What Is Pi (π) in Maths?

Pi (π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

The formula is:

π = Circumference ÷ Diameter

For every circle, no matter how large or small it is, this ratio remains the same.

The value of pi is approximately:

π ≈ 3.14159265359

For many school calculations, students commonly use:

π ≈ 3.14

or

π ≈ 22/7

However, 3.14 and 22/7 are approximations, not the exact value of π.

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Quick Answer: What Is Pi?

• Symbol: π

• Meaning: Ratio of circumference to diameter of a circle

• Approximate decimal value: 3.14159265359

• Common school approximation: 3.14

• Common fractional approximation: 22/7

• Type of number: Irrational number

What Is the Value of Pi (π)?

The exact value of π cannot be written as a terminating or repeating decimal.

Its decimal expansion begins:

π = 3.14159265358979323846...

The digits continue indefinitely without forming a repeating pattern.

Therefore:

π ≈ 3.14

is a rounded approximation, while

π ≈ 22/7

is a commonly used fractional approximation.

Important: Is 22/7 the Exact Value of Pi?

No.

22/7 is slightly greater than π.

In school mathematics, 22/7 is often used as an approximation because it makes some calculations easier, especially when the radius or diameter is a multiple of 7.

For example:

π ≈ 3.14159

while

22/7 ≈ 3.142857...

So, they are close but not exactly equal.

What Is the Full Value of Pi?

There is no finite “full decimal value” of π.

Pi is an irrational number, so its decimal expansion goes on forever without repeating.

The beginning of π is:

3.141592653589793238462643383279...

For most school calculations, only a few digits are needed.

Common Values of Pi

If a question specifically says use π = 22/7, use 22/7.

If it says use π = 3.14, use 3.14.

Read More: Parallelogram

What Does Pi (π) Mean?

Pi means the constant ratio between the circumference and diameter of any circle.

Suppose a circle has:

• Circumference = C

• Diameter = d

Then:

π = C/d

Therefore:

C = πd

Since diameter d = 2r, where r is the radius:

C = 2πr

This is why π appears in many formulas involving circles and curved surfaces.

Students can practise using π in circle-related calculations on CuriousJr to understand how the constant is used in circumference and other geometry formulas.

What Is the Pi Symbol?

The symbol for pi is:

π

It is the lowercase Greek letter pi.

The symbol π is widely used in mathematics, especially in geometry, trigonometry, calculus and other areas involving circles and periodic phenomena.

Who Introduced the π Symbol?

The symbol π was used by William Jones in 1706 to represent the circle constant. It was later popularised by mathematician Leonhard Euler.

The symbol is associated with the Greek word perimetros, meaning perimeter or circumference.

Why Is Pi an Irrational Number?

A number is irrational if it cannot be expressed exactly as a fraction of two integers.

Pi is irrational because its decimal expansion:

• Does not terminate.

• Does not repeat in a fixed pattern.

• Continues indefinitely.

So:

π ≠ 22/7 exactly

and

π ≠ 3.14 exactly

These are approximations used for calculations.

Read More: Binary to Octal Conversion

Pi (π) Formulas

Pi appears in many formulas involving circles and other curved shapes.

Circumference of a Circle

The circumference of a circle is:

C = 2πr

where:

• C = circumference

• r = radius

Using diameter:

C = πd

where d is the diameter.

Area of a Circle

The area of a circle is:

A = πr²

where r is the radius.

Volume of a Cylinder

The volume of a cylinder is:

V = πr²h

where:

• r = radius of the circular base

• h = height of the cylinder

Surface Area of a Sphere

The surface area of a sphere is:

SA = 4πr²

where r is the radius.

Volume of a Sphere

The volume of a sphere is:

V = 4/3 πr³

where r is the radius.

Volume of a Hemisphere

The volume of a hemisphere is:

V = 2/3 πr³

where r is the radius.

Pi Formula Quick Table

Pi (π) Examples

Example 1: Find the Circumference of a Circle

Find the circumference of a circle with radius 14 cm. Use π = 22/7.

Solution

Formula:

C = 2πr

Substitute the values:

C = 2 × 22/7 × 14

C = 88 cm

Answer:

The circumference is 88 cm.

Example 2: Find the Area of a Circle

Find the area of a circle with diameter 10 cm. Use π = 3.14.

Step 1: Find the radius

r = d/2

r = 10/2 = 5 cm

Step 2: Use the area formula

A = πr²

A = 3.14 × 5²

A = 3.14 × 25

A = 78.5 cm²

Answer:

The area is 78.5 cm².

Example 3: Find the Volume of a Sphere

Find the volume of a sphere with radius 3 cm. Use π = 3.14.

Solution

Formula:

V = 4/3 πr³

Substitute:

V = 4/3 × 3.14 × 3³

V = 4/3 × 3.14 × 27

V = 113.04 cm³

Answer:

The volume is approximately 113.04 cm³.

Why Is Pi Used in Circle Formulas?

A circle has a special relationship between its circumference and diameter.

For every circle:

Circumference ÷ Diameter = π

So:

Circumference = π × Diameter

Since:

Diameter = 2 × Radius

we get:

Circumference = 2πr

The area formula also contains π:

Area = πr²

This is why π appears throughout geometry whenever circles or curved surfaces are involved.

Pi (π) in Degrees and Radians

Pi is also important when measuring angles.

A complete revolution around a circle is:

360° = 2π radians

Dividing both sides by 2:

180° = π radians

Therefore:

π radians = 180°

This gives the common degree-radian conversions:

Example: Convert 45° to Radians

Use:

180° = π radians

Therefore:

45° = 45/180 × π

45° = π/4 radians

So:

45° = π/4 radians

How to Calculate the Value of Pi

You can estimate π experimentally by measuring the circumference and diameter of a circular object.

Step 1: Choose a circular object

For example, use a plate, lid or circular container.

Step 2: Measure its circumference

Use a thread to wrap around the circular edge.

Measure the length of the thread using a ruler.

Step 3: Measure the diameter

Measure the distance across the circle through its centre.

Step 4: Divide circumference by diameter

Use:

π ≈ Circumference ÷ Diameter

For example, if:

• Circumference ≈ 31.4 cm

• Diameter ≈ 10 cm

then:

π ≈ 31.4 ÷ 10

π ≈ 3.14

The result will be close to π. Measurement errors can prevent an experiment from giving many accurate decimal places.

Why Does Pi Have So Many Digits?

Pi is an irrational number, so its decimal expansion never ends and does not repeat.

For example:

3.14159265358979323846...

There is no final decimal digit that completes the number.

Computers can calculate trillions of digits of π, but those are still only digits from its continuing decimal expansion. They do not represent a final “full decimal value.”

For ordinary school calculations, a small number of digits is usually enough.

Interesting Facts About Pi

• The symbol for pi is π.

• Pi is an irrational number.

• Pi is approximately 3.14159.

• The ratio of a circle's circumference to its diameter is π.

• 22/7 is a commonly used approximation of π, not its exact value.

• Pi is used in formulas for circles, cylinders, spheres and many other mathematical applications.

• Pi Day is observed on March 14 (3/14) in many places because the date resembles the first three digits of π, 3.14.

Applications of Pi (π)

Pi is used far beyond basic circle calculations.

Geometry

Pi is used to calculate:

• Circumference

• Area of circles

• Surface area of spheres

• Volume of cylinders

• Volume of spheres

• Other measurements involving curved shapes

Engineering

Engineers use π when working with circular parts such as:

• Wheels

• Pipes

• Gears

• Rotating components

Architecture and Construction

Pi is useful when designing and measuring:

• Domes

• Arches

• Circular structures

• Cylindrical structures

Science

Pi appears in many mathematical formulas used in physics, astronomy and other sciences.

Technology

Pi is also used in areas such as signal processing, mathematics, computer graphics and engineering calculations.

Common Mistakes About Pi

Mistake 1: Saying π = 22/7 exactly

Incorrect: π = 22/7

Better: π ≈ 22/7

22/7 is an approximation.

Mistake 2: Saying π = 3.14 exactly

Incorrect: π = 3.14

Better: π ≈ 3.14

3.14 is a rounded approximation.

Mistake 3: Confusing radius and diameter

Remember:

d = 2r

and

r = d/2

Mistake 4: Using the wrong area formula

The area of a circle is:

A = πr²

not:

A = 2πr

The formula 2πr gives the circumference.

Mistake 5: Writing π as a degree value

π itself is not “180°.”

The correct relationship is:

π radians = 180°

Quick Revision of Pi (π)

• π = Circumference ÷ Diameter

• π ≈ 3.14159265359

• π ≈ 3.14 for many basic calculations

• π ≈ 22/7 as a common fractional approximation

• π is an irrational number

• π is represented by the Greek letter π

• C = 2πr

• A = πr²

• V of cylinder = πr²h

• Surface area of sphere = 4πr²

• Volume of sphere = 4/3πr³

• π radians = 180°