Value of Pi

The value of Pi is approximately equal to 3.14159. It is defined as the ratio of circumference of a circle to it’s diameter. If we divide the total circumference of circle with the diameter of circle, then it will always in ratio of 22/7. Pi is denoted by the Greek symbol π.

Its exact value is unknown and can not be calculated by the available means as it is an irrational number, i.e. non-recurring and non-terminating decimal. We define the π as the ratio of the circumference to the diameter of a circle. It is a constant used widely in every branch of Science and Mathematics.

Even if the size of circle is same, the value of Pi will always be same. Finding the exact decimal values of the π is tedious. The value of π up to a million decimal places is found using supercomputers and advanced algorithms. For general use and convenience the value of π in fractions is assumed to be 22/7 and in decimal is assumed to be 3.1415926 . . .

What is Pi?

Pi is is a symbol used in  Mathematics. It is represented by the symbol π. It is a ratio of the Circumference of the Circle and the Diameter of the Circle. The value of Pi is an irrational number. Thus the exact value of the π is not found yet.

We can also define π as the total number of times the diameter is wrapped around the circumference of any circle. The approximate value of (π) pi is 3.14 or 22/7. The following illustration represents the value of pi and its relation with the circumference and diameter of the circle.

Pi Values in Fraction and Decimal

We usually express the value of Pi in two ways that are

• Value of Pi in Fraction
• Value of Pi in Decimal

Approximate Value of Pi

Below is the approx. value of pie in fraction and decimal form.

Value of Pi (π) in Fractions

The pi value can be approximated as the fraction of 22/7. It is known that pi is an irrational number which means that the digits after the decimal point are never-ending and are a non-terminating value. Therefore, 22/7 is used for everyday calculations. ‘π’ is not equal to the ratio of any two numbers, which makes it an irrational number.

The approximate value of Pi is the value of the Pi in fractions or up to 2 decimals places. As Pi is an irrational number its exact value is not known and so we take the approximate value of Pi in our calculation. The approximate value of Pi in terms of fractions is,

π = 22/7 (Approx)

Value of Pi (π) in Decimal

The approximate value of Pi in terms of decimals is

π = 3.14 (Approx)

The pi value up to the first 100 decimal places is:

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 . . .

Formula of Pi

The formula used to calculate the value of the Pi is

π = C/D

Where,

• C is the Circumference of the Circle
• D is the Diameter of the Circle

Using this formula we can easily get the value of pi, But as we know pi is an irrational number so its exact value is unknown and we can only find the approximate value of pi using this formula. The value of the Pi found using this formula is 3.14

Learn more

• Diameter of a Circle

How to Calculate the Value of Pi?

Pi is an irrational number and it has an infinite number of decimal values that are non-repeating,. There are various methods to calculate the value of pi up to a hundredth of a place The most common method to find the value of pi is taking the ratio of the Circumference of the circle to the diameter of the circle.

π = Circumference of Circle/Diameter of Circle

Thus, by drawing various circles and then taking the ratio of the Circumference and the diameter of the circle we get the value of the circle. The table added below shows the circumference of the circle, the diameter of the circle and their ratio as well.

Circumference(C)	Diameter(D)	C/D
3.1	1	3.1
6.24	2	3.12
9.378	3	3.126
12.5678	4	3.141
15.7075	5	3.1415

As we take higher values of circumference and diameter then we find to get the more accurate value of pi.

Different Values of Pi

Other then fractions and decimals there are some other values of Pi as well.

Value of Pi in Degree

The value of Pi in degrees can easily be found using the relation, of the ratio of circumference of the circle and the diameter of the circle. We know that the circumference of the circle is 2πr, and the diameter of the circle is 2r where r is the radius of the circle. Also, incase of the complete circle the angle subtended at the centre of the circle is 360°also we have two half circle in a circle that is divided by a diameter.

Now, then the ratio of the circumference and the diameter gives the value of pi.

2πr/2r = 360°/2

π radians = 180°

Solved Examples on Pi Value

Example 1: Find the circumference of a circle which has a radius of 12 cm.

Solution:

Given,

• Radius of Circle(r) = 12 cm

Circumfernce of Circle(C) = 2πr

Value of Pi = 3.14

⇒ C = 2 ⨉ (3.14) ⨉ (12)

⇒ C = 75.36 cm

Example 2: Find the area of a circle which has a radius of 8 cm.

Solution:

Given,

• Radius of Circle(r) = 8 cm

Area of Circle(A) = πr²

As, Value of Pi = 3.14

⇒ A = (3.14) ⨉ (8)²

⇒ A = 200.96 cm²

Example 3: Find the circumference and the area of the circle which has a radius of 9 cm.

Solution:

Given,

• Radius of Circle(r) = 9 cm

Circumfernce of Circle(C) = 2πr

Area of Circle(A) = πr²

As, Value of Pi = 3.14

⇒ C = 2 ⨉ (3.14) ⨉ (12)

⇒ C = 56.52 cm

⇒ A = π ⨉ (9)²

⇒ A = 254.34 cm²

Practice Problems on Value of Pi

Problem 1: Calculate the circumference of a circle with a radius of 5 units. [Circumference = 2πr.]

Problem 2: If the diameter of a circle is 12 inches, what is its circumference? [Use the formula C = πd.]

Problem 3: Given the area of a circle is 64 square meters, find the radius. [The formula for the area of a circle is A = πr².]

Problem 4: The side of a square is equal to the diameter of a circle. If the circle’s area is 144π square units, what is the side length of the square?

Problem 5: The Leibniz formula for π alternates signs in an infinite series: π/4 = 1 – 1/3 + 1/5 – 1/7 + 1/9 – . . . Calculate an approximation of π using the first 10 terms of this series.

Value of Pi – FAQs

What is Pi in Math?

Pi(π) in Mathematics is a constant in mathematics that has highest importance. It is used for various purposes, i.e it is used for finding the area of the circle, circumference of the circle, and for other puposes.

What is the Symbol of Pi?

Pi in mathematics is denoted using Greek letter, π.

What is the Decimal Value of Pi?

Pi(π) is an irrational number and it has a non-terminating and non-repeating dcimal value and its approximate value is, 3.1415926535 . . .

What is the Value of Pi in Fraction?

Value of Pi(π) is approximated in many rational numbers, such as 333/106, 355/113, 103993/33102, etc. But out of all these Fractions, the most popular one is 22/7 which approximates the value of Pi(π), up to 2 decimal places.

What is the Approximate Value of Pi?

The most famous approximation of Pi is 3.14(in decimals) and 22/7 (in fractions).

What is the Exact Value of Pi?

As Pi is an Irrational Number, we can’t find its exact value in the decimal form we can only approximate it to some certain number of digits.

Is Pi an Irrational Number?

Yes, Pi(π) is an Irrational Numebr as it’s decimal expansion is non-terminating and non-repeating.

Who Discovered the Value of Pi?

Archimedes of Syracuse is credited with one of the first calculations of the Value of Pi.

How is the Value of Pi Calculated?

As Pi can be defined as the ratio between the circumference and diameter of any circle, we can use measurements of any circle to approximately calculate the value of Pi.

Why is π = 22/7?

22/7 is the simplest approximation of Pi, which can approximate the value to 2 decimal Places. Thus, at the academic level, π = 22/7 is used.