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1. Introduction

The Math class in Java provides built-in mathematical functions such as:

power and square root
rounding methods
absolute value
min/max comparisons
trigonometry (sin, cos, tan)
random number generation

It belongs to java.lang, so it is automatically available without importing anything.

Most methods in Math are:

static
pure functions (no object state)
used directly as Math.methodName(...)

2. Why Math Class Exists

In real projects, you frequently need mathematical operations without writing custom logic repeatedly.

Math class helps by providing:

tested, optimized implementations
readable and clean code
common operations in one place

Example:

int max = Math.max(10, 20);
double root = Math.sqrt(25);

3. Basic Usage Pattern

You do not create object of Math.

// Math m = new Math(); // Not allowed (Math has private constructor)

You call methods directly:

double p = Math.pow(2, 5);
System.out.println(p); // 32.0

4. Commonly Used Methods

4.1 abs()

Returns absolute value.

System.out.println(Math.abs(-10)); // 10
System.out.println(Math.abs(5));   // 5

4.2 max() and min()

Returns maximum / minimum.

System.out.println(Math.max(10, 20)); // 20
System.out.println(Math.min(10, 20)); // 10

4.3 pow()

Returns a raised to the power of b.

System.out.println(Math.pow(3, 2)); // 9.0
System.out.println(Math.pow(2, 10)); // 1024.0

Note: Return type is double.

4.4 sqrt()

Returns square root.

System.out.println(Math.sqrt(49)); // 7.0

4.5 cbrt()

Returns cube root.

System.out.println(Math.cbrt(27)); // 3.0

5. Rounding Methods (Very Important)

Rounding is common in billing systems, discounts, stats, etc.

5.1 round()

Rounds to nearest integer.

System.out.println(Math.round(4.4)); // 4
System.out.println(Math.round(4.6)); // 5

round(float) returns int
round(double) returns long

5.2 ceil()

Rounds up to next integer (returns double).

System.out.println(Math.ceil(4.1)); // 5.0
System.out.println(Math.ceil(4.0)); // 4.0

5.3 floor()

Rounds down to previous integer (returns double).

System.out.println(Math.floor(4.9)); // 4.0
System.out.println(Math.floor(4.0)); // 4.0

6. Trigonometry Methods

All trig methods take angles in radians, not degrees.

Common methods:

sin(), cos(), tan()
toRadians(), toDegrees()

Example:

double angle = Math.toRadians(90);
System.out.println(Math.sin(angle)); // close to 1.0

7. Random Numbers Using Math.random()

Math.random() returns a double in range:

0.0 (inclusive) to 1.0 (exclusive)

Example:

double r = Math.random();
System.out.println(r);

Generating random integer between 0 and 9:

int n = (int)(Math.random() * 10);
System.out.println(n);

If you need better control, use java.util.Random (covered separately).

8. Constants in Math Class

Math provides some important constants:

Math.PI → value of π
Math.E → value of Euler’s number

Example:

System.out.println(Math.PI);
System.out.println(Math.E);

9. Practical Example: Bill Rounding

Suppose you have a bill amount and want to round it up to the next integer.

double bill = 149.2;
int payable = (int) Math.ceil(bill);
System.out.println(payable); // 150

This is common in pricing systems.

10. Common Mistakes

10.1 Confusing ceil() and round()

round(4.1) → 4
ceil(4.1) → 5

10.2 Forgetting radians in trigonometry

System.out.println(Math.sin(90)); // wrong if you expect 1

Correct:

System.out.println(Math.sin(Math.toRadians(90)));

10.3 Assuming pow() returns int

Math.pow() returns double, so type casting might be needed.

11. Summary

Math class is in java.lang and is automatically available.
All methods are static, so you call them as Math.method().
Common methods: abs, min, max, pow, sqrt, round, ceil, floor.
Trigonometric functions use radians.
Math.random() generates a value between 0.0 and 1.0.
Very useful for real-world calculations and rounding.

Written By: Shiva Srivastava

Math Class

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