Square in a Circle Calculator

Square in a Circle Geometry

A square in a circle (or circle in a square) appears in construction, design, and everyday planning. This calculator finds the largest square that fits inside a circle, the largest circle inside a square, and equal-area conversions between the two shapes.

See also: Square Area Calculator, Circle Equation Calculator, and Area Calculator.

Key Formulas

Largest square inside a circle: $s = r\sqrt{2}$

Largest circle inside a square: $r = s / 2$

Square with same area as a circle: $s = r\sqrt{\pi}$

Circle with same area as a square: $r = s / \sqrt{\pi}$

Worked Example

For a circle with radius 10 cm, the largest inscribed square has side $10\sqrt{2} \approx 14.14$ cm and area 200 cm².