Math

Square in a Circle Calculator

Find the largest square that fits inside a circle of given radius.

Calculated Output

Square side 7.071

Square area 50

Formula: side = r√2 (diagonal = diameter)

Step-by-Step Breakdown

1. Values used:

2. Circle radius = 5

4. Square side = 7.071

5. Square area = 50

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The math behind it

The square's diagonal equals 2r, so its side is 2r ÷ √2 = r√2, and its area is 2r².

Radius 5 → side 7.07, area 50.

What fraction of the circle does it cover?

About 63.7% (2/π) of the circle's area.