## What Is the Circumference to Diameter Calculator?

The circumference to diameter calculator is used to find the value of the diameter of a circle for a given value of circumference. To use the calculator, simply enter the measurement of the circumference and click on “**Calculate**” to get the result.

What is the circumference of a circle? **Circumference is the total length of the boundary of the circle**. The formula for finding the circumference of the circle is

$C = 2\pi r$ where r is the radius of the circle.

**Diameter is**** ****a line segment through the center of a circle with its ends on the circle’s circumference**. In the circle given below, AB is the diameter. Diameter is twice the radius.

$d = 2r$ where r stands for radius of the circle.

Thus, we can write $C = \pi d$

where, C is the circumference and d is the diameter.

To find the diameter, we can rewrite this equation as

$d = \frac{C}{\pi}$

So, to find the value of the diameter from circumference, simply divide the circumference by $\pi$.

## Circumference to Diameter Ratio

**Circumference to diameter ratio is the ratio that defines Pi **$(\pi)$**.**

The radius, diameter, and circumference of a circle are all related through the mathematical constant $\pi$** (pi)**, which is the ratio of a circle’s circumference to its diameter. π is an irrational number. The value of π is approximately considered as 3.14159 or $\frac{22}{7}$.

**Any two circles with different radii are similar as they have the same shape but different size**. Thus, the ratio of a circumference of a circle to diameter is always constant for all circles. It never depends on the radius. This value is called pi $(\pi)$. It is an irrational number.

$C = 2\pi r = \pi d$

Thus, $\pi = \frac{C}{d}$

This formula also describes how to find the diameter of a circle with the circumference C. How can we find the diameter of a circle with the circumference C? Divide the circumference value by the number pi $(\pi)$, or use the formula $d = \frac{C}{\pi}$ .

When the circumference C is placed in a ratio with the diameter d, we get $\pi$.

## Circumference to Diameter Formula

We can find the circumference of a circle either by using the radius or the diameter of the circle. The following are the formulas for finding the circumference of the circle.

**Circumference of circle with radius: **$C = 2\pi r$

**Circumference of circle with diameter: **$C = \pi d$

where

- $C =$ Circumference
- $r =$ Radius
- $d =$ Diameter
- $\pi = \frac{22}{7}$or $3.14$ (approx)

Thus, the circumference to diameter formula, which is used to find diameter using circumference, can be given as

**Circumference to diameter formula:** $d = 2r = \frac{C}{\pi}$

## How to Find the Diameter from Circumference

**To find diameter from circumference, simply substitute the value of the diameter in the formula **$d = \frac{C}{\pi}$ .

Example: Find the diameter of a circle whose circumference is 6.28 inches.

Here, $C = 6.28$

$d = \frac{C}{\pi} = \frac{6.28}{3.14} = 2$ in

## How to Find the Circumference from Diameter

**To find circumference from diameter, simply substitute the value of the diameter in the formula **C=πd.

**Example:** The diameter of the playground is 70 feet. Find its circumference.

Circumference of the playground $= C= \pi d$

$C = \frac{22}{7}\times70 = 220$ feet

## How to Find the Circumference of the Circle When Area Is Given

Sometimes, we only know the area of a circle and we have to find the circumference. How to proceed in such cases? Consider an example.

**Example:** Area of a circular park is 6.16 square yards. What is the length of the boundary of the park?

Length of the boundary of circular park $=$ Circumference of the circle

Area $= 6.16$ square yards

Area of a circle$ = \pi r^2$

$\frac{22}{7} \times r^2 = 6.16$

$r^2 = \frac{6.16 \times 7}{22} = 1.96$

$r = 1.4$ yards

$d = 2 \times 1.4 = 2.8$ yards

Circumference of the circular park $= \pi d = \frac{22}{7}\times2.8 = 8.8$ yards

## Conclusion

In this article, we learned how to find the diameter of a circle using its circumference. We also explored the important formulas along with examples. Let’s look at some solved examples and practice problems to understand the concepts better.

## Solved Examples on Circumference to Diameter

**1. i) What is the circumference of the circle if the diameter is ****1.4**** inches? **

** ii) What is the diameter of a circle if its circumference is ****1.4**** inches?**

**Solution: **

i) Diameter $(d) = 1.4$ inches

$C = \pi d$

$C = \frac{22}{7}\times1.4$

$C = 22\times0.2$

$C = 4.4$ inches

ii) Circumference $= C = 1.4$ inches

$d = \frac{C}{pi}$

$d = \frac{1.4}{3.14}$

$d = 0.4456$ in

**2. Find the circumference of the circle if the radius is 2.75 inches (Use **$\pi = 3.14$**).**

**Solution:**

Radius $(r) = 2.75$ inches

Diameter $= 2r = 2\times2.75 = 5.5$ inches

$C = \pi d = 3.14\times5.5 = 17.27$ inches

**3. What is the circumference of the circle if the area of the circle is is ****38.5**** square feet?**

**Solution:**

Area $= \pi r^2$

$38.5 = \frac{22}{7} \times r^2$

$r^2 = \frac{38.5\times7}{22} = 12.25$

$r = 3.5$ feet

Diameter $= 2r = 2\times3.5 = 7$ feet

$C = d = \frac{22}{7}\times7 = 22$ feet

**4. ****Find the diameter of a circular garden with circumference 132 feet.**

**Solution:**

Circumference $(C) = 132$ feet

Diameter $(d) = \frac{C}{\pi}$

Diameter $(d) = \frac{132}{\pi}$

Diameter $(d)= \frac{132}{1} \times \frac{7}{22}$

Diameter $(d)= 42$ feet

**5. The circumference of a circle is ****33**** inches. Find the diameter of the circle. **

**Solution: **

$C = 33$ inches

$C = \pi d$

$33 = \frac{22}{7} \times d$

$d = \frac{33\times 7}{22} = 10.5$ inches

## Practice Problems on Circumference to Diameter

## Circumference to Diameter: Conversion, Formula, Meaning, Example

### Find the circumference of painting the circular wall of radius 31.5 yards?

Radius $(r) = 31.5$ yards

Diameter $= 2r = 23 \times 1.5 = 63$ yards

$C = \pi d = \frac{22}{7} \times 63 = 462$ yards

### What will be the radius of the circle whose circumference is 242 feet?

$C = 242$ feet

$\pi d = 242$

$\frac{22d}{7} = 242$

$d = \frac{242 \times 7}{22} = 77$ feet

$r = \frac{d}{2} = \frac{77}{2} = 38.5$ feet

### What will be the area of the circle whose circumference is 44 square inches?

$C = 44$ square inches

$d = 44$

$\frac{22d}{7} = 44$

$d = \frac{44 \times 7}{22} = 14$ inches

$r = \frac{d}{2} = \frac{14}{2} = 7$ inches

Area $= \pi r^2 = \frac{22}{7}\times7\times7 = 154$ square inches

### Find the circumference of the circle whose diameter is 8.4 yards?

$d = 8.4$ yards

Circumference $= C = \pi d = \frac{22}{7}\times8.4 = 26.4$ yards

### If the diameter is doubled, then the circumference will ____.

Let the new diameter be $2d$.

New Circumference $= \pi \times 2d = 2d$.

### Find diameter in terms of Pi using circumference. 6 inch circumference to diameter $=$ ?

Diameter $(d) = C \pi$

Diameter $(d) = 6 \pi$

## Frequently Asked Questions on Circumference to Diameter

**Is the diameter half of the circumference of a circle?**

No, the diameter is not half of a circle’s circumference. The diameter is twice the radius of a circle.

**How many diameters make a circumference?**

The circumference of a circle is equal to pi $(\pi = 3.14159…)$ times the diameter.

Circumference is said to be about three times (little more than 3 times) the diameter of a circle.

**How does the diameter affect the circumference of the circle?**

There is a direct relation between the diameter of a circle and the circumference of that same circle. As the diameter increases, the circumference of the circle also increases. As the diameter decreases, the circumference of the circle also decreases.

**Can the circumference and diameter of a circle be the same?**

The circumference and diameter can never be the same no matter what the diameter of the circle is.

**Which is longer—circumference or diameter?**

The diameter of a circle is always smaller than its circumference.

**Is the ratio of circumference to the diameter of a circle always constant?**

Yes, it is given by pi ().