Quarter Circle Calculator

Our quarter circle calculator is a solution to so many problems and concerns you have for the quarter of a circle. The quarter of a circle is a simple shape yet has many parameters: we will try to cover them all: from the area and perimeter to the chord of a quarter circle.

As much as we love to eat cakes, it's rarely a chance that we ever get a whole quarter, and before you know it, we are craving for more. But our tool is your friend, and it will not let you crave anything.
So, you want to determine all you can about the quarter circle. The only thing our tools ask of you is to input the radius of the quarter circle. And the list of results is ready.

For instance, you input the radius as 13 cm. The results are:

1. Chord = $18.38 \text{ cm}$
2. Quarter arc = $20.42\text{ cm}$
3. Perimeter = $46.42\text{ cm}$
4. Quarter area = $132.73\text{ cm}^2$
5. External area= $36.27\text{ cm}^2$

The features of the quarter circle are the parameters of a quarter that are provided in our tool. Let's dive in and look at them individually and also their formulas.

• Chord of a quarter circle
  The chord of the circle is a line segment joining the two radii. It makes it seem like a right-angled triangle inside the quarter. The formula to determine the chord is:

  $c = r \times \sqrt{2}$

• Arc of a quarter circle
  The arc of a quarter circle is the arc that would be the part of the circumference of the circle. It is the curved line joining the two radii. The formula to calculate the arc length is:

  $L = \frac{1}{2} \times \pi \times r$

• Perimeter of a quarter circle
  The perimeter of a quarter circle is the outer boundary of the quarter, it includes the 2 radii and the arc. The formula you may use to find out the perimeter is:
  $P = L + (2 \times r)$

• Area of a quarter circle
  The area of the circle is, as the name indicates, the space covered by the quarter circle. The formula to figure out the area is:
  $A_1 = \frac{1}{4} \times \pi \times {r^2}$

• External area of a quarter circle
  The external area is the area outside the quarter itself. The formula for the external area is:
  $A_2 = r^2 - A_1$

where:

• $r$ - Radius of the quarter circle;
• $c$ - Chord of the quarter circle;
• $L$ - Arc length of the quarter circle;
• $P$ - Perimeter of the quarter circle;
• $A_1$ - Quarter area; and
• $A_2$ - External area of the quarter circle.

Let's take an example of the odd quarter-shaped pot you have on your table, which carries a wonderful baby cactus.
You might wonder how much area it covers among all the clutter.
All you have to do is grab a measuring tape or a ruler from your desk and measure the radius of the pot. Let's say it is $9\text{ cm}$. Put the radius in the formula:

$A_1 = \pi \times \frac{r^2}{4}$

$A_1 = 3.14 \times \frac{9^2}{4}$

$A_1 = 3.14 \times \frac{81}{4}$

$A_1 = 3.14 \times 20.25$

$A_1 = 63.615$

$A_1 = 63.62 \text{ cm}^2$

The sector of a circle is versatile. Could be any segment of a circle to a quarter of a circle. Hence we at Omni have dedicated some tools to the sector of a circle. Check them out!

• Sector area calculator;
• Perimeter of a sector calculator;
• Quarter circle area calculator; and
• Quarter circle perimeter calculator.