Bolt Circle Calculator

A bolt circle, also known as a pitch circle, is a concentric circle upon which a series of bolt holes or other features are centered. To find the exact Cartesian coordinates (X, Y) of each hole, the calculator uses fundamental trigonometric functions based on polar coordinates. Given a radius (R), a total number of holes (N), and an initial angular offset (A), the angle for any specific hole index (i) is calculated using the formula: θ_i = A + (i * 360° / N). Once the angle is established, the X and Y coordinates relative to the center origin (Offset X, Offset Y) are found using X = Offset_X + R * cos(θ_i) and Y = Offset_Y + R * sin(θ_i).

Imagine you are designing a custom pipe flange and need to layout 4 mounting holes on a 5-inch radius. You want the first hole to start at a 0-degree angle with a center offset of X = 2.0 inches and Y = 3.0 inches. First, determine the angular spacing between each of the 4 holes: 360° / 4 = 90°. For the first hole (i = 0), the angle is 0°. The X coordinate is 2.0 + 5.0 * cos(0°) = 7.0 inches, and the Y coordinate is 3.0 + 5.0 * sin(0°) = 3.0 inches. For the second hole (i = 1) at 90°, X is 2.0 + 5.0 * cos(90°) = 2.0 inches, and Y is 3.0 + 5.0 * sin(90°) = 8.0 inches. Repeating this process for all indices yields the complete coordinate set for fabrication.

Always double-check your starting angle reference. In standard cartesian planes, 0 degrees points directly along the positive X-axis, but your specific mechanical drawing might reference the vertical Y-axis as zero. When preparing values for CNC programming, ensure your center offsets (Offset X and Offset Y) match your part's designated work coordinate system (WCS) origin, such as G54. Finally, always dry-fit or simulate your coordinate outputs before committing expensive material to the mill or plasma cutter.