The Java programming language supports basic arithmetic with its arithmetic operators: +, -, *, /, and %. TheMath
class in thejava.lang
package provides methods and constants for doing more advanced mathematical computation.The methods in the
Math
class are all static, so you call them directly from the class, like this:Math.cos(angle);
Note: Using thestatic import
language feature, you don't have to writeMath
in front of every math function:This allows you to invoke theimport static java.lang.Math.*;Math
class methods by their simple names. For example:cos(angle);Constants and Basic Methods
TheMath
class includes two constants:The
Math.E
, which is the base of natural logarithms, andMath.PI
, which is the ratio of the circumference of a circle to its diameter.Math
class also includes more than 40 static methods. The following table lists a number of the basic methods.
Basic Math Methods Method Description double abs(double d)
float abs(float f)
int abs(int i)
long abs(long lng)Returns the absolute value of the argument. double ceil(double d)
Returns the smallest integer that is greater than or equal to the argument. Returned as a double. double floor(double d)
Returns the largest integer that is less than or equal to the argument. Returned as a double. double rint(double d)
Returns the integer that is closest in value to the argument. Returned as a double. long round(double d)
int round(float f)Returns the closest long or int, as indicated by the method's return type, to the argument. double min(double arg1, double arg2)
float min(float arg1, float arg2)
int min(int arg1, int arg2)
long min(long arg1, long arg2)Returns the smaller of the two arguments. double max(double arg1, double arg2)
float max(float arg1, float arg2)
int max(int arg1, int arg2)
long max(long arg1, long arg2)Returns the larger of the two arguments. The following program,
BasicMathDemo
, illustrates how to use some of these methods:Here's the output from this program:public class BasicMathDemo { public static void main(String[] args) { double a = -191.635; double b = 43.74; int c = 16, d = 45; System.out.printf("The absolute value of %.3f is %.3f%n", a, Math.abs(a)); System.out.printf("The ceiling of %.2f is %.0f%n", b, Math.ceil(b)); System.out.printf("The floor of %.2f is %.0f%n", b, Math.floor(b)); System.out.printf("The rint of %.2f is %.0f%n", b, Math.rint(b)); System.out.printf("The max of %d and %d is %d%n",c, d, Math.max(c, d)); System.out.printf("The min of of %d and %d is %d%n",c, d, Math.min(c, d)); } }The absolute value of -191.635 is 191.635 The ceiling of 43.74 is 44 The floor of 43.74 is 43 The rint of 43.74 is 44 The max of 16 and 45 is 45 The min of 16 and 45 is 16
Exponential and Logarithmic Methods
The next table lists exponential and logarithmic methods of theMath
class.
Exponential and Logarithmic Methods Method Description double exp(double d)
Returns the base of the natural logarithms, e, to the power of the argument. double log(double d)
Returns the natural logarithm of the argument. double pow(double base, double exponent
Returns of value of the first argument raised to the power of the second argument. double sqrt(double d)
Returns the square root of the argument. The following program,
ExponentialDemo
, displays the value ofe
, then calls each of the methods listed in the previous table on arbitrarily chosen numbers:Here's the output you'll see when you runpublic class ExponentialDemo { public static void main(String[] args) { double x = 11.635; double y = 2.76; System.out.printf("The value of e is %.4f%n", Math.E); System.out.printf("exp(%.3f) is %.3f%n", x, Math.exp(x)); System.out.printf("log(%.3f) is %.3f%n", x, Math.log(x)); System.out.printf("pow(%.3f, %.3f) is %.3f%n", x, y, Math.pow(x, y)); System.out.printf("sqrt(%.3f) is %.3f%n", x, Math.sqrt(x)); } }ExponentialDemo
:The value of e is 2.7183 exp(11.635) is 112983.831 log(11.635) is 2.454 pow(11.635, 2.760) is 874.008 sqrt(11.635) is 3.411Trigonometric Methods
TheMath
class also provides a collection of trigonometric functions, which are summarized in the following table. The value passed into each of these methods is an angle expressed in radians. You can use thetoDegrees
method to convert from degrees to radians.
Trigonometric Methods Method Description double sin(double d)
Returns the sine of the specified double value. double cos(double d)
Returns the cosine of the specified double value. double tan(double d)
Returns the tangent of the specified double value. double asin(double d)
Returns the arcsine of the specified double value. double acos(double d)
Returns the arccosine of the specified double value. double atan(double d)
Returns the arctangent of the specified double value. double atan2(double y, double x)
Converts rectangular coordinates (x, y)
to polar coordinate(r, theta)
and returnstheta
.double toDegrees(double d)
double toRadians(double d)Converts the argument to degrees or radians. Here's a program,
TrigonometricDemo
, that uses each of these methods to compute various trigonometric values for a 45-degree angle:The output of this program is as follows:public class TrigonometricDemo { public static void main(String[] args) { double degrees = 45.0; double radians = Math.toRadians(degrees); System.out.format("The value of pi is %.4f%n", Math.PI); System.out.format("The sine of %.1f degrees is %.4f%n", degrees, Math.sin(radians)); System.out.format("The cosine of %.1f degrees is %.4f%n", degrees, Math.cos(radians)); System.out.format("The tangent of %.1f degrees is %.4f%n", degrees, Math.tan(radians)); System.out.format("The arcsine of %.4f is %.4f degrees %n", Math.sin(radians), Math.toDegrees(Math.asin(Math.sin(radians)))); System.out.format("The arccosine of %.4f is %.4f degrees %n", Math.cos(radians), Math.toDegrees(Math.acos(Math.cos(radians)))); System.out.format("The arctangent of %.4f is %.4f degrees %n", Math.tan(radians), Math.toDegrees(Math.atan(Math.tan(radians)))); } }The value of pi is 3.1416 The sine of 45.0 degrees is 0.7071 The cosine of 45.0 degrees is 0.7071 The tangent of 45.0 degrees is 1.0000 The arcsine of 0.7071 is 45.0000 degrees The arccosine of 0.7071 is 45.0000 degrees The arctangent of 1.0000 is 45.0000 degrees
Random Numbers
Therandom()
method returns a pseudo-randomly selected number between 0.0 and 1.0. The range includes 0.0 but not 1.0. In other words:0.0 <= Math.random() < 1.0
. To get a number in a different range, you can perform arithmetic on the value returned by the random method. For example, to generate an integer between 1 and 10, you would write:By multiplying the value by 10, the range of possible values becomesint number = (Math.random() * 10).intValue();0.0 <= number < 10.0
. The compiler boxes the primitive double, (Math.random() * 10), which is then converted to a primitive in with theintValue()
method of theDouble
class.Using
Math.random
works well when you need to generate a single random number. If you need to generate a series of random numbers, you should create an instance ofjava.util.Random
and invoke methods on that object to generate numbers.