Java Math Class
Last modified: April 13, 2025
The java.lang.Math class provides static methods for performing
various mathematical operations. These include exponential, logarithmic,
trigonometric, rounding, and random number functions. Since all methods
are static, the class cannot be instantiated.
The Math class works with primitive types like double and
int. For applications requiring higher precision, consider
using BigDecimal, which offers better accuracy for financial
calculations and scientific computations.
This class also defines two essential constants: Math.PI, the
mathematical constant for π (~3.14159), and Math.E, the base of
the natural logarithm (~2.71828). These constants are widely used in geometry,
physics, and numerical analysis.
Math Class Overview
The Math class provides methods for basic arithmetic, trigonometry, exponentiation, logarithms, rounding, and random number generation. Since all methods are static and thread-safe, they can be used without object creation and are safe for concurrent operations.
This class belongs to the java.lang package, meaning it's automatically imported in all Java programs, allowing immediate access to its functionalities without explicit import statements.
Basic Arithmetic Operations
The Math class provides methods for basic arithmetic operations like absolute value, maximum/minimum values, and square roots. These methods are optimized for performance and handle edge cases properly.
package com.zetcode;
public class Main {
public static void main(String[] args) {
// Absolute value
int absValue = Math.abs(-15);
System.out.println("Absolute value of -15: " + absValue);
// Maximum and minimum
int max = Math.max(10, 20);
int min = Math.min(10, 20);
System.out.println("Max of 10 and 20: " + max);
System.out.println("Min of 10 and 20: " + min);
// Square root
double sqrt = Math.sqrt(25);
System.out.println("Square root of 25: " + sqrt);
// Power
double power = Math.pow(2, 3);
System.out.println("2 raised to power 3: " + power);
}
}
This example demonstrates basic arithmetic operations. Math.abs
returns the absolute value, Math.max/min compare values,
Math.sqrt calculates square roots, and Math.pow
handles exponents. All methods are straightforward to use.
Trigonometric Functions
The Math class provides standard trigonometric functions including sine, cosine,
and tangent. These methods take angles in radians. For degree conversion, use
Math.toRadians or Math.toDegrees.
package com.zetcode;
public class Main {
public static void main(String[] args) {
// Convert 30 degrees to radians
double radians = Math.toRadians(30);
System.out.println("30 degrees in radians: " + radians);
// Trigonometric functions
double sinValue = Math.sin(radians);
double cosValue = Math.cos(radians);
double tanValue = Math.tan(radians);
System.out.println("Sine of 30°: " + sinValue);
System.out.println("Cosine of 30°: " + cosValue);
System.out.println("Tangent of 30°: " + tanValue);
// Inverse trigonometric functions
double asinValue = Math.asin(sinValue);
System.out.println("Arcsine of sin(30°): " +
Math.toDegrees(asinValue) + "°");
}
}
This example shows trigonometric operations. We first convert degrees to radians, then calculate sine, cosine, and tangent. The inverse functions return results in radians which we convert back to degrees for readability.
Exponential and Logarithmic Functions
The Math class provides methods for exponential and logarithmic calculations.
Math.exp computes e^x, while Math.log computes
natural logarithms (base e). For base 10 logarithms, use Math.log10.
package com.zetcode;
public class Main {
public static void main(String[] args) {
// Exponential function
double expValue = Math.exp(1);
System.out.println("e^1: " + expValue);
System.out.println("Math.E: " + Math.E);
// Natural logarithm
double logValue = Math.log(Math.E);
System.out.println("ln(e): " + logValue);
// Base 10 logarithm
double log10Value = Math.log10(100);
System.out.println("log10(100): " + log10Value);
// Combining operations
double result = Math.pow(2, Math.log10(100));
System.out.println("2^log10(100): " + result);
}
}
This example demonstrates exponential and logarithmic functions. We show the
relationship between Math.exp and Math.log, and how
they relate to the constant Math.E. The example also shows how to
combine these operations with other Math methods.
Rounding Methods
The Math class provides several rounding methods with different behaviors.
Math.round performs standard rounding, while Math.ceil
always rounds up and Math.floor always rounds down.
package com.zetcode;
public class Main {
public static void main(String[] args) {
double num1 = 3.4;
double num2 = 3.6;
double num3 = -3.4;
// Standard rounding
System.out.println("Round 3.4: " + Math.round(num1));
System.out.println("Round 3.6: " + Math.round(num2));
// Ceiling (round up)
System.out.println("Ceil 3.4: " + Math.ceil(num1));
System.out.println("Ceil -3.4: " + Math.ceil(num3));
// Floor (round down)
System.out.println("Floor 3.6: " + Math.floor(num2));
System.out.println("Floor -3.4: " + Math.floor(num3));
// Truncate using casting
System.out.println("Truncate 3.6: " + (int) num2);
}
}
This example shows different rounding approaches. Math.round follows
standard rounding rules, while Math.ceil and Math.floor
always round in specific directions. The example also shows how casting can be
used for truncation.
Random Number Generation
The Math.random method generates pseudorandom numbers between 0.0
(inclusive) and 1.0 (exclusive). For more control over random numbers, consider
using the Random class from java.util package.
package com.zetcode;
public class Main {
public static void main(String[] args) {
// Simple random number
double random1 = Math.random();
System.out.println("Random between 0 and 1: " + random1);
// Random number in range
int min = 10;
int max = 20;
int randomInRange = (int) (Math.random() * (max - min + 1)) + min;
System.out.println("Random between 10 and 20: " + randomInRange);
// Multiple random numbers
System.out.println("\nFive random numbers:");
for (int i = 0; i < 5; i++) {
System.out.println(Math.random());
}
}
}
This example demonstrates random number generation. We show how to get a simple random number and how to scale it to a specific range. The formula for range scaling is important for practical applications of random numbers.
Mathematical Constants
The Math class provides two important mathematical constants: Math.PI
(π) and Math.E (base of natural logarithms). These constants are
defined with high precision and are useful in many mathematical calculations.
package com.zetcode;
public class Main {
public static void main(String[] args) {
// Circle calculations using PI
double radius = 5.0;
double circumference = 2 * Math.PI * radius;
double area = Math.PI * Math.pow(radius, 2);
System.out.println("Circle with radius 5:");
System.out.println("Circumference: " + circumference);
System.out.println("Area: " + area);
// Exponential growth using E
double initial = 100;
double rate = 0.05;
double time = 10;
double finalAmount = initial * Math.exp(rate * time);
System.out.println("\nExponential growth:");
System.out.println("Initial: " + initial);
System.out.println("Final after 10 years at 5%: " + finalAmount);
}
}
This example shows practical uses of mathematical constants. We calculate circle
properties using Math.PI and model exponential growth using
Math.E. These constants are essential for many scientific and
engineering calculations.
Advanced Mathematical Operations
The Math class also provides more advanced operations like hyperbolic functions, angle conversions, and IEEE remainder. These methods are useful for specialized mathematical computations.
package com.zetcode;
public class Main {
public static void main(String[] args) {
// Hyperbolic functions
double x = 1.0;
System.out.println("sinh(1.0): " + Math.sinh(x));
System.out.println("cosh(1.0): " + Math.cosh(x));
System.out.println("tanh(1.0): " + Math.tanh(x));
// IEEE remainder
System.out.println("\nIEEE remainder:");
System.out.println("IEEEremainder(10, 3): " +
Math.IEEEremainder(10, 3));
System.out.println("10 % 3: " + (10 % 3));
// Copy sign
System.out.println("\nCopy sign:");
System.out.println("copySign(5.0, -1.0): " +
Math.copySign(5.0, -1.0));
System.out.println("copySign(-5.0, 1.0): " +
Math.copySign(-5.0, 1.0));
}
}
This example demonstrates advanced Math class operations. Hyperbolic functions
are similar to trigonometric functions but based on hyperbolas. The IEEE
remainder differs from the modulo operator in how it handles negative numbers.
copySign is useful for manipulating number signs.
Source
In this article, we've covered all major methods of the Java Math class with practical examples. These methods provide essential mathematical operations that are fundamental to many programming tasks.
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