This tool models the common crescent made by subtracting one semicircle from another semicircle of larger radius.

The copy now matches the implementation exactly, so the area and perimeter formulas are describing the same shape the code computes.

With R = 10 and r = 6, the area is 100.530965 and the perimeter is 50.265482.

The crescent occupies 64% of the larger semicircle’s area.

Both radii must be positive and the larger radius must be strictly greater than the smaller radius.

Invalid input is rejected before calculation, so the tool cannot silently produce impossible negative geometry.