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 ($r$):

   $$r=\frac{d}{2}=\frac{10}{2}=5\text{cm}$$

2. Circumference ($C$):

   $$C=\pi d=\pi \times 10=31.4159\text{cm}$$

3. Area ($A$):

   $$A=\pi r^2=\pi \times 5^2=78.5398{\text{cm}}^2$$

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 ($r$):

   $$r=\sqrt{\frac{A}{\pi }}=\sqrt{\frac{50}{3.14159265359}}=3.9894\text{cm}$$

2. Diameter ($d$):

   $$d=2r=2\times 3.9894=7.9788\text{cm}$$

3. Circumference ($C$):

   $$C=2\pi r=2\times 3.14159265359\times 3.9894=25.0672\text{cm}$$

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 ($r$):

   $$r=\frac{C}{2\pi }=\frac{20}{2\times 3.14159265359}=3.1831\text{cm}$$

2. Diameter ($d$):

   $$d = 2r = 2 \times 3.1831 = 6.3662 \, \text{cm}$$

3. Area ($A$):

   $$A=\pi r^2=\pi \times 3.1831^2=31.8310{\text{cm}}^2$$

Results:

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

Formulas Used

1. Radius (r):

   $$r=\frac{d}{\mathrm{2<span\; style="color:\; initial;\; font-family:\; Verdana,\; BlinkMacSystemFont,\; -apple-system,\; \text{'}Segoe\; UI\text{'},\; Roboto,\; Oxygen,\; Ubuntu,\; Cantarell,\; \text{'}Open\; Sans\text{'},\; \text{'}Helvetica\; Neue\text{'},\; sans-serif;"></span>}}$$$$r = \sqrt{\frac{A}{\pi}}$$$$r=\frac{C}{2\mathrm{\pi <span\; style="font-family:\; Verdana,\; BlinkMacSystemFont,\; -apple-system,\; \text{'}Segoe\; UI\text{'},\; Roboto,\; Oxygen,\; Ubuntu,\; Cantarell,\; \text{'}Open\; Sans\text{'},\; \text{'}Helvetica\; Neue\text{'},\; sans-serif;\; color:\; initial;"></span>}}$$

2. Diameter (d):

   $$d = 2r$$
   $$d=\frac{C}{\mathrm{\pi <span\; style="color:\; initial;\; font-family:\; Verdana,\; BlinkMacSystemFont,\; -apple-system,\; \text{'}Segoe\; UI\text{'},\; Roboto,\; Oxygen,\; Ubuntu,\; Cantarell,\; \text{'}Open\; Sans\text{'},\; \text{'}Helvetica\; Neue\text{'},\; sans-serif;"></span>}}$$

3. Circumference (C):

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

4. Area (A):

   $$A=\pi r^2$$