Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation, or simply postfix notation, is a mathematical notation in which operators follow their operands, in contrast to Polish notation (PN), in which operators precede their operands. It does not need any parentheses as long as each operator has a fixed number of operands. The description "Polish" refers to the nationality of logician Jan Łukasiewicz, who invented Polish notation in 1924.

In reverse Polish notation, the operators follow their operands. For example, to add 3 and 4 together, the expression is 3 4 + rather than 3 + 4. The expression 3 − 4 + 5 in conventional notation is 3 4 − 5 + in reverse Polish notation: 4 is first subtracted from 3, then 5 is added to it.

The concept of a stack, a last-in/first-out construct, is integral to the left-to-right evaluation of RPN. In example 3 4 -, first the 3 is put onto the stack, then the 4; the 4 is now on top and the 3 below it. The subtraction operator removes the top two items from the stack, performs 3 - 4, and puts the result of -1 onto the stack.

The common terminology is that added items are pushed on the stack and removed items are popped.

The advantage of reverse Polish notation is that it removes the need for an order of operations and parentheses that are required by infix notation and can be evaluated linearly, left to 
right.
For example, the infix expression (3 × 4) + (5 × 6) becomes 3 4 × 5 6 × + in reverse Polish notation.