= | circumference | |

= | the constant pi | |

= | the radius of the circle |

Table of Contents

## What is the circumference?

The circumference of a circle is defined as **the linear distance around it**. In other words, if a circle is opened to form a straight line, then the length of that line will be the circle’s circumference.

In geometry, the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure. Wikipedia

## How do you find a circumference?

To calculate the circumference, you need the radius of the circle: Multiply the radius by 2 to get the diameter. Multiply the result by π, or 3.14 for an estimation. That’s it; you found the circumference of the circle.

## What are circumference and pi?

Circles are all similar, and “the circumference divided by the diameter” produces the same value regardless of their radius. This value is **the ratio of the circumference of a circle to its diameter** and is called π (Pi).

### Is the circumference 2 pi r?

The perimeter or circumference of the circle can be found using the equation **C=2π(r)**, where r= the radius of the circle.

### What are circumference and diameter?

**The circumference is the length of one complete ‘lap’ around a circle, and the diameter is the length of the line segment that cuts a circle in half**. Think of circumference as an outer measurement and diameter as an inner measurement of the circle!

## What is the formula for the area of circumference?

What are the 3 circle formulas?

**What are all Circle Formulas?**

- The diameter of a Circle D = 2 × r.
- Circumference of a Circle C = 2 × π × r.
- Area of a Circle A = π × r
^{2}

### Formulas Related to Circles

Diameter of a Circle | D = 2 × r |
---|---|

Circumference of a Circle | C = 2 × π × r |

Area of a Circle | A = π × r^{2} |

#### What value is pi?

3.141592653589793238

In decimal form, the value of pi is **approximately 3.14**. But pi is an irrational number, meaning that its decimal form neither ends (like 1/4 = 0.25) nor becomes repetitive (like 1/6 = 0.166666…). (To only 18 decimal places, pi is 3.141592653589793238.)

#### What is the pi formula?

By definition, pi is the ratio of the circumference of a circle to its diameter. In other words, pi equals the circumference divided by the diameter (**π = c/d**).

#### Is the diameter half of the circumference?

Explanation: The circumference of a circle is equal to π⋅d where d is the diameter of the circle. π=3.14159… which is =~3 , so **the circumference is about 3 times the diameter**.

## Is the diameter bigger than the circumference?

**The diameter is ALWAYS approximately 3 times smaller than the circumference**! Or to put it another way, the circumference is approximately 3 times bigger than the diameter. Look at the table below and see if you can spot the pattern.

## What are the 5 properties of a circle?

**Circle Properties**

- The circles are said to be congruent if they have equal radii.
- The diameter of a circle is the longest chord of a circle.
- Equal chords of a circle subtend equal angles at the centre.
- The radius drawn perpendicular to the chord bisects the chord.
- Circles having different radius are similar.

# Circumference of Circle

The **circumference of a circle** is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant π and the diameter of the circle. A person walking across a circular park, or a circular table to be bordered requires this metric of the circumference of a circle. The circumference is a linear value and its units are the same as the units of length.

A circle** **is a **round closed figure** where all its boundary points are equidistant from a fixed point called the center. The two important metrics of a circle is the area of a circle and the circumference of a circle. Here we shall aim at understanding the formula and calculation of the circumference of a circle.

## What is the Circumference of a Circle?

The **circumference** of a circle is its boundary or the length of the complete arc of a circle. Let us understand this concept using an example. Consider a circular park shown below.

If a boy starts running from point ‘A’ and reaches the same point after taking one complete round of the park, a distance is covered by him. This **distance** or **boundary** is called the **circumference** of the park which is in the shape of a circle. The circumference is the length of the boundary.

### Circumference of a Circle Definition

The circumference of a circle refers to the measure of its boundary. If we open a circle and measure the boundary just like we measure a straight line, we get the circumference of the circle in terms of units of length like centimeters, meters, or kilometers.

Now let us learn about the elements that make up circumference. These are the three most important elements of a circle.

**Center:**The center of the circle is a point that is at a fixed distance from any other point from the circumference.**Diameter:**The diameter is the distance across the circle through the center, it is a line that meets the circumference at both ends and it needs to pass through the center.**Radius:**The radius of a circle is the distance from the center of a circle to any point on the circumference of the circle.

## Circumference of Circle Formula

The formula for the circumference of a circle is expressed using the radius ‘r’ of the circle and the value of ‘pi’. It is expressed as, Circumference of a circle formula = 2πr. While using this circumference formula, if we do not have the value of the radius, we can find it using the diameter. That is, if the diameter is known, it can be divided by 2 to obtain the value of the radius because of the diameter of a circle = 2 × radius. Another way to calculate the circumference of a circle is by using the formula: Circumference = π × Diameter. If we need to calculate the radius or diameter, when the circumference of a circle is given, we use the formula: Radius = Circumference/2π

## How to Find the Circumference of Circle?

Although the circumference of a circle is the length of its boundary, it cannot be calculated with the help of a ruler (scale) like it is usually done for other polygons. This is because a circle is a curved figure. Therefore, to calculate the circumference of a circle, we apply a formula that uses the **radius** or the **diameter** of the circle and the **value of Pi **(π).

Pi is a special mathematical constant with a value approximated to 3.14159 or π = 22/7. The value of π = 22/7 is used in various formulas. It is the ratio of circumference to diameter, where C = πD. Let us consider a practical illustration to understand how to calculate the circumference of a circle with the help of the circumference formula.

**Example:** If the radius of the circle is 25 units, find the circumference of the circle. (Take π = 3.14)

**Solution:** Given, radius = 25 units

Let us write the circumference formula and then we will substitute the value of r (radius) in it.

Circumference of circle formula = 2πr

C = 2 × π × 25

C = 2 × 3.14 × 25 = 157 units

Therefore, the circumference of a circle is 157 units.

## Circumference to Diameter

The circumference to diameter of a circle is a ratio used to define the standard definition of Pi (π). If you know the diameter ‘d’ of a circle, then you can easily find the circumference C using the relation: C = πd. So, when the circumference C is placed in a ratio with the diameter d, the answer we get is π.

**Important Notes on Circumference of a Circle**

- π(Pi) is a mathematical constant that is the ratio of the circumference of a circle to its diameter. It is approximated to π = 22/7 or 3.14
- If the radius of a circle is extended further and touches the boundary of the circle, it becomes the diameter of a circle. Therefore, Diameter = 2 × Radius
- The circumference is the distance around a circle or the length of a circle.
- We can find the circumference of a circle using the radius or diameter.
- Circumference formula = π× Diameter; Circumference = 2πr.