Java's Primitive Data Types

boolean: 1-bit. May take on the values true and false only.

byte: 1 signed byte (two's complement). Covers values from -128 to 127.

short: 2 bytes, signed (two's complement), -32,768 to 32,767

int: 4 bytes, signed (two's complement). -2,147,483,648 to 2,147,483,647.

long: 8 bytes signed (two's complement). Ranges from -9,223,372,036,854,775,808 to +9,223,372,036,854,775,807.

float: 4 bytes, IEEE 754. Covers a range from 1.40129846432481707e-45 to 3.40282346638528860e+38 (positive or negative).

double: 8 bytes IEEE 754. Covers a range from 4.94065645841246544e-324d to 1.79769313486231570e+308d (positive or negative).

char: 2 bytes, unsigned, Unicode, 0 to 65,535

write the float into a ByteArrayOutputStream and get the length of the result.

import java.io.*;
class Test
    {
    public static void main(String[] args)  throws Exception
        {

        ByteArrayOutputStream baos =new ByteArrayOutputStream();
        DataOutputStream dos=new DataOutputStream(baos);
        dos.writeFloat(0f);
        System.err.println(baos.toByteArray().length);
        }
    }

$ javac Test.java 
$ java Test 
4

The Wikipedia page on it is a good place to start.

To sum up:

• float is represented in 32 bits, with 1 sign bit, 8 bits of exponent, and 23 bits of the significand (or what follows from a scientific-notation number: 2.33728*10¹²; 33728 is the significand).

• double is represented in 64 bits, with 1 sign bit, 11 bits of exponent, and 52 bits of significand.

By default, Java uses double to represent its floating-point numerals (so a literal 3.14 is typed double). It's also the data type that will give you a much larger number range, so I would strongly encourage its use over float.

There may be certain libraries that actually force your usage of float, but in general - unless you can guarantee that your result will be small enough to fit in float's prescribed range, then it's best to opt with double.

If you require accuracy - for instance, you can't have a decimal value that is inaccurate (like 1/10 + 2/10), or you're doing anything with currency (for example, representing $10.33 in the system), then use a BigDecimal, which can support an arbitrary amount of precision and handle situations like that elegantly.

• float stores floating-point values, that is, values that have potential decimal places
• int only stores integral values, that is, whole numbers

So while both are 32 bits wide, their use (and representation) is quite different. You cannot store 3.141 in an integer, but you can in a float.

Dissecting them both a little further:

In an integer, all bits except the leftmost one are used to store the number value. This is (in Java and many computers too) done in the so-called two's complement, which support negatives values. Two's complement uses the leftmost bit to store the positive (0) or negative sign (1). This basically means that you can represent the values of −2³¹ to 2³¹ − 1.

In a float, those 32 bits are divided between three distinct parts: The sign bit, the exponent and the mantissa. They are laid out as follows:

S EEEEEEEE MMMMMMMMMMMMMMMMMMMMMMM

There is a single bit that determines whether the number is negative or non-negative (zero is neither positive nor negative, but has the sign bit set to zero). Then there are eight bits of an exponent and 23 bits of mantissa. To get a useful number from that, (roughly) the following calculation is performed:

M × 2^E

(There is more to it, but this should suffice for the purpose of this discussion)

The mantissa is in essence not much more than a 24-bit integer number. This gets multiplied by 2 to the power of the exponent part, which, roughly, is a number between −128 and 127.

Therefore you can accurately represent all numbers that would fit in a 24-bit integer but the numeric range is also much greater as larger exponents allow for larger values. For example, the maximum value for a float is around 3.4 × 10³⁸ whereas int only allows values up to 2.1 × 10⁹.

But that also means, since 32 bits only have 4.2 × 10⁹ different states (which are all used to represent the values int can store), that at the larger end of float's numeric range the numbers are spaced wider apart (since there cannot be more unique float numbers than there are unique int numbers). You cannot represent some numbers exactly, then. For example, the number 2 × 10¹² has a representation in float of 1,999,999,991,808. That might be close to 2,000,000,000,000 but it's not exact. Likewise, adding 1 to that number does not change it because 1 is too small to make a difference in the larger scales float is using there.

Similarly, you can also represent very small numbers (between 0 and 1) in a float but regardless of whether the numbers are very large or very small, float only has a precision of around 6 or 7 decimal digits. If you have large numbers those digits are at the start of the number (e.g. 4.51534 × 10³⁵, which is nothing more than 451534 follows by 30 zeroes – and float cannot tell anything useful about whether those 30 digits are actually zeroes or something else), for very small numbers (e.g. 3.14159 × 10⁻²⁷) they are at the far end of the number, way beyond the starting digits of 0.0000...