Subtract a fully contained unshaded rectangle, circle, triangle, or ellipse from an outer shape. Use one consistent length unit; the result is in square units. Dimensions alone do not verify placement.

Use one consistent length unit for every dimension. The unshaded shape must lie entirely inside the outer shape; dimensions alone do not verify its placement. Areas are reported in square units.

Shaded Area Formula

In general, shaded area equals outer area minus unshaded area. The formula below is the special case of a circle inscribed in a square.

SA = Lยฒ - pi ร— (L / 2)ยฒ
  • Where SA is the area inside the square and outside its inscribed circle
  • L is the square side length and the inscribed circle diameter; the circle radius is L/2.

For this special case, select Rectangle for the outer shape, enter L for both dimensions, select Circle for the unshaded shape, and enter radius L/2. The calculator also supports other shape pairs when the unshaded shape is fully contained.

How to Calculate Shaded Area?

The following example problems outline how to calculate Shaded Area.

Example Problem #1:

  1. First, determine the side length of the square and the diameter of its inscribed circle.
    • The square side and circle diameter are 25 length units, so the circle radius is 12.5 units.
  2. Finally, calculate the Shaded Area using the equation above: 

SA = L^2 – pi*(L/2)^2

The values provided above are inserted into the equation below and computed.

SA = 25^2 – pi*(25/2)^2 โ‰ˆ 134.1261 square units (134.13 to two decimal places)

Example Problem #2: 

For this problem, the variables required are provided below:

Square side and inscribed circle diameter = 30 length units

Circle radius = 15 length units

Test your knowledge using the equation and check your answer with the calculator.

SA = 30^2 – pi*(30/2)^2 โ‰ˆ 193.1417 square units