Square In Circle Calculator

Square in a Circle Calculator

Find the side length and area of a square inscribed in a circle.

Last updated: June 2026 | By Patchworkr Team

Inscribed Square
Result

Enter a real number.

What is the Formula?

For an inscribed square, the diagonal equals the circle diameter, so the side is r sqrt(2).

side = r sqrt(2)
area = 2 r^2

How to Use

1. Enter the circle radius.

2. Read the live side length and area for the inscribed square.

3. Check the area against the enclosing circle if needed.

Worked Example

For radius 5:

side = 5 sqrt(2) ≈ 7.0711

area = 2 * 5^2 = 50

FAQ

Why is the side r sqrt(2)?

Because the diagonal of the square equals the circle diameter and a square diagonal is side times sqrt(2).

Is the area always 2r^2?

Yes, for a square inscribed in a circle of radius r.

Can the radius be decimal?

Yes, as long as it is a positive finite number.

Does the square fit exactly?

Yes. All four vertices lie on the circle.

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