Calculating with Math APIs

Overview

The java.lang.Math class provides static utility methods for common mathematical operations. Because it is in java.lang, no import is needed. All methods are static — you call them directly on the class.

java
double result = Math.sqrt(16.0); // no import needed

Minimum and Maximum

Math.min and Math.max compare two values and return the smaller or larger one. They are overloaded for int, long, float, and double.

java
System.out.println(Math.min(10, 20));    // 10
System.out.println(Math.max(10, 20));    // 20
System.out.println(Math.min(3.5, 3.1)); // 3.1
System.out.println(Math.max(-5, -3));   // -3

Absolute Value

Math.abs returns the non-negative magnitude of a number.

java
System.out.println(Math.abs(-7));    // 7
System.out.println(Math.abs(7));     // 7
System.out.println(Math.abs(-3.14)); // 3.14

Note: Math.abs(Integer.MIN_VALUE) returns Integer.MIN_VALUE (still negative) due to integer overflow. This is an exam-tested edge case.

Rounding Methods

java
System.out.println(Math.round(2.4));  // 2
System.out.println(Math.round(2.5));  // 3
System.out.println(Math.round(-2.5)); // -2 (rounds toward positive infinity)

System.out.println(Math.ceil(3.1));   // 4.0
System.out.println(Math.ceil(-3.9));  // -3.0

System.out.println(Math.floor(3.9));  // 3.0
System.out.println(Math.floor(-3.1)); // -4.0

Math.round returns long when given a double, and int when given a float.

Power and Square Root

java
System.out.println(Math.pow(2, 10));  // 1024.0  (2 to the power of 10)
System.out.println(Math.pow(9, 0.5)); // 3.0     (square root via fractional exponent)
System.out.println(Math.sqrt(25.0));  // 5.0
System.out.println(Math.sqrt(2.0));   // 1.4142135623730951

Math.pow(base, exponent) always returns a double.

Random Numbers

Math.random() returns a double in the range [0.0, 1.0) — inclusive of 0.0, exclusive of 1.0.

java
double rand = Math.random();      // e.g. 0.7341...

// Integer in range [0, n-1]
int d6 = (int)(Math.random() * 6);  // 0 to 5

// Integer in range [1, n]
int die = (int)(Math.random() * 6) + 1; // 1 to 6

For production code, prefer java.util.Random or java.security.SecureRandom, but know Math.random() for the exam.

Mathematical Constants

java
System.out.println(Math.PI);  // 3.141592653589793
System.out.println(Math.E);   // 2.718281828459045  (base of natural logarithm)

Logarithms and Trigonometry

These are less commonly tested but worth recognising:

java
Math.log(Math.E);    // 1.0  (natural logarithm)
Math.log10(1000);    // 3.0
Math.sin(Math.PI/2); // 1.0
Math.cos(0);         // 1.0

Quick Reference Table

Practical Example

java
public class CircleCalculator {
    public static double area(double radius) {
        return Math.PI * Math.pow(radius, 2);
    }

    public static double hypotenuse(double a, double b) {
        return Math.sqrt(Math.pow(a, 2) + Math.pow(b, 2));
    }

    public static void main(String[] args) {
        System.out.printf("Area: %.2f%n", area(5));           // Area: 78.54
        System.out.printf("Hypotenuse: %.2f%n", hypotenuse(3, 4)); // Hypotenuse: 5.00
    }
}

Exam Tips

• All Math methods are static — call them as Math.methodName(...).
• Math.round(-2.5) returns -2, not -3 — it rounds toward positive infinity.
• Math.ceil and Math.floor return double, even though the value is a whole number (3.0, not 3).
• Math.pow always returns double; cast to int or long if needed.
• Math.random() range is [0.0, 1.0) — 0.0 can occur, 1.0 cannot.