Math
Instant, private, and free
Square in a Circle Calculator.
Find the side length of the largest square inscribed in a circle.
Set your values
Results update as you type.
Use Cases
Crafting and DIY Projects
When cutting a square from a circular piece of material (like wood, fabric, or paper), this calculator tells you the maximum square side you can cut without wasting material.
Example: If you have a circular tabletop with radius 2 feet, the largest square you can cut is about 2.83 feet per side.
Design and Architecture
Architects and designers often need to fit square elements inside circular structures or layouts. This tool quickly gives the maximum square dimension for a given circular space.
Example: For a circular atrium with radius 5 meters, the largest square floor plan would be about 7.07 meters per side.
Frequently Asked Questions
- How do I find the side of the largest square inside a circle?
- The largest square that fits inside a circle has its diagonal equal to the circle's diameter. If the circle radius is r, the square side is r times the square root of 2. Simply enter the radius in the calculator to get the side length.
- What is the formula for the largest square in a circle?
- The formula is side = radius × √2. This comes from the Pythagorean theorem: the square's diagonal (diameter = 2r) equals side × √2, so side = 2r / √2 = r√2.
- Can I use this calculator for any circle size?
- Yes, as long as you enter a positive radius. The calculator works for any circle, whether it's a small craft project or a large architectural design. Just input the radius in any unit, and the side will be in the same unit.
Tips & Common Mistakes
Tips
- Ensure the radius is positive; a zero or negative radius will not produce a valid square.
- The side length will be in the same unit as the radius you enter (e.g., if radius is in inches, side is in inches).
- For a quick mental estimate, multiply the radius by 1.414 (√2) to get the side length.
- If you need the square's area, square the side length after calculating it.
Common Mistakes to Avoid
- Using the diameter instead of the radius: the formula requires the radius, not the diameter. If you have the diameter, divide it by 2 first.
- Forgetting that the square's diagonal equals the circle's diameter, not the side. Some might mistakenly use the radius as the side.
- Confusing the largest inscribed square with a square that is not centered: the largest square is always centered with its vertices on the circle.
Last updated: August 13, 2026