Square in a Circle Calculator

Using this square in a circle calculator, you can find the biggest square in a circle. It also helps you find the largest circle inside a square. Be it geometry 📐, construction 🏗️, or daily life 🚶, we often come across composite shapes such as a square circumscribing a circle 🔵 or a square inscribed in a circle. This calculator helps you find the dimensions 📏 of such shapes when one of the measurements is known!

Have you ever wondered ‘What is the largest circular pizza 🍕 I can fit into this square 🔲 ?’ or ‘What is the largest square piece of cake 🎂 I can fit into this circular plate 🍽️?’ or ‘What is the largest circular indoor pool 🏊 I can fit into this square room?’ Well, wonder no more! Because our square in a circle calculator will help you find the answers to these questions and more!

## How do I use the square in a circle calculator?

Using the square-in-a-circle calculator, you can find any of the following:

• Dimensions of the biggest square in a circle:

• To find this, enter the value of the circle’s radius or area.
• The calculator will display the side length and area of the largest square that can fit inside the circle!
• Dimensions of the largest circle inside a square:

• To find this, enter the value of the square’s side or area.
• The calculator will display the radius and area of the largest circle that can fit inside the square!
• Dimensions of a square with the same area as a circle:

• To find this, enter the value of the circle’s radius or area.
• The calculator will display the side length of the square with the same area as the circle!
• Dimensions of a circle with the same area as a square:

• To find this, enter the value of the square’s side or area.
• The calculator will display the radius of the circle with the same area as the square!

You can thus use this square-in-a-circle calculator in several different ways, depending on your need!

## How do I find the maximal square in a circle?

To know how to find the largest square in a circle using the square inside a circle calculator, do the following:

1. Key in the value of the circle’s radius or area.

2. The calculator will find what size square fits in the circle using the formula:

`side length = √2 × radius`

3. The side length and the area of the square inside the circle will be displayed!

In this manner, you can find the maximal square that you can draw within a given circle.

## How do I find the largest circle in a square?

To know how to find the largest circle in a square using the square inside a circle calculator, do the following:

1. Key in the value of the side or area of the square circumscribed about a circle.

2. The calculator will find what size circle fits in the square using the formula:

3. The radius and the area of the circle inside the square will be displayed!

In this manner, when a square is circumscribing a circle, you can find the radius and area of the circle.

## What is it meant by squaring a circle?

Squaring a circle refers to finding a square with the same area as that of the circle.

For a circle with radius `r`, a square with the same area will have a side length of `r√π`. So, for example, if a given circle has a radius of `10 cm`, then a square with the same area as the circle will have a side length of `10√π cm`.

Alternatively, we can also convert a given square to a round shape by doing the reverse operation.

It’s interesting to note that we can approximate a square to a circle by incrementally increasing the number of sides to get regular polygons such as pentagon, hexagon, heptagon, octagon, etc. until we end up with a circle ⭕.

🙋 Explore the different properties of these regular polygons by checking out our pentagon calculator, our hexagon calculator, and our octagon calculator.

## FAQ

### How do I convert a square to a circle?

Converting a square to a circle refers to finding a circle with the same area as the square. So if we want to convert a square to a round figure, the radius of the resulting circle will be `s/√π`, where `s` is the side of the square.

What is the largest square possible in a circle with radius 10 cm?

If we have a circle of radius `10 cm`, then we can do the following to find the largest square inscribed in the circle:

1. The largest square inscribed in a circle of radius r will have a side length of `r√2`.
2. So for a circle of radius 10 cm, the largest square in it will have a side length of `10√2 cm`.
3. This value of the side length can be approximated to `14.1421 cm`.
4. The area of the square will be `200 cm²`.

What is the largest circle possible in a square with side 10 cm?

If we have a square circumscribed about a circle with side `10 cm`, then we can find the largest circle inscribed in the square as follows:

1. The largest circle inscribed in a square of side s will have a radius of `s/2`.
2. So for a square of side 10 cm, the largest circle in it will have a radius of `5 cm`.
3. The area of the circle will be `78.54 cm²`.

What is the radius of a circle with the same area as a 10 cm sided square?

If we have a square of side `10 cm`, its area will be `100 cm²`. A circle with the same area will therefore have a radius of `10/√π`, or `5.64 cm`.

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