A bit simplified you can think of it as arrays being a special case and not ordinary classes (a bit like primitives, but not). String and all the collections are classes, hence the methods to get size, length or similar things.

I guess the reason at the time of the design was performance. If they created it today they had probably come up with something like array-backed collection classes instead.

If anyone is interested, here is a small snippet of code to illustrate the difference between the two in generated code, first the source:

public class LengthTest {
  public static void main(String[] args) {
    int[] array = {12,1,4};
    String string = "Hoo";
    System.out.println(array.length);
    System.out.println(string.length());
  }
}

Cutting a way the not so important part of the byte code, running javap -c on the class results in the following for the two last lines:

20: getstatic   #3; //Field java/lang/System.out:Ljava/io/PrintStream;
23: aload_1
24: arraylength
25: invokevirtual   #4; //Method java/io/PrintStream.println:(I)V
28: getstatic   #3; //Field java/lang/System.out:Ljava/io/PrintStream;
31: aload_2
32: invokevirtual   #5; //Method java/lang/String.length:()I
35: invokevirtual   #4; //Method java/io/PrintStream.println:(I)V

In the first case (20-25) the code just asks the JVM for the size of the array (in JNI this would have been a call to GetArrayLength()) whereas in the String case (28-35) it needs to do a method call to get the length.

In the mid 1990s, without good JITs and stuff, it would have killed performance totally to only have the java.util.Vector (or something similar) and not a language construct which didn't really behave like a class but was fast. They could of course have masked the property as a method call and handled it in the compiler but I think it would have been even more confusing to have a method on something that isn't a real class.

length is constant which is used to find out the array storing capacity not the number of elements in the array

Example:

int[] a = new int[5]

a.length always returns 5, which is called the capacity of an array. But

number of elements in the array is called size

Example:

int[] a = new int[5]
a[0] = 10

Here the size would be 1, but a.length is still 5. Mind that there is no actual property or method called size on an array so you can't just call a.size or a.size() to get the value 1.

The size() method is available for collections, length works with arrays in Java.

You can use the java.lang.instrumentation package.

It has a method that can be used to get the implementation specific approximation of object size, as well as overhead associated with the object.

The answer that Sergey linked has a great example, which I'll repost here, but you should have already looked at from his comment:

import java.lang.instrument.Instrumentation;

public class ObjectSizeFetcher {
    private static Instrumentation instrumentation;

    public static void premain(String args, Instrumentation inst) {
        instrumentation = inst;
    }

    public static long getObjectSize(Object o) {
        return instrumentation.getObjectSize(o);
    }
}

Use getObjectSize:

public class C {
    private int x;
    private int y;

    public static void main(String [] args) {
        System.out.println(ObjectSizeFetcher.getObjectSize(new C()));
    }
}

Source