when marking around a curved surface.
Subtracting the hole diameter from the chord gives the metal left between holes, 53.684 mm with 13.5 mm holes. The circle plus one hole diameter is the smallest part the pattern fits on, and the circle minus one hole diameter is the largest center bore that stays clear of the holes.
Finding the Bolt Circle From a Measured Part
Switch the mode to Find the Circle Size when you have a part but no drawing. Measure center to center between two holes, pick how those holes relate, and enter the hole count. A thread on The Hobby-Machinist works through the general form, where m is the number of holes skipped between the two you measured.
$$D = \frac{a}{\sin\left(\frac{(m+1)\,180^\circ}{n}\right)}$$
Neighboring holes use m = 0, skipping one hole uses m = 1, and holes straight across an even pattern give the diameter directly. A common mistake is measuring edge to edge instead of center to center.
On a caliper, measure inside edge to outside edge of the two holes, which lands on the same center-to-center value without guessing where each center is. The calculator checks whether the chosen method makes sense for the hole count, since a skip needs at least 4 holes on a full circle and an across-center reading needs an even count.
Measuring a 5-Lug Wheel With a Tape
Discount Tire’s bolt pattern guide describes the usual shortcut of measuring from the back of one hole to the center of the third, and calls it an estimate. The geometry shows why. Holes with one between them sit 0.951 times the circle diameter apart, so the shortcut only reads true when the hole radius makes up the missing 4.9 percent. On a 5×114.3 hub with 13.5 mm holes it reads about 115.5 mm, roughly 1.2 mm high.
That is close enough to separate 5×114.3 from 5×120.65, which are more than 6 mm apart. It cannot separate 5×120 from 5×4.75, which is 120.65 mm. Those two differ by 0.65 mm on the circle and about 0.6 mm on the skip-one chord, and owners on the ThirdGen forum still debate whether one fits the other. For close pairs like that, enter a caliper reading in the Bolt Hole Circle Calculator rather than trusting a tape.
Caliper Check Values for Common Lug Patterns
The table below applies the chord formula to common wheel patterns. On a 4-lug pattern the holes with one between them sit straight across, so that column equals the circle diameter. The inch names come from dividing by 25.4, and the pattern card in the calculator shows the same conversion. A wheel also needs the right center bore, stud thread and seat type, so a matching circle is only the first check.
| Pattern | Inch name | Neighboring holes | One hole between |
|---|---|---|---|
| 4×100 | 4×3.94 in | 70.71 mm | 100.00 mm |
| 4×114.3 | 4×4.5 in | 80.82 mm | 114.30 mm |
| 5×100 | 5×3.94 in | 58.78 mm | 95.11 mm |
| 5×108 | 5×4.25 in | 63.48 mm | 102.71 mm |
| 5×112 | 5×4.41 in | 65.83 mm | 106.52 mm |
| 5×114.3 | 5×4.5 in | 67.18 mm | 108.71 mm |
| 5×120 | 5×4.72 in | 70.53 mm | 114.13 mm |
| 5×120.65 | 5×4.75 in | 70.92 mm | 114.74 mm |
| 5×127 | 5×5 in | 74.65 mm | 120.78 mm |
| 5×139.7 | 5×5.5 in | 82.11 mm | 132.86 mm |
| 6×139.7 | 6×5.5 in | 69.85 mm | 120.98 mm |
| 8×165.1 | 8×6.5 in | 63.18 mm | 116.74 mm |
G-Code From the Bolt Hole Circle Calculator
The drilling block uses G21 for millimeters or G20 for inches, then a G81 drill cycle at hole 1 followed by the remaining X and Y positions. G80 at the end cancels the cycle. The Z depth, R plane and feed are placeholders, so set them for your tool and material before running, as the Haas G81 reference explains for each word. The coordinate table also lists move-to-next values for anyone working from a DRO instead of a program.
The Bolt Hole Circle Calculator accepts 2 to 360 holes as whole numbers, a start angle from −360° to 360°, and an arc span above 0° up to 360°. A hole diameter of zero skips the wall check. When neighboring holes overlap, the alert says so, and when the wall between them drops below half a hole diameter it warns of a thin wall that can tear out under load. That half-diameter line is the calculator’s own caution level rather than a published standard, so follow your joint design where one applies.
Setup Errors That Shift Every Hole
Entering the radius where the diameter belongs puts every hole twice as far from center, and a 57.15 mm entry for a 114.3 mm circle is the usual form of it. On even patterns, choosing Skipping One Hole after measuring straight across makes the circle too large, by about 15 percent on 6 holes and 41 percent on 8. A drawing dimensioned from 12 o’clock but entered with the 3 o’clock convention rotates the whole pattern. Check hole 1 against the print before drilling.
Bolt Pattern and Bolt Circle Questions
Is bolt circle diameter the same as PCD?
Yes, BCD and PCD name the same dimension, the diameter of the circle through the hole centers. Wheel specs usually write it after the lug count, so 5×114.3 means five holes on a 114.3 mm circle. Piping and machine drawings more often say PCD or bolt circle. The Bolt Hole Circle Calculator labels the field with both names for that reason.
How do you measure a 5-lug bolt pattern accurately?
Measure center to center between two neighboring studs with calipers, then enter it with Between Neighboring Holes selected. Five holes means the result is that reading divided by 0.5878. A reading of 67.18 mm returns 114.3 mm, which is 5×4.5 in. Measuring the front and rear hubs as well confirms both ends of the car share the pattern.
Can you lay out a bolt circle without a CNC or DRO?
Yes, by scribing the circle and stepping off the chord length with dividers. Set the dividers to the neighboring-hole spacing, walk them around, and the last step should land back on the first mark. Any gap shows the setting is slightly off, and you adjust and repeat. For a 6-hole pattern this is easiest, because the chord equals the radius.
Does a matching bolt pattern mean the wheel fits?
No, the bolt pattern only confirms the wheel will line up with the studs. The center bore, stud thread, lug seat type and offset all have to suit the vehicle too. Offset decides whether the wheel clears the strut and fender, which you can check with the Wheel Offset Calculator. Brake caliper clearance behind the spokes needs its own check on the actual wheel.