Math & Numbers

The Math class provides the functions you need for calculations — powers, roots, rounding, minimums and maximums, random numbers — and BigDecimal handles exact decimal arithmetic for money. This lesson covers both, plus how to generate random values properly.

Common Math methods

JAVA

void main() {
    System.out.println(Math.max(4, 9));
    System.out.println(Math.min(-2, 3));
    System.out.println(Math.abs(-7.5));
    System.out.println(Math.pow(2, 10));
    System.out.println(Math.sqrt(144));
    System.out.println(Math.cbrt(27));
    System.out.println(Math.hypot(3, 4));
}

Output

9
-2
7.5
1024.0
12.0
3.0
5.0

Math methods are static — you call them on the class itself. Note that pow and sqrt always return a double.

Rounding

JAVA

void main() {
    double x = 7.45;
    System.out.println(Math.round(x));
    System.out.println(Math.floor(x));
    System.out.println(Math.ceil(x));
    System.out.println(Math.round(x * 10) / 10.0);
    System.out.println("%.1f".formatted(x));
}

Output

7
7.0
8.0
7.5
7.5

To round to decimal places for display, prefer formatting (%.1f). For calculations that must round exactly, use BigDecimal.

Constants and more functions

JAVA

void main() {
    double r = 2.0;
    System.out.println(Math.PI * r * r);
    System.out.println(Math.E);
    System.out.println(Math.floorMod(-7, 3));
    System.out.println(-7 % 3);
    System.out.println(Math.clamp(150, 0, 100));
}

Output

12.566370614359172
2.718281828459045
2
-1
100

% keeps the sign of the left operand; Math.floorMod always returns a non-negative result for a positive divisor — what you want for wrapping indexes. Math.clamp (Java 21+) keeps a value within a range. There are also trigonometric (sin, cos…), logarithmic (log, log10) and exact-arithmetic (addExact, multiplyExact) methods.

Random numbers

JAVA

void main() {
    var random = new java.util.Random(42);
    System.out.println(random.nextInt(1, 7));
    System.out.println(random.nextInt(1, 7));
    System.out.println(random.nextDouble() < 1.0);
}

Output

3
4
true

nextInt(origin, bound) returns a number from origin up to but excluding bound — here a dice roll from 1 to 6. Passing a seed (42) makes the sequence repeatable, which is useful for tests; leave it out for different numbers each run. Math.random() returns a double in [0, 1). For passwords and tokens, use java.security.SecureRandom.

BigDecimal for money

JAVA

import java.math.BigDecimal;
import java.math.RoundingMode;

void main() {
    System.out.println(0.1 + 0.2);

    BigDecimal a = new BigDecimal("0.1");
    BigDecimal b = new BigDecimal("0.2");
    System.out.println(a.add(b));

    BigDecimal price = new BigDecimal("19.99");
    BigDecimal withVat = price.multiply(new BigDecimal("1.23")).setScale(2, RoundingMode.HALF_UP);
    System.out.println(withVat);
}

Output

0.30000000000000004
0.3
24.59

BigDecimal stores decimal numbers exactly. Create values from strings (new BigDecimal("0.1")) — creating them from a double copies the binary rounding error. Arithmetic uses methods (add, subtract, multiply, divide), and setScale rounds to a number of decimal places with an explicit rounding rule.

BigInteger

JAVA

import java.math.BigInteger;

void main() {
    BigInteger factorial = BigInteger.ONE;
    for (int i = 2; i <= 30; i++) {
        factorial = factorial.multiply(BigInteger.valueOf(i));
    }
    System.out.println(factorial);
}

Output

265252859812191058636308480000000

BigInteger handles whole numbers of any size — 30! overflows even a long.

Try it yourself

Calculate monthly loan repayments with the standard formula.

Output

Monthly payment: 460.59
Total paid: 22108.12

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