Java Expressions and Operators

Real Java code rarely contains a single operator. A single line often combines arithmetic, comparisons, logical tests, and assignment, and each of those operators must be applied in some sequence. Before reading any further, try to predict the result of the following expression, working only from what you already know. Do not run anything yet.

If your prediction differed from 13, you have found the exact spot where your mental model and the language's rules disagree. The rest of this article explains the rules that decide the order, and shows how to read an expression without guessing.

Precedence is the rule that decides which operator is evaluated first when several operators appear in one expression without parentheses. The source describes precedence as a language-defined ranking, from highest to lowest, where higher-ranked operators are evaluated first. Java does not decide the order by reading position alone. The diagram below shows the nesting that Java applies to the expression from the opening question.

Read the tree from the bottom up. The multiplication 3 * 4 sits deepest, so it is completed first and produces 12. That result feeds the addition, giving 2 + 12, which is 14. The subtraction is the outermost operation, so it runs last and gives 14 - 1, which is 13. The tree shows nesting, but the same sequence can be written as three short steps.

The source presents the ranking as a table listing operators from highest precedence, which are evaluated first, to lowest precedence, which are evaluated last. Each row is a group of operators that share one precedence level, and higher rows bind more tightly than lower rows. Read the table from the top down. The source notes that the assignment operators sit at the bottom, which fits the logic of the ranking: the operators that compute values come before the operators that store them. The ranking covers the operators this section discusses, so treat it as the reference for those operators rather than a list of every Java operator.

Precedence answers one question: when the levels of two operators differ, which one binds more tightly? It does not decide anything when the operators share a level. That is the job of associativity, which is covered next.

Operators written on the same row of the ranking have the same precedence. When operators of one level are strung together without parentheses, precedence gives no preference between them. The second rule, associativity, decides the grouping. The source states it this way: unary operators and assignment operators are evaluated right-to-left, and the remaining operators are evaluated left-to-right.

Keep the two questions separate. Precedence asks which operator binds more tightly when the levels differ. Associativity asks how to group a chain when the levels are the same. Learners often make errors by answering the first question when the second was being asked.

The source gives the example A * B / C, which means (A * B) / C. Multiplication and division share a level, and neither is a unary or assignment operator, so the chain is grouped left-to-right. The multiplication is completed first, and its result is then divided by C. The diagram below applies the same left-to-right rule to a subtraction chain, where the grouping changes the answer.

Java groups 100 - 20 - 5 left-to-right, as (100 - 20) - 5. The first subtraction gives 80, and then 80 - 5 gives 75. If the operators were grouped right-to-left, the expression would instead be 100 - (20 - 5), which gives 85. The default grouping decides the answer, so a learner who assumes the wrong grouping gets a different result without any syntax error.

Assignment is the other case the source names, and it is grouped right-to-left. A = B = C is read as A = (B = C). The inner assignment runs first, and the value it produces is then assigned to A. The source asks a useful question here: because the value of B = C as an expression equals the value assigned to B, the form A = B = C can store one value in two variables at once. Think about what happens to a single value that must be stored in two places.

Parentheses let you replace the default grouping with the grouping you actually want. The operations inside parentheses are settled before the operators outside them. The source gives direct advice on this: if you do not use parentheses to indicate the order of evaluation, you must rely on the precedence rules, and to avoid confusing yourself or a reader, you should use parentheses liberally.

The comparison below shows what happens when the same numbers are combined with and without parentheses. The first column follows the default precedence rules. The second column forces the grouping the author might have intended, and the results diverge at the first step.

The two columns use the same numbers and the same operators, but the groupings differ. The unparenthesized line is evaluated as 2 + (3 * 4) - 1, giving 13. The parenthesized line forces the additions and subtractions to be settled first, giving 15. The divergence occurs at the first step: the unparenthesized version multiplies 3 by 4, while the parenthesized version adds 2 and 3. Locating that first differing step is the most reliable way to find where a surprising result came from.