RPN looks strange for about ten minutes. There's no equals key, and the plus key comes after the numbers. Then it clicks, and the old way starts to feel slow. This guide gets you there in an hour with any RPN calculator. The keystrokes below work on an HP 12C, an HP-11C, a 15C or a 32SII, with small differences in where the shifted keys sit.
The idea in one sentence
You enter the numbers first, then the operation. To add 3 and 4, you type 3, press ENTER, type 4 and press +. The display shows 7. That's the whole trick. ENTER separates one number from the next, and an operation key like +, minus, times or divide works on the last two numbers right away, so there's never anything waiting to be finished.
The stack
An HP keeps your numbers in a stack of four registers, named X, Y, Z and T from the bottom. X is the one on the display. When you press ENTER, the number in X is copied up into Y, and everything above moves up one, with the top value falling off T. When you type a new number after ENTER, it replaces the copy in X. When you press +, the calculator adds Y and X, puts the answer in X, and drops everything above down a level.
Try it with 3 ENTER 4 +. After 3 ENTER, X and Y both hold 3. Typing 4 puts 4 in X, with 3 still in Y. Pressing + adds them and leaves 7 in X. Four levels sound small, but they're plenty, because RPN always works on the newest numbers first.
Where it comes from
The Polish in the name is the logician Jan Łukasiewicz, who invented Polish notation in 1924, which puts the operation before the numbers. RPN turns it around and puts the operation last. HP's 9100A desktop calculator of 1968 used it with a three-level stack, and the HP-35 of 1972, the first handheld scientific calculator, brought the four-level X, Y, Z and T stack you'll find on every model here. HP Journal explained the point at the time: each operation runs the moment you press it, and the numbers it works on are always at the bottom of the stack. Through the 1970s and 1980s, HP used RPN in all its calculators.
Chained sums, with no parentheses
This is where RPN pays off. Work out (3 + 4) times (5 + 6):
- 3 ENTER 4 + gives 7.
- 5 ENTER 6 + gives 11. The 7 is still waiting in Y.
- Times gives 77.
You never typed a parenthesis, and you saw the two halves as you went, so a typing slip shows up at once. Try the length of a diagonal, the square root of 3 squared plus 4 squared:
- 3 ENTER times gives 9. ENTER copies 3 into Y, and times multiplies the two copies.
- 4 ENTER times gives 16, with the 9 still in Y.
- Plus gives 25, and the square root key gives 5.
The habit to build is working from the inside out, the way you'd do it on paper. Each finished piece sits in the stack until the next operation uses it.
Four keys that make it easy
x<>y swaps X and Y. Use it when the numbers are in the wrong order for subtraction or division. Say 0.25 is on the display and you want 1 minus 0.25. Type 1, press x<>y, then minus. The answer is 0.75.
Roll down, marked R with a down arrow, turns the stack one level, so you can look at what's in Y, Z and T. Four presses bring you back where you started, with nothing lost.
LAST X brings back the number that was in X before the last operation. It's handy for reusing a number. Work out 14 divided by 7, then 21 divided by 7: type 14 ENTER 7 and divide to get 2, then type 21, press LAST X to bring back the 7, and divide again to get 3. On a 12C it's the shifted function on the ENTER key. The 12C Platinum moved it to the + key.
CHS changes the sign of the number you're typing. Pressing minus always subtracts on an RPN calculator, so you use CHS to make a number negative.
Percent
An HP's percent key leaves the base number in Y, so the next step is often one key. Find 15 percent of 200 and add it on: type 200 ENTER 15 and press the percent key. The display shows 30, the 15 percent, and 200 is still in Y. Press + and you get 230. To take it off instead, press minus and you get 170. On a 12C the delta-percent key gives the percent change from Y to X the same way.
A loan payment on a 12C
The 12C puts time value of money across its top row: n for the number of periods, i for the interest rate per period, PV for present value, PMT for the payment and FV for future value. You fill in the ones you know and press the one you want. For a loan of 200,000 over 30 years at 6 percent a year, paid monthly:
- Press f then CLx (CLEAR REG) to clear the registers.
- Type 360 and press n, for 360 months. The shifted 12x key on n does the multiplying for you if you type 30 instead.
- Type 6, press g, then the 12 divided key on i. That stores 0.5 percent a month.
- Type 200000 and press PV.
- Press PMT. The display shows -1,199.10, the monthly payment.
The minus sign is the 12C's cash-flow convention. Money you receive is positive and money you pay out is negative, so the loan comes in and the payments go out. Change any one value and press another key to solve for it, like FV to see what's left after a number of payments. This is why the 12C is still made, and why the CFA Institute still allows it in the exam room. See calculators for the CFA exam.
Common slips
- Pressing ENTER before an operation. You only need ENTER between two numbers you type one after the other. 3 ENTER 4 + is right. 3 ENTER 4 ENTER + adds 4 and 4.
- Using minus for a negative number. Use CHS after typing the number.
- Clearing too much. CLx clears only X, so you can retype a wrong number without losing the stack.
- Mixing modes. The 12C Platinum and the 17BII switch between RPN and algebraic entry. Check which mode it's in, since the same keystrokes give different answers. Wikipedia notes the Platinum's change-sign key also behaves a little differently from the 12C's in RPN.
Which calculator to learn on
Pick the one that fits the work you'll do with it:
- For finance: the HP 12C. It's still made, so a used one is easy to find, and it's allowed on the CFA exam.
- For a simple scientific: the HP-11C, a Voyager with a full scientific keyboard and programming.
- For a pocket scientific with a solver: the HP 32SII.
- For the classic 15C with modern speed: the 15C Limited Edition, which runs the original firmware at least 150 times faster, or the Collector's Edition.
Our calculators for learning RPN page lists them together. Whichever you buy, run it through the condition checklist first, since a key that registers twice will make RPN look much harder than it is.
Your first hour
Spend ten minutes on simple sums, saying the stack out loud as you go. Spend twenty on chained sums from a textbook or your own work, inside out, without writing anything down. Spend ten playing with x<>y, roll down and LAST X until you reach for them without thinking. If you have a 12C, spend the last twenty on loans and savings, changing one value at a time. By the end, the equals key you're used to will feel like the extra step.
