Equivalent does not mean identical cookware. In PanRatio it means only that total ideal base areas are equal or close enough for the chosen dimensions and pan counts.
Measure the inside, not the outer rim
Recipes normally describe the usable baking cavity. An outer lip, handles, rolled edge, or wall thickness does not hold batter, so using the outside dimension overstates area. Measure the inside diameter, side, length, and width at the level that represents the batter footprint.
Pi cancels only between circular areas
For an 8-inch round to a 9-inch round, both areas contain π ÷ 4, so the factor is exactly 9² ÷ 8². For a 9-inch round to an 8-inch square, π remains in the denominator. PanRatio keeps a 50-digit pi value for calculation and marks the displayed result with ≈.
Area equivalence is not capacity equivalence
Two pans with equal base area can have different heights, slopes, corners, centre tubes, or safe fill lines. Area is useful for preserving average depth when those factors are comparable. It cannot prove that all batter fits, that overflow is impossible, or that the finished cake releases the same way.