Quarter Circle Area Calculator
You've finally reached the quarter circle area calculator; this tool offers everything you need to know about the area of a quarter circle and its formula. Keep on reading to find out more! ⤵️
We'll teach you:
 How to find the area of a quarter circle;
 How to use the 1/4 circle formula and the quarter circle perimeter equation;
 What's the chord of the 4th part of a circle; and
 How to calculate the quarter arc.
💡 Looking for different types of circles? Try other tools from the sector area calculator series:
How to calculate the arc of a quarter circle?
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?
How to calculate the chord of a quarter circle?
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.
How to calculate the quarter circle perimeter?
 The quarter circle perimeter consists of two components:

Two radiuses;
2 × r

Arc of the quarter circle.
(π × r²)/ 2
 Let's combine them together:
The quarter circle perimeter = (2 × r) + (π × r²/ 2)
How to calculate the area of a quarter circle?
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.
How to use the quarter circle area calculator?
It just couldn't be easier  and we sure mean it!
 Enter the radius of your quarter circle.
And well.. that's it. Enjoy your results. 🎉
FAQ
How many quarter circles equal a whole circle?
4 quarter circles equal a whole circle.
That's why, if you want to compute the area of a quarter circle, you need to divide the area of a whole circle by 4.
Quarter circle area = Full circle area/ 4
How to calculate the area of a quarter circle with radius = 2?
 It's pretty effortless  if we know that the radius = 2, and π= 3.14, we just need to follow the equation below:
Quarter circle area = (π × r²)/ 4
Quarter circle area = (π × 2²)/ 4
Quarter circle area = (π × 4)/ 4
Quarter circle area = π
 We already know the answer: the quarter circle area with the radius of 2 equals π!