6 holes on a 100 mm pitch circle. Hole 1 at X 50.000, Y 0.000 mm; angular pitch 60.000°.
- Radius (PCD ÷ 2)
- 50.000 mm
- Angular pitch (360° ÷ n)
- 60.000 degrees
- Chord between neighboring holes
- 50.000 mm
| Hole | Angle (°) | X | Y |
|---|---|---|---|
| 1 | 0.000 | 50.000 | 0.000 |
| 2 | 60.000 | 25.000 | 43.301 |
| 3 | 120.000 | −25.000 | 43.301 |
| 4 | 180.000 | −50.000 | 0.000 |
| 5 | 240.000 | −25.000 | −43.301 |
| 6 | 300.000 | 25.000 | −43.301 |
Coordinates away from the 90° marks and the 30° half-value angles come from irrational sines and cosines (such as √2/2 and √3/2), so they are rounded.
Basic positions only: the drawing's position tolerance applies to each hole.
What it computes
A drawing usually dimensions a bolt circle by its pitch circle diameter (PCD), the number of holes and an angle, for example 6X Ø9 EQSP on Ø100. A machining setup, a CMM routine or a CAD sketch needs each hole as an X and Y from a datum. The calculator turns the first form into the second, and does the same for a rectangular grid dimensioned by its pitches.
For a bolt circle it also gives the radius, the angular pitch between neighboring holes and the chord: the straight distance from one hole center to the next. The chord is the figure to check with calipers across two holes, or to compare with a clearance between fastener heads.
Formulas
- Radius r = PCD / 2.
- Angular pitch = 360° / n for n equally spaced holes.
- Angle of hole i: θᵢ = θ₁ + (i − 1) × 360° / n counterclockwise, or θ₁ − (i − 1) × 360° / n clockwise.
- Hole i: x = x꜀ + r cos θᵢ and y = y꜀ + r sin θᵢ, with the angle measured from the +X axis, counterclockwise positive.
- Chord between neighboring holes = PCD × sin(180° / n).
- Grid hole in column c and row r: x = x₁ + (c − 1) × pitch X and y = y₁ + (r − 1) × pitch Y.
Conventions
Angles follow plane geometry: zero along +X (three o'clock) and positive counterclockwise. Drawings do not always agree. Some put the first hole at twelve o'clock, some number clockwise, and some place the holes straddling a centerline, so the first hole sits half a pitch off the axis. Enter the start angle and direction the drawing shows. The table numbers the holes in that order.
Grid holes are listed row by row from the first hole, which is the one at the given origin. A single row or column needs no pitch in that direction, so a pitch of zero is accepted there. Between two holes the pitch must be greater than zero.
Exact values and rounded ones
Grid coordinates are sums of the values you typed, so they are exact decimals. A bolt circle needs sines and cosines. The calculator keeps each angle as an exact number of degrees, so a hole at 90° or 180° lands on the axis with a coordinate of exactly zero, and not the 6.1e-17 that plain floating point gives for cos 90°. Coordinates that use 0, ±1/2 or ±1 as their sine or cosine are exact. All other coordinates, such as those at 45° or 60° off the axis, are irrational. They are shown rounded to the decimals you choose, with the full double-precision value marked ≈.
Worked example
01 Read the callout
Six holes, equally spaced on a 100 mm pitch circle, centered on the origin, the first on the +X axis.
02 Work out the spacing
Radius 50 mm. Angular pitch 360° / 6 = 60°. Chord 100 × sin 30° = 50.000 mm, exact.
03 Work out the first two holes
Hole 1 at 0°: X 50.000, Y 0.000. Hole 2 at 60°: X 50 cos 60° = 25.000, exact; Y 50 sin 60° ≈ 43.301 mm.
04 Check one by symmetry
Hole 4 is opposite hole 1, at 180°: X −50.000, Y 0.000. Holes 5 and 6 mirror holes 3 and 2 about the X axis.
05 A grid for comparison
Three columns and two rows at a 20 mm X pitch and a 15 mm Y pitch, first hole at (10, 10): the last hole is at (50, 25), and the spans are 40 and 15 mm.
Limitations
- Equally spaced bolt circles and full rectangular grids only. Unequal spacing, partial arcs and staggered grids need their angles or positions entered one pattern at a time.
- Positions only. The figures are the basic, theoretically exact locations. The drawing's position tolerance, and the datums it refers to, still apply to each hole.
- It does not choose the hole size, the fastener or the edge distance.
- One pattern lists at most 360 holes. Values take a decimal point and at most 15 significant digits.
When to involve a qualified engineer
Ask the drawing's owner when the drawing does not say where the first hole is, which way the holes are numbered, or which feature the pattern is located from. Ask, too, when a pattern must line up with a mating part. A hole that is right to the drawing can still miss a mating part toleranced from a different datum.
What the product builds
In the Technical Preview, TruePart builds one hole pattern: a centered rectangular pattern of through holes on a rectangular plate.
Questions
What is the difference between PCD and bolt circle diameter?
None. Pitch circle diameter (PCD) and bolt circle diameter (BCD) name the same circle, the one through the hole centers.
How do I find the distance between two neighboring holes?
Use the chord: PCD × sin(180° / n). Six holes on a 100 mm circle are 50 mm apart, center to center.
Why is a coordinate shown with ≈?
Its sine or cosine is irrational, such as √3/2 at 60°, so no decimal can be exact. The rounded figure is correct to the decimals shown.
Can I enter a pattern that starts at twelve o'clock and runs clockwise?
Yes. Enter a start angle of 90° and choose clockwise. The table then lists the holes in the drawing's order.
Sources
- ASME Y14.5-2018, Dimensioning and Tolerancing · ASMEBasic dimensions, patterns of features and position tolerancing.
- ISO 1101:2017, Geometrical product specifications (GPS), Geometrical tolerancing: Tolerances of form, orientation, location and run-out · ISOTheoretically exact dimensions and the position tolerance that applies to each hole.
What TruePart does today
- TodayIn the Technical Preview, TruePart builds one hole pattern: a centered rectangular pattern of through holes on a rectangular plate.