# Circle Calculator

## Circle Calculator

### How to Use the Circle Calculator

1. Choose a Calculation Type:

• Find A, C, and r | Given d: Calculate the area (A), circumference (C), and radius (r) based on the diameter (d) you provide.
• Find A, C, and d | Given r: Calculate the area (A), circumference (C), and diameter (d) based on the radius (r) you provide.
• Find A, r, and d | Given C: Calculate the area (A), radius (r), and diameter (d) based on the circumference (C) you provide.
• Find C, r, and d | Given A: Calculate the circumference (C), radius (r), and diameter (d) based on the area (A) you provide.
2. Enter the Known Value: Depending on your selected calculation type, input the known value:

• Radius ($r$) in units of your choice.
• Diameter ($d$) in units of your choice.
• Circumference ($C$) in units of your choice.
• Area ($A$) in square units of your choice.
3. Set the Value of Pi (π): You can use the default value $\pi = 3.14159265359$, or input a different value if necessary.

4. Select Units and Significant Figures: Choose the desired units (e.g., cm, m, inches) and set the number of significant figures for the result.

5. Click Calculate: The calculator will compute the unknown values and display the results.

### Examples

#### Example 1: Find Circumference and Area Given Diameter

Given:

• Diameter ($d$) = 10 cm

To Find:

• Radius ($r$)
• Circumference ($C$)
• Area ($A$)

Calculations:

1. Radius ($r$):

$r=\frac{d}{2}=\frac{10}{2}=5\text{\hspace{0.17em}}\text{cm}$
2. Circumference ($C$):

$C=\pi d=\pi ×10=31.4159\text{\hspace{0.17em}}\text{cm}$
3. Area ($A$):

$A=\pi {r}^{2}=\pi ×{5}^{2}=78.5398\text{\hspace{0.17em}}{\text{cm}}^{2}$

Results:

• Radius ($r$) = 5 cm
• Circumference ($C$) = 31.4159 cm
• Area ($A$) = 78.5398 cm²

#### Example 2: Find Radius and Diameter Given Area

Given:

• Area ($A$) = 50 cm²

To Find:

• Radius ($r$)
• Diameter ($d$)
• Circumference ($C$)

Calculations:

1. Radius ($r$):

$r=\sqrt{\frac{A}{\pi }}=\sqrt{\frac{50}{3.14159265359}}=3.9894\text{\hspace{0.17em}}\text{cm}$
2. Diameter ($d$):

$d=2r=2×3.9894=7.9788\text{\hspace{0.17em}}\text{cm}$
3. Circumference ($C$):

$C=2\pi r=2×3.14159265359×3.9894=25.0672\text{\hspace{0.17em}}\text{cm}$

Results:

• Radius ($r$) = 3.9894 cm
• Diameter ($d$) = 7.9788 cm
• Circumference ($C$) = 25.0672 cm

#### Example 3: Find Area and Radius Given Circumference

Given:

• Circumference ($C$) = 20 cm

To Find:

• Radius ($r$)
• Diameter ($d$)
• Area ($A$)

Calculations:

1. Radius ($r$):

$r=\frac{C}{2\pi }=\frac{20}{2×3.14159265359}=3.1831\text{\hspace{0.17em}}\text{cm}$
2. Diameter ($d$):

$d = 2r = 2 \times 3.1831 = 6.3662 \, \text{cm}$
3. Area ($A$):

$A=\pi {r}^{2}=\pi ×3.183{1}^{2}=31.8310\text{\hspace{0.17em}}{\text{cm}}^{2}$

Results:

• Radius ($r$) = 3.1831 cm
• Diameter ($d$) = 6.3662 cm
• Area ($A$) = 31.8310 cm²

#### Formulas Used

$r=\frac{d}{2}$$r = \sqrt{\frac{A}{\pi}}$$r=\frac{C}{2\mathrm{\pi }}$
2. Diameter (d):

$d = 2r$
$d=\frac{C}{\mathrm{\pi }}$
3. Circumference (C):

$C = \pi d$
$C = 2\pi r$
4. Area (A):

$A=\pi {r}^{2}$