The grid calculation, without the app
Subtract twice the outside margin from each sheet dimension. For each orientation, columns = floor((usable width + gap) ÷ (piece width + gap)); rows use the same calculation for height. Their product is the grid capacity. A gap is counted between pieces, not added beyond the final piece. When rotation is allowed, compare the original and 90° layouts and keep the larger capacity.
An editable example
An 8.5 × 11 inch sheet with a 0.25 inch margin on every outside edge has an 8 × 10.5 inch usable area. Two 4 × 6 inch pieces fit in a uniform grid with no gap. Ten pieces therefore require five sheets; at an example $0.50 per sheet, the sheet purchase is $2.50 before delivery and tax.
What this estimate cannot establish
Mixed orientations or a different cut sequence may fit more pieces. The planner does not optimize those arrangements, calculate folded dimensions, check envelope fit, or infer grain direction. Turn rotation off when a print or grain requirement prevents it. Margin and gap are your allowances; they are not measured cutter precision or a universal blade kerf. The calculator supports up to 1,000,000 grid positions per sheet; dense diagrams show only the first 200 positions.
Changing units converts the displayed dimensions. For a folded card, enter the unfolded cut size. Keep required bleed in the piece dimensions and check whether trim spacing needs an additional gap. Test a layout on scrap before committing good material.