Find the area of circle whose diameter is d

The area of a circle calculator helps you compute the surface of a circle given a diameter or radius. Our tool works both ways - no matter if you're looking for an area to radius calculator or a radius to the area one, you've found the right place ◔

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We'll give you a tour of the most essential pieces of information regarding the area of a circle, its diameter, and its radius. We'll learn how to find the area of a circle, talk about the area of a circle formula, and discuss the other branches of mathematics that use the very same equation.

So, let's see how to find the area of a circle. There are several ways to achieve it. Here, we can calculate the area of a circle using a diameter or using a radius.

💡 The diameter is the line that crosses the center of the figure and touches both of its margins. The radius begins at the center of the figure and ends at the figure's margin.

You can find the diameter of a circle by multiplying the radius of a circle by two:

Diameter = 2 * Radius

Area of a circle radius. The radius of a circle calculator uses the following area of a circle formula:

Area of a circle = π * r2

Area of a circle diameter. The diameter of a circle calculator uses the following equation:

Area of a circle = π * (d/2)2

Where:

π is approximately equal to 3.14. It doesn't matter whether you want to find the area of a circle using diameter or radius - you'll need to use this constant in almost every case.

🔎 Another relevant aspect of circles is their circumference. You can learn more about it and its relationship with area in our circle formula calculator

Now that you know how to calculate the area of a circle, we encourage you to try our other circle calculators:

A sector of a circle is section of a circle between two radii. You can think of it as a giant slice of pizza.

It's a "cut-off" part of a circle, limited by a chord or a secant.

It's an angle with the vertex in the center, whose arms extend to the circumference.

You can easily calculate everything, the area of a circle, its diameter, and its radius, using our area of a circle calculator in a blink of an eye:

Determine whether your given value is a diameter or a radius using the picture on the right and definitions available in the section above (you can calculate the area of a circle using its diameter as well as radius).
Enter your value into the proper field of the calculator.
It didn't take long - your results are here! We decided to include the step-by-step solution and all the most important data right below the calculator.

That is how to calculate the area of a circle in no time 😉.

The circle's area found with both the radius and diameter calculators serves as a base for many other equations - not only in mathematics but also in everyday life! Here are a few examples where knowing how to find the area of a circle might be useful:

We need to know the surface area of a circle in order to calculate a cone's volume and its surface area 🎉
Your pizza party wouldn't be complete without our pizza tool based on the diameter to area calculator 🍕
We use calculations similar to this one when obtaining information about a sphere, such as sphere volume.🌐
Do you fancy nice dresses? Maybe you love to sew? Discover our circle skirt calculator! Efficient sewing has never been easier. 👗

Updated November 16, 2020

By Melissa Mayer

A circle is one of the most widely recognizable geometric shapes, but exploring the mathematical concepts of diameter and area can sometimes feel tricky. Whether you are measuring the size of round rug you need to purchase or determining the space you need to construct a round garden or patio, knowing how to calculate the area of a circle from its diameter is a valuable skill.

The area of a circle is the amount of space the circle covers. The formula for calculating the area of a circle is A = πr2 where pi (π) equals 3.14 and the radius (r) is half the diameter.

The first step for calculating the area of a circle from its diameter is to find that diameter. While math problems often list this value, in the real world, you must find the diameter yourself. The diameter is the length of a line that begins at the edge of the circle, passes through the center of the circle, and ends at the opposite edge of the circle. To measure, you will need a ruler for small circles or a tape measure for large circles.

Once you have the diameter (d) of the circle, you can find the radius (r) using the equation d=2r. The radius of a circle is the distance from the center of the circle to any point on the edge of the circle. The radius is also half of the diameter. If your diameter is a simple number, you can likely calculate the radius in your head. If not, rearrange the equation to find for r

r = \frac{d}{2}

You are now ready to use the equation for area:

A = πr^2

Pi (π) is a non-algebraic number that represents the ratio of the distance around the circle (circumference) to its diameter, usually estimated as 3.14. To solve for area, square the radius (radius times radius) then multiply by 3.14.

Since area is a measure of two dimensions, you always report area in square units like square inches (in2) or square feet (ft2). This is especially important when calculating the area of a circle for an assignment since an answer without correctly reported units is likely incorrect or incomplete.

Any time you need to determine the space inside a circle or the amount of space a circle covers, you can use the equation for the area of a circle. Especially for real world applications of this skill, measuring diameter is often the simplest way to start.

The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr2, where r is the radius of the circle. The unit of area is the square unit, for example, m2, cm2, in2, etc. Area of Circle = πr2 or πd2/4 in square units, where (Pi) π = 22/7 or 3.14. Pi (π) is the ratio of circumference to diameter of any circle. It is a special mathematical constant.

The area of a circle formula is useful for measuring the region occupied by a circular field or a plot. Suppose, if you have a circular table, then the area formula will help us to know how much cloth is needed to cover it completely. The area formula will also help us to know the boundary length i.e., the circumference of the circle. Does a circle have volume? No, a circle doesn't have a volume. A circle is a two-dimensional shape, it does not have volume. A circle only has an area and perimeter/circumference. Let us learn in detail about the area of a circle, surface area, and its circumference with examples.

Circle and Parts of a Circle

A circle is a collection of points that are at a fixed distance from the center of the circle. A circle is a closed geometric shape. We see circles in everyday life such as a wheel, pizzas, a circular ground, etc. The measure of the space or region enclosed inside the circle is known as the area of the circle.

Radius: The distance from the center to a point on the boundary is called the radius of a circle. It is represented by the letter 'r' or 'R'. Radius plays an important role in the formula for the area and circumference of a circle, which we will learn later.

Diameter: A line that passes through the center and its endpoints lie on the circle is called the diameter of a circle. It is represented by the letter 'd' or 'D'.

Diameter formula: The diameter formula of a circle is twice its radius. Diameter = 2 × Radius

d = 2r or D = 2R

If the diameter of a circle is known, its radius can be calculated as:

r = d/2 or R = D/2

Circumference: The circumference of the circle is equal to the length of its boundary. This means that the perimeter of a circle is equal to its circumference. The length of the rope that wraps around the circle's boundary perfectly will be equal to its circumference. The below-given figure helps you visualize the same. The circumference can be measured by using the given formula:

where 'r' is the radius of the circle and π is the mathematical constant whose value is approximated to 3.14 or 22/7. The circumference of a circle can be used to find the area of that circle.

For a circle with radius ‘r’ and circumference ‘C’:

π = Circumference/Diameter
π = C/2r = C/d
C = 2πr

Let us understand the different parts of a circle using the following real-life example.

Consider a circular-shaped park as shown in the figure below. We can identify the various parts of a circle with the help of the figure and table given below.

In a Circle	In our park	Named by the letter
Centre	Fountain	F
Circumference	Boundary
Chord	Play area entrance	PQ
Radius	Distance from the fountain to the Entrance gate	FA
Diameter	Straight Line Distance between Entrance Gate and Exit Gate through the fountain	AFB
Minor segment	The smaller area of the park, which is shown as the Play area
Major segment	The bigger area of the park, other than the Play area
Interior part of the circle	The green area of the whole park
Exterior part of the circle	The area outside the boundary of the park
Arc	Any curved part on the circumference.

What is the Area of Circle?

The area of a circle is the amount of space enclosed within the boundary of a circle. The region within the boundary of the circle is the area occupied by the circle. It may also be referred to as the total number of square units inside that circle.

Area of Circle Formulas

The area of a circle can be calculated in intermediate steps from the diameter, and the circumference of a circle. From the diameter and the circumference, we can find the radius and then find the area of a circle. But these formulae provide the shortest method to find the area of a circle. Suppose a circle has a radius 'r' then the area of circle = πr2 or πd2/4 in square units, where π = 22/7 or 3.14, and d is the diameter.

Area of a circle, A = πr2 square units

Circumference / Perimeter = 2πr units

Area of a circle can be calculated by using the formulas:

Area = π × r2, where 'r' is the radius.
Area = (π/4) × d2, where 'd' is the diameter.
Area = C2/4π, where 'C' is the circumference.

Examples using Area of Circle Formula

Let us consider the following illustrations based on the area of circle formula.

Example 1: If the length of the radius of a circle is 4 units. Calculate its area.

Solution: Radius(r) = 4 units(given) Using the formula for the circle's area,

Area of a Circle = πr2

Put the values,

A = π42

A =π × 16

A = 16π ≈ 50.27

Answer: The area of the circle is 50.27 squared units.

Example 2: The length of the largest chord of a circle is 12 units. Find the area of the circle.

Solution: Diameter(d) = 12 units(given) Using the formula for the circle's area,

Area of a Circle = (π/4)×d2

Put the values,

A = (π/4) × 122

A = (π/4) × 144

A = 36π ≈ 113.1

Answer: The area of the circle is 113.1 square units.

Area of a Circle Using Diameter

The area of the circle formula in terms of the diameter is: Area of a Circle = πd2/4. Here 'd' is the diameter of the circle. The diameter of the circle is twice the radius of the circle. d = 2r. Generally from the diameter, we need to first find the radius of the circle and then find the area of the circle. With this formula, we can directly find the area of the circle, from the measure of the diameter of the circle.

Area of a Circle Using Circumference

The area of a circle formula in terms of the circumference is given by the formula \(\dfrac{(Circumference)^2}{4\pi}\). There are two simple steps to find the area of a circle from the given circumference of a circle. The circumference of a circle is first used to find the radius of the circle. This radius is further helpful to find the area of a circle. But in this formulae, we will be able to directly find the area of a circle from the circumference of the circle.

Area of a Circle-Calculation

The area of the circle can be conveniently calculated either from the radius, diameter, or circumference of the circle. The constant used in the calculation of the area of a circle is pi, and it has a fractional numeric value of 22/7 or a decimal value of 3.14. Any of the values of pi can be used based on the requirement and the need of the equations. The below table shows the list of formulae if we know the radius, the diameter, or the circumference of a circle.

Area of a circle when the radius is known.	πr2
Area of a circle when the diameter is known.	πd2/4
Area of a circle when the circumference is known.	C2/4π

Derivation of Area of a Circle

Why is the area of the circle is πr2? To understand this, let's first understand how the formula for the area of a circle is derived.

Observe the above figure carefully, if we split up the circle into smaller sections and arrange them systematically it forms a shape of a parallelogram. When the circle is divided into even smaller sectors, it gradually becomes the shape of a rectangle. The more the number of sections it has more it tends to have a shape of a rectangle as shown above.

The area of a rectangle is = length × breadth

The breadth of a rectangle = radius of a circle (r)

When we compare the length of a rectangle and the circumference of a circle we can see that the length is = ½ the circumference of a circle

Area of circle = Area of rectangle formed = ½ (2πr) × r

Therefore, the area of the circle is πr2, where r, is the radius of the circle and the value of π is 22/7 or 3.14.

Surface Area of Circle Formula

The surface area of a circle is the same as the area of a circle. In fact, when we say the area of a circle, we mean nothing but its total surface area. Surface area is the area occupied by the surface of a 3-D shape. The surface of a sphere will be spherical in shape but a circle is a simple plane 2-dimensional shape.

If the length of the radius or diameter or even the circumference of the circle is given, then we can find out the surface area. It is represented in square units. The surface area of circle formula = πr2 where 'r' is the radius of the circle and the value of π is approximately 3.14 or 22/7.

Real-World Example on Area of Circle

Ron and his friends ordered a pizza on Friday night. Each slice was 15 cm in length.

Calculate the area of the pizza that was ordered by Ron. You can assume that the length of the pizza slice is equal to the pizza’s radius.

Solution:

A pizza is circular in shape. So we can use the area of a circle formula to calculate the area of the pizza.

Radius is 15 cm

Area of Circle formula = πr2 = 3.14 × 15 × 15 = 706.5

Area of the Pizza = 706.5 sq. cm.

Example 1: Find the circumference and the area of a circle whose radius is 14 cm.

Solution:

Given: Radius of the circle = 14 cm

Circumference of the Circle = 2πr

= 2 × 22/7 × 14

= 2 × 22 × 2

= 88 cm

Using area of Circle formula = πr2

= 22/7 × 14 × 14

= 22 × 2 × 14

= 616 sq. cm.

Area of the Circle = 616 sq. cm.
Example 2: The ratio of the area of 2 circles is 4:9. With the help of the area of circle formula find the ratio of their radii.

Solution:

Let us assume the following:

The radius of the 1st circle = R1

Area of the 1st circle = A1

The radius of the 2nd circle = R2

Area of the 2nd circle = A2

It is given that A1:A2 = 4:9

Area of a Circle = πr2

π\(R_1\)2 : π\(R_2\)2 = 4 : 9

Taking square roots of both sides,

R1 : R2 = 2 : 3

Therefore, the ratio of the radii = 2:3
Example 3: A race track is in the form of a circular ring. The inner radius of the track is 58 yd and the outer radius is 63 yd. Find the area of the race track.

Solution:

Given: R = 63 yd, r = 56 yd.

Let the area of outer circle be A1 and the area of inner circle be A2

Area of race track = A1 - A2 = πR2 - πr2 = π(632 - 562) = 22/7 × 833 = 2,618 square yards.

Therefore, the area of the race track is 2618 square yards.
Example 4: A wire is in the shape of an equilateral triangle. Each side of the triangle measures 7 in. The wire is bent into the shape of a circle. Find the area of the circle that is formed.

Solution:

Perimeter of the Equilateral Triangle: Perimeter of the triangle = 3 × side = 3 × 7 = 21 inches.

Since the perimeter of the equilateral triangle = Circumference of the circle formed.

Thus, the perimeter of the triangle is 21 inches.

Circumference of a Circle = 2πr = 2 × 22/7 × r = 21. r = (21 × 7)/(44) = 3.34.

Therefore, the Radius of the circle is 3.34 cm. Area of a circle = πr2 = 22/7 ×(3.34)2 = 35.042 square inches.

Therefore, the area of a circle is 35.042 square inches.
Example 5: The time shown in a circular clock is 3:00 pm. The length of the minute hand is 21 units. Find the distance traveled by the tip of the minute hand when the time is 3:30 pm.

Solution:

When the minute hand is at 3:30 pm, it covers half of the circle. So, the distance traveled by the minute hand is actually half of the circumference. Distance \(= \pi\) (where r is the length of the minute hand). Hence the distance covered = 22/7 × 21 = 22 × 3 = 66 units. Therefore, the distance traveled is 66 units.

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FAQs on Area of Circle

The area of circle is calculated by using the following listed formulas:

Area = π × r2, where 'r' is the radius.
Area = (π/4) × d2, where 'd' is the diameter.
Area = C2/4π, where 'C' is the circumference.

What Is the Area of Circle Formula?

Area of circle formula = π × r2. The area of a circle is π multiplied by the square of the radius. The area of a circle when the radius 'r' is given is πr2. The area of a circle when the diameter 'd' is known is πd2/4. π is approx 3.14 or 22/7. Area(A) could also be found using the formulas A = (π/4) × d2, where 'd' is the radius and A= C2/4π, where 'C' is the given circumference.

What Is the Perimeter and Area of a Circle?

The circumference of the circle is equal to the length of its boundary. This means that the perimeter of a circle is equal to its circumference. The area of a circle is πr2 and the perimeter (circumference) is 2πr when the radius is 'r' units, π is approx 3.14 or 22/7. The circumference and the radius length of a circle are important parameters to find the area of that circle. For a circle with radius ‘r’ and circumference ‘C’:

π = Circumference ÷ Diameter
π = C/2r
Therefore, C = 2πr

Why Is the Area of a Circle Formula is πr2?

A circle can be divided into many small sectors which can then be rearranged accordingly to form a parallelogram. When the circle is divided into even smaller sectors, it gradually becomes the shape of a rectangle. We can clearly see that one of the sides of the rectangle will be the radius and the other will be half the length of the circumference, i.e, π. As we know that the area of a rectangle is its length multiplied by the breadth which is π multiplied to 'r'. Therefore, the area of the circle is πr2.

What Is the Area of a Circle Formula in Terms of π?

The value of pi (π) is approximately 3.14. Pi is an irrational number. This means that its decimal form neither ends (like 1/5 = 0.2) nor becomes repetitive (like 1/3 = 0.3333...). Pi is 3.141592653589793238... (to only 18 decimal places). Hence the area of a circle formula in terms of pi is given as πr2 square units.

How Do You Find the Circumference and Area of a Circle?

The area and circumference of a circle can be calculated using the following formulas. Circumference = 2πr ; Area = πr2. The circumference of the circle can be taken as π times the diameter of the circle. And the area of the circle is π times the square of the radius of the circle.

How to Calculate the Area of a Circle With Diameter?

The diameter of the circle is double the radius of the circle. Hence the area of the circle formula using the diameter is equal to π/4 times the square of the diameter of the circle. The formula for the area of the circle, using the diameter of the circle π/4 × diameter2.

How Do You Find the Area of a Circle Given the Circumference?

The area of a circle can also be found using the circumference of the circle. The radius of the circle can be found from the circumference of the circle and this value can be used to find the area of the circle. Assume that the circumference of the circle is 'C'. We have C = 2πr, or r = C/2π. Now applying this 'C' value in the Area formula we have A = πr2 = π × (C/2π)2 = C2/4π.

What Is the Area of Circle With Radius 3 m?

The area of a circle is π multiplied by the square of the radius. The area of a circle(A) when the radius 'r' is given is πr2. π is approx 3.14 or 22/7. Therefore, area = 3.14 × 3 × 3 = 28.26 sq. m.