What is RPN?

Reverse Polish Notation puts the operation after the numbers it works on. Instead of 3 + 4 =, you key 3 ENTER 4 +.

Where it came from

Polish notation was devised in the 1920s by the logician Jan Łukasiewicz, who put operators before their operands to do away with parentheses. Reversing it, operators after operands, suits a machine with a stack. Desktop and handheld calculators adopted it in the 1960s and 70s, and financial calculators built on it became standard equipment in banking, real estate and corporate finance.

How it works

An RPN calculator keeps a stack of four registers, X, Y, Z and T. Numbers go onto the stack, and each operation takes its inputs from the bottom of the stack and leaves its result there. Because results stay on the stack, you rarely need to write anything down or use memory registers for a chain of calculations.

There are no parentheses: the order you press the keys is the order the work is done. There’s no equals key: every operation completes the moment you press it, so you see each intermediate result.

Why it’s still used

Fewer keystrokes, fewer mistakes from mismatched parentheses, and a clear view of each step. For financial work, the stack also passes results straight into the financial keys: subtract a down payment and press PV, with no retyping.

Generations of finance courses and handbooks give their answers as RPN keystrokes, which is why many people who learned it keep using it.

Try it

The RPN basics guide walks through a first calculation, keystroke by keystroke.