Square in a Circle Calculator
Use our square in a circle calculator to seamlessly determine fitting dimensions for squares in circles and circles in squares.
The formulas
the square’s diagonal equals the circle’s diameter
The ratio never changes
A square inscribed in a circle always covers 2/π ≈ 63.66% of it, no matter the size — the two areas scale together. Turning it around, the smallest circle that contains a square has π/2 ≈ 157% of the square’s area.
Everything follows from the radius
A circle has one degree of freedom, so any single measurement fixes all the others:
d = 2rC = 2πr = πdA = πr² = πd²/4 = C²/4π
Going backwards, r = C/2π and r = √(A/π). The calculator above accepts whichever you happen to have.
Area grows with the square
Double the radius and the circumference doubles, but the area quadruples. That is why a 16-inch pizza is more than twice the food of a an 11-inch one, and why pipe capacity rises so sharply with bore.