Inputs

Set the geometry

Choose a unit, set the circle, spacing, square, and edge dead zone, then calculate.

Changing unit converts every dimension; calculate to refresh the result.

Spacing input
Edge gap, pitch, and diameter measurement diagram Two equal circles showing pitch measured center to center, edge gap measured between the nearest edges, and diameter measured through a circle center. Pitch p Gap g Diameter d p = d + g
Pitch p is center-to-center. Edge gap g is the clear distance between neighboring circle edges.
d
mm

g
mm

Center pitch = 12 mm.

S
mm

z
mm

Reserved inside all four square edges; 0 means none.

Pitch = diameter + gap. The selected gap applies between circles. Dead zone z is an unusable band inside every square edge. Usable side = S − 2z; circles may touch the usable boundary.

Ready to calculate.

Best standard count —
Winning layout —
Area coverage —
Center pitch —

Packing view

Packing result

Circle packing arrangement No packing result has been calculated.
Select Calculate packing to draw the layout.

Calculate a valid result to enable PNG export.

Layout comparison

Two repeatable patterns

The larger count is reported. Use the layout buttons to inspect or export either pattern.

Layout Rows × circles Vertical pitch (mm) Count
Square grid — — —
Staggered — — —

What “maximum” means here: the result is the larger of an aligned square grid and a staggered triangular grid. Staggered rows use vertical pitch p × √3 / 2. Unrestricted irregular circle packing is outside this calculator’s scope.