1.11 - Math Class

The Math class lives in the java.lang package, and everything in java.lang is available automatically, no import needed. Every method in Math is a class method (static).

Here are the ones on the AP Java Quick Reference:


static int abs(int x)            // absolute value of an int
static double abs(double x)      // absolute value of a double
static double pow(double base, double exponent)  // base raised to exponent
static double sqrt(double x)     // non-negative square root
static double random()           // random double, 0.0 <= x < 1.0

A few details that show up on the exam:

Math.abs is overloaded. Give it an int and you get an int back, give it a double and you get a double back. Math.abs(-7) is 7, but Math.abs(-7.5) is 7.5.

Math.pow and Math.sqrt always return a double, even when the answer is a whole number. Math.pow(2, 3) is 8.0 and Math.sqrt(16) is 4.0.

Because of that, int x = Math.pow(2, 3); won’t compile. You need a cast: int x = (int) Math.pow(2, 3); stores 8.

Math calls can go inside bigger expressions, even inside other Math calls. For a right triangle with legs 3 and 4:


double a = 3;
double b = 4;
double hyp = Math.sqrt(Math.pow(a, 2) + Math.pow(b, 2)); // Math.sqrt(9.0 + 16.0) = 5.0

Example usage:


int a = Math.abs(-7);       // 7
double p = Math.pow(2, 3);  // 8.0
double s = Math.sqrt(16.0); // 4.0
double r = Math.random();   // some value like 0.372

You can manipulate Math.random() with arithmetic and casting to get a random int or double within a specific range. Just keep track of whether each endpoint is inclusive (included) or exclusive (not included).


// random int from 0 to 9 (inclusive)
int randomNum = (int)(Math.random() * 10);

// random int from 1 to 6 (inclusive), like a die roll
int diceRoll = (int)(Math.random() * 6) + 1;

Here’s how the dice roll works, one step at a time:

Math.random() gives a double from 0.0 up to, but not including, 1.0.

Multiplying by 6 stretches that to a double from 0.0 up to, but not including, 6.0.

Casting to int truncates it to 0, 1, 2, 3, 4, or 5.

Adding 1 shifts it to 1, 2, 3, 4, 5, or 6.

In general, to get a random int from min to max (both inclusive), multiply by how many values are possible and add the smallest one:


int n = (int) (Math.random() * (max - min + 1)) + min;

// random int from 5 to 15 inclusive (11 possible values)
int r = (int) (Math.random() * 11) + 5;

For a random double, skip the cast. Math.random() * 5 + 10 gives a double from 10.0 (inclusive) up to 15.0 (exclusive).

Careful with parentheses: (int) Math.random() * 6 is always 0. The cast happens first, and since Math.random() is less than 1.0, it truncates to 0. Then 0 times 6 is 0.

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