Square in a Circle Calculator
Largest square side and area in a circle.
What it does
A square hides inside every circle with corners on the rim. The diagonal spans the full diameter, so side follows at diameter over root two. Ten centimeters of circle yields a 7.07 side.
The tool above runs side, area, and round together. Defaults give 7.07 cm side with 50 cm2 inside a 31.4 cm round. An 8 inch circle gives 5.66 inch side with 32 square inches. A 14 cm circle gives 9.9 side with 98 square.
Rotation never matters here. Axis aligned or diamond poses share the same diagonal, so shops cut whichever fits the grain. Area fills two over pi of the circle either way.
This page fits the largest square only. It does not pack rectangles, allow clearance, or add kerf. For inlays, subtract the blade from the side shown.
How to use
- Pick metric (cm) or imperial (in).
- Enter the circle diameter.
- Read square side first.
- Read square area.
- Read circle round for trim.
- Cut square to the side shown.
Formula
- D
- Circle diameter in cm or in.
- side
- Square edge.
- diagonal
- Square corner to corner.
Largest inscribed square with diagonal on the diameter. At zero diameter all outputs are zero. Units stay in one system per calculation.
Worked example
Example: square in 10 cm circle
Defaults: metric 10 cm diameter. Imperial mirror uses inches. Diagonal equals diameter.
- Inputs (metric default): circle diameter 10 cm.
- Side: 10 / root 2 is 7.07 cm side.
- Area: 7.07 squared is 50 cm2.
- Round: pi times 10 is 31.4 cm round.
- An 8 in circle gives 5.66 in side. Tool shows the same.
Reference table
| Circle | Square side | Square area |
|---|---|---|
| 10 cm circle | 7.07 cm side | 50 cm2 |
| 8 in circle | 5.66 in side | 32 in2 |
| 14 cm circle | 9.9 cm side | 98 cm2 |
| 6 in circle | 4.24 in side | 18 in2 |
| 20 cm circle | 14.14 cm side | 200 cm2 |
Limits
- Largest fit only. Clearance excluded.
- Flat shapes. No thickness.
- Exact to floating point.
- No kerf allowance.
Common mistakes
- Using radius as diameter, halving side.
- Reading diagonal as side.
- Mixing cm with inches.
- Cutting to area instead of side.
- Forgetting blade kerf.
Try it yourself
Quick checks. Answers sit tucked under each question.
8 in circle?
Side is 8 / 1.4142 is 5.66 in side with 32 in2 and 25.1 in round.
14 cm circle?
Side is 14 / 1.4142 is 9.9 cm side with 98 cm2 and 44 cm round.
Questions
How is the square side figured?
Diameter / root 2. Here 7.07 cm side.
How is square area figured?
Side squared. Here 50 cm2.
What is the circle round?
Pi times diameter. Here 31.4 cm round.
Do corners touch the circle?
Yes. Corner to corner spans the diameter exactly.
Does rotation matter?
No. This is the largest axis aligned or rotated square; both share the diagonal.
What share fills the circle?
Area halves the circle ratio: square is 2/pi of the circle.