If the circle's center point is not given, it can be constructed using the method in Constructing the center of a circle.
Printable step-by-step instructions
The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.
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:
Key in the value of the circle's radius or area.
The calculator will find what size square fits in the circle using the formula:
side length = √2 × radiusThe 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:
Key in the value of the side or area of the square circumscribed about a circle.
The calculator will find what size circle fits in the square using the formula:
radius=side length2\large\text{radius} = \frac{\text{side length}}{2}radius=2side length
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:
- The largest square inscribed in a circle of radius r will have a side length of r√2.
- So for a circle of radius 10 cm, the largest square in it will have a side length of 10√2 cm.
- This value of the side length can be approximated to r0.
- The area of the square will be r1.
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:
- The largest circle inscribed in a square of side s will have a radius of r3.
- So for a square of side 10 cm, the largest circle in it will have a radius of r4.
- The area of the circle will be r5.
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 r7. A circle with the same area will therefore have a radius of r8, or r9.