Symbol, Examples, Pi Values | What Is Pi? - Cuemath

Value of Pi

The value of pi is the ratio of the circumference of a circle to its diameter. The pi symbol is denoted as π. It is also called Archimedes' constant which was named after the Greek mathematician, Archimedes, who created an algorithm to approximate the pi value. The value of pi is irrational, which means that the count of digits after the decimal point is infinite. It is used as either 3.1415929 or 22/7. In geometry, it is used in calculating the surface area, volume, and circumference of various three-dimensional shapes.

1.	What is the Value of Pi?
2.	Symbol for Pi
3.	Formula for Pi
4.	How to Calculate the Value of Pi?
5.	Value of Pi in Decimals
6.	Value of Pi in Fraction
7.	Value of Pi in Degree
8.	FAQs on Value of Pi

What is the Value of Pi?

The value of 'pi' is constant, which means it cannot be changed. It is an irrational number usually approximated to 3.14. It is used in various formulas for the measurement of surface area and volume of various solid shapes. 'Pi' is defined as the ratio of the circumference of the circle to the diameter of the circle. We know that the diameter of a circle is the longest line segment that passes through the center of the circle. Imagine the line of diameter is bent such that it covers a part of the circumference of the circle. Now, π is defined as the total number of times the diameter is wrapped around the circumference of the circle which is 3.14 times approximately.

If we divide the circumference by the diameter, we get approximately 3.14. It should be noted that no matter what size of a circle we draw, the ratio of the circumference to its diameter will always be the same.

Symbol for Pi

The symbol used to denote pi in math is π, which is used in Greek letters. It is known as a mathematical constant as its value does not change. The pi symbol represents 22/7 in fractions or 3.14 (approximately) in decimals.

Formula for Pi

The value of pi can be obtained by dividing the circumference of a circle by its diameter. Since pi is the ratio of the circumference of a circle to its diameter, the formula for calculating π is:

π = Circumference/Diameter

One interesting statement that helps us to remember the value of pi is "How I wish I could calculate pi". By counting the number of letters in each word, we can easily write the value of pi. Since 'How' has 3 letters; 'I' - 1 letter, 'wish' - 4 letters, 'I' - 1 letter, 'could' - 5 letters, 'calculate' - 9 letters, 'pi' - 2 letters. Therefore, the value of pi approximated to 6 decimal places is 3.141592.

How to Calculate the Value of Pi?

The value of pi can be calculated with the help of a simple activity. Follow the steps given below to know why the value of pi is the ratio of the circumference to the diameter of the circle:

• Step 1: Draw a circle of diameter 1 unit.
• Step 2: After this step, take a thread and place it along the border of the circle (the circumference).
• Step 3: Now, place the thread on the ruler and note the length.

Repeat the process with diameters of 2 units, 3 units, 4 units, 5 units, and record your observations in the table.

Diameter	Circumference	Circumference/Diameter
1 unit	3.1 units	3.1/1
2 units	6.2 units (approx.)	6.2/2 = 3.1
3 units	9.3 units (approx.)	9.3/3 = 3.1
4 units	12.4 units (approx.)	12.4/4 = 3.1
5 units	15.5 units (approx.)	15.5/5 = 3.1

We can observe that the ratio of circumference to diameter is always the same which is 3.1.

Value of Pi in Decimals

As discussed above, the value of pi is an irrational number, which means there are infinite decimal places after the number 3. The 100 decimal places of pi consist of all digits from 0 to 9. There are eight 0s, eight 1s, twelve 2s, eleven 3s, ten 4s, eight 5s, nine 6s, eight 7s, twelve 8s, and fourteen 9s. Observe the figure given below which shows that the value of pi in decimals starts with 3 and the 100th decimal digit holds the number 9.

The value of pi in decimals is non-terminating and non-recurring and is approximated to 100 decimal places as 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679. For ease of calculations, it is often approximated to 3.14.

Value of Pi in Fraction

The value of pi in fraction is 22/7. We know that the value of pi is an irrational number in which the digits after the decimal point are infinite. Therefore, to make calculations easier the value of pi is also defined in the form of a fraction and is expressed as 22/7.

Value of Pi in Degree

The value of pi in degree is 180 degrees, as π radians is equal to 180°. To understand this, we will be looking at the concept of radians which is the SI unit of measuring angles. We know that in a circle, one complete revolution makes the circumference of the circle. It means if we rotate by 360° around a point (known as the center of the circle) at a fixed distance (radius), we will get the circumference, which is equal to 2πr, where r denoted the radius of the circle. So, we can write, Circumference = 2πr = 360 degrees. And, for half a circle, the angle is 180° and the length of the arc will be 2πr/2 = πr. The formula of radians is arc length/radius. So, for half a circle, the arc length is πr and the radius is r.

⇒ πr/r radians = 180°

⇒ π radians = 180°

Therefore, the value of pi in degree is 180 degrees.

Important Notes:

Some important points about the pi symbol and value are given below:

• 'Pi' is a mathematical constant that is the ratio of the circumference of a circle to its diameter. It is an irrational number often approximated to 3.14159.
• Based on the problem, for ease of calculation, we use the value of pi as 22/7 or 3.14.
• A few basic circle formulas using pi are, a) Circumference = π × Diameter b) Area = πr2

► Related Topics

Check these interesting articles related to the value of pi in math.

• Pi Calculator
• Volume of Cylinder in Terms of Pi
• Volume of a Cone in Terms of Pi

Cuemath is one of the world's leading math learning platforms that offers LIVE 1-to-1 online math classes for grades K-12. Our mission is to transform the way children learn math, to help them excel in school and competitive exams. Our expert tutors conduct 2 or more live classes per week, at a pace that matches the child's learning needs.