This interface imposes a total ordering on the objects of each class that implements it. This ordering is referred to as the class's natural ordering, and the class's compareTo method is referred to as its natural comparison method.

Lists (and arrays) of objects that implement this interface can be sorted automatically by Collections.sort (and Arrays.sort). Objects that implement this interface can be used as keys in a sorted map or as elements in a sorted set, without the need to specify a comparator.

The natural ordering for a class C is said to be consistent with equals if and only if e1.compareTo(e2) == 0 has the same boolean value as e1.equals(e2) for every e1 and e2 of class C. Note that null is not an instance of any class, and e.compareTo(null) should throw a NullPointerException even though e.equals(null) returns false.

It is strongly recommended (though not required) that natural orderings be consistent with equals. This is so because sorted sets (and sorted maps) without explicit comparators behave "strangely" when they are used with elements (or keys) whose natural ordering is inconsistent with equals. In particular, such a sorted set (or sorted map) violates the general contract for set (or map), which is defined in terms of the equals method.

For example, if one adds two keys a and b such that (!a.equals(b) && a.compareTo(b) == 0) to a sorted set that does not use an explicit comparator, the second add operation returns false (and the size of the sorted set does not increase) because a and b are equivalent from the sorted set's perspective.

Virtually all Java core classes that implement Comparable have natural orderings that are consistent with equals. One exception is java.math.BigDecimal, whose natural ordering equates BigDecimal objects with equal numerical values and different representations (such as 4.0 and 4.00). For BigDecimal.equals() to return true, the representation and numerical value of the two BigDecimal objects must be the same.

For the mathematically inclined, the relation that defines the natural ordering on a given class C is:

{(x, y) such that x.compareTo(y) <= 0}.

The quotient for this total order is:

{(x, y) such that x.compareTo(y) == 0}.

It follows immediately from the contract for compareTo that the quotient is an equivalence relation on C, and that the natural ordering is a total order on C. When we say that a class's natural ordering is consistent with equals, we mean that the quotient for the natural ordering is the equivalence relation defined by the class's equals(Object) method:

    {(x, y) such that x.equals(y)}. 

In other words, when a class's natural ordering is consistent with equals, the equivalence classes defined by the equivalence relation of the equals method and the equivalence classes defined by the quotient of the compareTo method are the same.

This interface is a member of the Java Collections Framework.