Circlemark / the layout method

A coordinate for
every position.

Circlemark divides a full turn into equal angular steps and locates each point on a circle. It is a geometry tool for checking positions, with an explicit angle direction and coordinate datum.

What the circle diameter means

The diameter passes through the centres of the positions you want to mark. It is not the diameter of a hole, a washer, the outside of a plate or the space between adjacent holes. Radius is half of the entered circle diameter.

All length values use the chosen unit, either millimetres or inches. Changing the unit label does not convert existing entries: a diameter entered as 100 becomes 100 of the newly selected unit. Set the unit first, then enter the dimensions you intend.

Angles and numbering

Angles follow a front-view mathematical coordinate system: positive X points right, positive Y points up, and 0° is on the right-hand side of the circle. A 90° position is directly above the centre. The first point uses your start angle.

Angular step = 360° ÷ point count
Point angle = start angle ± (point number − 1) × angular step
X = centre X + radius × cos(angle)
Y = centre Y + radius × sin(angle)

Counterclockwise numbering adds the angular step. Clockwise numbering subtracts it. The angle column is normalised into the range from 0° up to, but not including, 360°, even when your starting angle is negative or greater than a full turn.

Example 1: four positions around a 100 mm circle

Set diameter to 100 mm, point count to 4, start angle to 0° and origin to the circle centre. Counterclockwise numbering gives (50, 0), (0, 50), (−50, 0), (0, −50) in millimetres. The angular step is 90°.

The straight distance between adjacent positions is not a quarter of the circumference. It is the chord: 100 × sin(45°) = approximately 70.710678 mm. The arc length along the circle between them is approximately 78.539816 mm.

Example 2: use a lower-left datum

For the same 100 mm circle, choose the lower-left corner of its bounding square as X 0, Y 0. The centre becomes (50, 50). The four positions are now (100, 50), (50, 100), (0, 50), (50, 0). The geometry has not changed; only its coordinate reference moved.

The bounding square's corner is a mathematical datum. It does not assert that your actual workpiece has that shape, size or material around the points.

Example 3: rotate six positions clockwise

A diameter of 80 mm, six points and start angle 30° gives a 60° angular step. With clockwise numbering, the listed angles are 30°, 330°, 270°, 210°, 150° and 90°. With the centre at (0, 0), the first point is approximately (34.641016, 20) mm. Adjacent chord length is 80 × sin(30°) = 40 mm.

Custom centre coordinates

Choose Custom circle centre coordinates when the circle is located relative to another datum. Enter X and Y for the centre in the selected length unit. Positive and negative coordinates are accepted. Every point receives the same centre translation, so chord lengths and angular spacing stay unchanged.

Spacing, single points and precision

For two or more points, adjacent chord spacing is diameter × sin(π ÷ count). With two points, the chord equals the diameter. With one point, there is no distinct neighbouring position, so chord spacing is shown as not applicable. The one-position angular step is a full 360° turn.

The calculator accepts up to 360 points and six decimal places per entered measurement or angle. Trigonometric calculations use ordinary double-precision arithmetic. Displayed coordinates and CSV values round to six decimal places, and extremely small displayed values become zero. This numerical output is not a machining or measurement tolerance.

CSV, SVG and physical marking

The CSV contains point number, normalised angle and X/Y columns with their units. It excludes a duplicate closing point. The self-contained SVG shows the circle, numbered points for layouts of up to 24 points, and centre crosshairs. All positions remain present when number labels are omitted.

The drawing is a front view with positive Y upward; SVG's downward screen axis is inverted when positions are drawn. It is not a verified full-size drilling template. Printing or importing it may change its scale. Use the coordinate list and verify actual dimensions in the application or marking process you choose.

No fastener dimensions, structural strength, material suitability, edge distances, loads, drilling clearances or required standards are evaluated. Those decisions are separate from locating equal positions on a circle. Create your circle layout →