Quarter Circle Area Calculator

The arc of a quarter circle equals 1/4 of a perimeter of the entire circle. If we want to calculate it, we need to divide the mentioned parameter by 4.

The entire circle perimeter = 2 × π × r²

The arc of a quarter circle = (π × r²)/ 2

It's that simple, isn't it?

Calculating the chord of a quarter circle is a little bit difficult since it encompasses a conversion of degrees to radians. Let's begin with the equation itself:

Chord = 2 × r × sin(1.57/ 2)
Chord = 2 × r × sin(0.79)

Where r stands for radius of the circle, and sine is given in radians.

How do we know it? The quarter circle contains a 90° angle equal to 1.57 radians.

1. The quarter circle perimeter consists of two components:

• Two radiuses;

  2 × r

• Arc of the quarter circle.

  (π × r²)/ 2

2. Let's combine them together:

The quarter circle perimeter = (2 × r) + (π × r²/ 2)

Let's make it nice and simple!

The quarter circle equals 1/4 of the entire circle; in order to calculate it, we need to divide the are of the whole circle by 4:

Whole circle area = π × r²

Quarter circle area = (π × r²)/ 4

r - the radius of the circle, equal to half of the diameter.

It just couldn't be easier - and we sure mean it!

1. Enter the radius of your quarter circle.

And well.. that's it. Enjoy your results. 🎉