What is the formula for calculating the area of a circle?

To calculate the area of a circle, the basic formula is S = r x r x π, where S is the area, r is the radius, and π is the constant (approximately 3.14159). Alternatively, if the circumference and diameter are known, the area of a circle can also be calculated.

VietNamNet•15/09/2025

What is a circle?

In planar geometry, a circle is the set of all points that are equidistant from a fixed point (called the center) at a defined distance called the radius.

The radius of the circle must be a positive number, greater than 0.

How is a circle different from a ring?

A circle and a circumference are two different concepts.

A circle is the set of all points that lie inside and on the circle. In other words, a circle is a cross-section and therefore has an area.

A circle is the locus of all points on a plane that are equidistant from a given point (called the center) - a closed curve (like a border or boundary) that has no area.

Formula for calculating the area of a circle

The area of a circle is calculated by multiplying the square of its radius by pi.

S = rxrxnbsp;π = r ² x π

In there:

S: Area of the circle

r: Radius of the circle - the distance from the center of the circle to any point on the circle.

π (pi): The number pi is a mathematical constant, approximately equal to 3.14159.

How to calculate the area of a circle when the diameter is known.

In mathematics and geometry, a diameter is a line segment that passes through the center of a circle and connects any two points on the circle. The diameter is the longest line segment in a circle, dividing the circle into two equal halves, and its length is twice the radius.

For problems where only the diameter is given, use the formula for calculating the area of a circle: square half the diameter multiplied by pi.

S = (d/2) ² x π

In there:

S: Area of the circle

d: Length of the circle's diameter

π (pi): The number pi is a mathematical constant, approximately equal to 3.14159.

How to calculate the area of a circle when the circumference is known.

The circumference of a circle is the length of the line enclosing the circle. The formula for calculating circumference (C) is C = π x d (where d is the diameter) or C = 2 x r x π (where r is the radius).

Given only the circumference as data, there are two ways to calculate the area of a circle.

Method 1: Using the general formula:

S = r ² x π

- Step 1: Find the radius (r) from the perimeter (C)

The circumference of the circle is C = 2 xrx π, so r =C/(2π)

Step 2: Apply the formula for calculating the area of a circle.

The area of the circle is S = ^r² x π. Substituting the value of r found in step 1, we have: S = (C/2π)² x π

After simplification, we get the final formula: S = (C) ² /4π.

Method 2: Apply the simplified formula for calculating the area of a circle by dividing the circumference squared by 4 times pi:

S = (C) ² / 4π

In there:

S: Area of the circle