Resurrecting the HP41cx

Hi Everone,

This is the first discussion I have done since I started this group. I know there are many of you that have used this calculator in the past and some may still do.

Whether or not, if it is the real calculator or an emulator on a device.There are PC's and phone emulators in use today for all types for this calculator.

This was one of my favorite calculators as we all saw the three verisons of it.The 41c,cv,and the cx. All three of these were used by NASA in the space programs.

It was the first time that I had used the alphanumeric RPN calculator. This is the most advanced RPN written that consisted of or was using both letters and numerals

in math or programming on the calculator.There may be more data and information or programming than any other calculator sold to the public to this date.

This was a dream come true when surveyors first got their hands on them with the survey Mod Surveying PAC, which plugs into the calculator. Not just surveyors used these 

Calculators and there MODS. There is a very large list of mods available, even extra memory and Quad memory mods. There was a large list of accessories available.

Printers, wands and many other peripherals. Even bar code programs. I will talk about these as time goes on. But now I will talk about some of the first steps in using this calculator

in manual mode.Manually using keystrokes to Traverse then Inverse. Without further adieu, here is Traverse.

HP 41CX Traverse manually without statistics registers using storage Registers

1. First store North in Reg.07

2.Next store East in REG.04

3.Next key in Azimuth in Decimal of a Degree then ENTER

4.Next key in Distance,but do not ENTER

5.Next key in P to R......., polar to rectangular

6.Next sto + 07

7.Next X to Y

8.Next sto + 04

9.Next RCL 07=New North

10.Next RCL 04 = New East

Now your ready for the next leg.

And no program used,  Traversing with the HP41

Most all RPN calculators can traverse like this or similar in this way.

Now Traversing using Statistics Registers

1. First clear all statistics Reg.,this can be done with a hard key or alpha keys.

This hard Key is a gold key above the X to Y, so shift gold and  CL acc. symbol..

Now you are ready, the statistics registers are 11 thru 16 ( I will list them later with their values.)

You will only use two of them that is 11 and 13, (11 is the summation of the X- values.)

(13 is the summation of the Y- values), so 11 will be the Eastings or Dep's and 13 will be Northings or Lat's

2.Now you are ready to store in them,so (5000) sto 11 and sto 13 reg's (as a example.)

If you like also store North in 07 and East in 04 as POB with 13 North and 11 East.

This way you can always RCL, POB or it can be also used as occupied PT.

3. Next key in Azimuth in Decimals of a degree,then ENTER.

4.Next key in Distance,but do not ENTER.

5. Next key in P to R,.......... polar to rectangular

6.Next Key in X to Y.

7. Next key in accumulation + key just above the X to Y key

and the number 1.0 will be in the display, the next time you will see 2.0 and so on.

8.Next recall RCL regs. 11 for the New Easting and regs.13 for the New Northing

9. Now you ready for the next leg of the traverse.

and that is how you can traverse using Statistics Registers.



Now on to Inversing, This is how I was taught. and it can be done different using RPN or algebraically

but this has always work for me. Algebraically the East 1 is subtracted  from East 2 and North 1 is subtracted from North 2

in most formulas used but RPN  is always backwards to other types of calculators as it seems to me..  But on to it.

1. East 1 or occupied looking at East 2

E1 - E2, so 

Key in East 1 ENTER.

2.Key in East 2 do not ENTER.

3. - (minus)

4. North 1 or occupied looking at North 2


Key in North 1 ENTER,

Key in North 2,do not ENTER

5.- (minus)

6. Now go Polar that is R to P

7.Distance will be in display

8.Next X to Y ,Azimuth will be in display

9.Next add 180 degrees and solved Azimuth will be in Display.

as in 180 +

When using bearings or Azimuth always make sure of your direction.

Most of my Inverse programs use these same steps.

Everyone solves math and writes programs differently.

Next I will show  how to write these simple programs.

traversing and Inversing programs on the HP41cx.

And compare them with other RPN Calculators.





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  •  Hi Everyone,

    Where is your calculator? Are the batteries dead? Is it covered in dust or placed deep somewhere in your desk the last time you saw it?

    I know computers have made it easy to answer yes to all these questions. And computers are more or just important as calculators.They even run the 

    emulators of the calculators that are important to us, old and new models alike. I could not believe my eyes the first time I saw a HP41cx emulator.

    How is this possible? Computers. Computers and calculators they both have played an important role on how a surveyor worked, as well as Total Station

    and GPS. Drones and Scanners are now becomming the norm for surveyors. All this integrated into each other, so who needs a calculator? I hope everyone!

    Once I was asked by a young engineer, I am taking my exam, I have to know how to solve a vertical curve on a calculator. I was told to ask you because no one at this large 

    Surveying/Engineering firm could help him. Yes we had all the new tech Gadgets that included Data collectors and GPS. But I was the only PC that also used calculators, so I helped him program his calculator

    for that and many other programs he needed as well as equations. Mastering your calculator does not have to be all programs. And students can not take there laptops to the exam room.

    NCEES calculators only and a small list of them. So can this only be taught in school? And if calculators are not important in a surveyors role everyday. Whats next computers at the exam ?

    Is this the direction we are headed too. I hope not. That young engineer could not thank me enough. as well as other young surveyors I have helped. It was all because no one used calculators

    around them. I hope I made an impression on them.  So on to the simple Traverse programs in resurrecting the HP41cx and comparing it to other RPN calculators.


    How to run the programs.

    Both these programs the HP33s and the HP 35s are programs asking for input. I have also shown one for the HP41cx.

    All three will work similar by XEQ the program. Once the program has been entered press GTO .. ,that's GTO dot,dot .

    This packs and sets the program to the top of the catalog on all three calculators.This also clears null bites and places the programs

    where they are protected from being changed by accidental input on program lines. This is also a good practice to do this

    everytime your're done running a program or before you turn it off.


    The 33s you XEQ T or  the label you used, same with the 35s but it will be XEQ T001 ( this can be XEQ T ENTER) because of indirectly accessing program lines.

    The HP41cx uses Alpha inputs. It will be XEQ alpha TRCX alpha. It also has indirectly accessing program lines, but it is also alphanumeric .

    The indirectly access memory or lines is the big difference between the HP33s and the HP35s.

    Once you have XEQ (executed) the program you will see the first input ( N1 ?) north 1

    Input IT and press run/stop R/S, next the second input (E 1?) east 1

    Input IT and press run/stop R/S, next the third input  ( A ? ) azimuth 

    input it and press run/stop R/S , next the forth input ( D ? ) Horizontal Distance

    Now press run/stop R/S and the program runs with your  new North and new East.

    Now the 33s and the 35s have a two line display. It depends on how the program is wrote and

    what will be displayed in the lines X and Y on the stack,(TZYX) This is all in what you want and how

    this works. Your answer could be one line or two lines at one time the north and the east at the same time.

     I will go over this later on. The HP41cx has only one display line so it will take two R/S to see the new North

    then the new East. Unfortunately, if you do not have a HP 33s the emulators are hard to find and that is only from HP.

    The HP35s and the HP41cx emulators  have many downloads available. If you do have a HP33s it best to keep it

    for they now sell for 300 to 600 dollars and the same for the HP41cx or even higher pricing.

    As I said the HP35s is a bargin @ $60.00 it is no 41 but it is the next best thing.

    Next on to inversing with these three calculators plus the HP 42s and the HP32s ii and the list goes on.


  • Hi Everyone,

    The small program I showed for √a² +b² is a HP25E program. This is a Rrp Register recall program.They were used when program memory was small .

    The 25 only had 49 lines to write a program and only one program at a time and you could not save the program. So the shorter you wrote the programs 

    the better off you were. The HP 65 worked the same but you could program it using a card. The calculator had a card reader so the  programs could be installed fast.

    Even if you had to turn it off there was no problem to reprogram it. But still all memory in the register was gone. CMOS changed all of this and it wasn't long the HP 25C

    came out as well as all other models. I showed this type of programming on the 41CX just as a compare of having the program ask for INPUT. Not because the HP41cx

    had little memory. This is not the case for it. You could also store ASCII files on the HP41cx also program files in this catalog. There are 6 catalogs on the calculator.

    The HP41cx could also program with bar codes and could use a card reader plus use MOD plugins plus could be attached to aTotal Station data input ,output

    data connection.This was the beginning of Data collection This is how surveying begin to evolve to where it is today. Lets compare 2 other HP calculators that came later with a simple Azimuth Traverse.

    These two are nowhere near being equivalent to the HP41cx, the only RPN calculator that can do that is the HP42s. It has been said it may be the ultimate RPN calculator.

    But that is another story. So here a simple Azimuth traverse in the HP 33s and the HP 35s, the only two HP's you can take your EXAM with, if that is the case.

    HP 33s Program T

    01.LBL T

    02.INPUT N........North

    03.INPUT E.......East

    04.INPUT A.......AZ

    05.INPUT D........H Dist

    06.RCL A

    07.→ HR........ go decimals of a degree

    08.RCL D

    09.Θ,r →y,x.......go rectangular

    10.RCL+ N

    11.STO N

    12.X ↔Y


    14.STO E

    15.GTO T

    16.RTN........return to program beginning


    This is a simple basic program and does what it is intended to do still no whistles or bells but it works.

    If you notice I used RCL + instead of STO + but as you see I used STO on the next line.

    Now the HP 35s the calculator that is still being made today and cost less.The HP33 and the HP41cx or a HP42s will cost you big bucks today.

    And they are used also. So here is AZ Traverse  simple again but asking for INPUTS

    HP 35s Program T

    01.LBL T001

    02.INPUT N........North

    03.INPUT E........East

    04.INPUT A........AZ

    05.INPUT D........H Dist

    06.RCL A

    07 HMS →......go decimals of a degree

    08.RCL D

    09. X↔Y..........Begin subroutine to go rectangular



    12.LAST X

    13 SIN


    15. x or *........(times)


    17.LAST X

    18. x or*.........(times).....End subroutine

    19.STO + N

    20. X↔Y

    21. STO + E

    22.RCL N

    23 .STOP

    24. RCL E

    25. STOP

    26.  GTO T001.....End program return to beginning


    Why did I need a subroutine,( a program inside a program) because the HP 35 does not have Polar to Rectangular Key, it can use complex numbers 

    or a program to solve this and there are many different versions of these programs to do this, but this is one of the simple one's.

    This is one I wrote it does not use any equations or use a varable (Storage  register) no matter what the stack does.

    It is simple and works. But there are many wrote that does not change the STACK using equations in the program lines.

    The HP 35s is a amazing calculator for 60 bucks. There is a lot more that can be done to improve this program

    or any that I have showed for any of these calculators but these are the foundations of what will come next. 

    In this neverending story of RPN calculators and how important they are then and now in surveying.

    And how the HP41cx stands up to the test of time.

    Next I will show how to RUN these two Programs and how to write inverse in them and compare inverse with the HP41cx.




    Hi Everyone,

    In about 1970 HP co-founder Bill Hewlett challenged his co-workers to create a "shirt-pocket sized HP-9100". At the time, slide rules were the only practical portable devices for performing trigonometric and exponential functions, as existing pocket calculators could only perform addition, subtraction, multiplication, and division. Introduced at $395 (equivalent to $2,366 in 2018),[2] Like HP's first scientific calculator, the desktop 9100A, it used Reverse Polish Notation (RPN) rather than what came to be called "algebraic" entry. The "35" in the calculator's name came from the number of keys.

    The original HP-35 was available from 1972 to 1975. In 2007 HP announced the release of the "retro"-look HP 35s in commemoration of the original HP-35..

    The HP-35 was named an IEEE Milestone in 2009.

    The calculator used a traditional floating decimal display for numbers that could be displayed in that format, but automatically switched to scientific notation for other numbers. The fifteen-digit LED display was capable of displaying a ten-digit mantissa plus its sign and a decimal point and a two-digit exponent plus its sign. The display used a unique form of multiplexing, illuminating a single LED segment at a time rather than a single LED digit, because HP research had shown that this method was perceived by the human eye as brighter for equivalent power. Light emitting diodes were relatively new at the time and were much dimmer than high efficiency diodes developed in subsequent decades.

    The calculator used three "AA"-sized NiCd batteries assembled into a removable proprietary battery pack. Replacement battery packs are no longer available, leaving existing HP-35 calculators to rely on AC power, or their users to rebuild the battery packs themselves using available cells. An external battery charger was available and the calculator could also run from the charger, with or without batteries installed.

    Internally, the calculator was organized around a serial (one-bit) processor chipset made under contract by Mostek, processing 56-bit floating-point numbers, The  HP-35 was Hewlett-Packard's first pocket calculator and the world's first scientific pocket calculator[1] – a calculator with trigonometric and exponential functions.Like what has been said,the worlds first.I still have my slide rule. Now what came next will change everything. What's that Programming. MY first programable calculator was the HP 25 E.

    It did not have CMOS, constance memory operating system,so when you turned it off so went everything in the memory. The HP25 was a cheaper version of the HP65 that could read memory program cards. The HP25 you had to key stroke all the programs and it only had 49 lines of program memory. So programs were wrote with that in mind. Most of these were call Register recall Prog. Or Rrp. for short. This would shorten the programs to make sure you would not run out of lines. For example a²+b² √ or √ a² + b² which is used a lot in surveying, but this could not be wrote as an equation at that time on a calculator. So I will write it as a program. Kept in mind you could only have one program at a time on the calculator.

    00 Clear prgm.

    01  RCL 1

    02 X²

    03 RCL 2

    04 X²

    05 +

    06 √ x

    07 R/s

    08 RTN....... Return to line 01 to begain new data.

     And here how all this worked. Lets store 3 in 1 and 4 in 2. Now Run the program.

    Press GSB 01, this will XEQ on program line 01  ( Go to subroutine) GSB

    program runs and your answer is  5.0 the program recalls 1 and x² it, then recalls 2 and X² it, then adds the two ,then takes the square root of this product then you see the answer as the final product.

    This is how a Register Recall program works you, Enter the data in the registers before you run the program. Now I will minic the manual input by recalling the registers that I have already stored

    in the registers first. This is as simple as it gets to write a traverse program in any RPN calculator or this Alphanumeric RPN.

    Traverse program Rrp in the HP41cx , name it what you like. I will call this one TRCC. This calculator does have upper and lower case but Global Labels are upper case.

    01.LBL TRCC

    02.LBL 00

    03. RCL 07....... North

    04.RCL 04.........East

    05. RCL 01.........AZ


    07. RCL 02........H Dist.

    08. P → R

    09.STO + 07

    10. X ↔ Y

    11.STO +04

    12.RCL 07........New North

    13.STOP or R/S

    14.RCL 04........New East

    15.STOP or R/S

    16.GTO 00...... return to LBL 00

    17. END........end of program

    Now that took seventeen lines to mimic the manual input on the same calculator. Now I will write the program asking for the INPUT, still  a mimic of the manual input.

    You can also recall all the data in the registers or ENTER new data to solve next leg of the Traverse.

    This I will call TRCX on the HP 41cx. Traverse.

    01.LBL TRCX

    02.LBL 00

    03.N 1 ?


    05.STO 07

    06. E 1 ?


    08.STO 04

    09. AZ ?

    10. PROMPT

    11.STO 01

    12. H Dist ?


    14.STO 02

    15. RCL 01

    16.→ HR

    17.RCL 02

    18.P→ R

    19.ST + 07

    20.X↔ Y

    21.ST + 04

    22.RCL 07.........New North

    23.STOP or R/S

    24.RCL 04.........New East

    25.STOP or R/S

    26.GTO 00........return to LBL 00

    27.END.........end of program

    That took twenty seven lines to add INPUT's and all that I showed  have been Azimuth Traverse programs.

    Next I will show the same programs on the HP 33s and the HP 35s using Inputs like this, that also ask for input. These two are in RPN only.

    When I am talking about the HP 41's and also the HP 42s these calculators use Alphanumeric RPN programming.Consisting of or using 2224781196?profile=RESIZE_710xboth letters and numerals. There are other brands that mimic these type calculators being made and sold today.

    Hp has shorten it's list of RPN calculators, the HP 35s remains the only one being made that you can take your survey EXAM with. The HP 33s and the HP 35 are the only HP's you can use. The calculator on the Right is the one that stated it all the 1972 HP 35 it only had 35 keys and that is how it got it's name. The New HP 35s

    only cost 60.00 Dollars +/- what a bargin.

    It cost 395 dollars back then.






    Bill Hewlett
    William Redington Hewlett ( HEW-lit; May 20, 1913 – January 12, 2001) was an American engineer and the co-founder, with David Packard, of the Hewlett…
  • Party Chief

    nice post Billy!

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