Formula Forensics No. 041 – Convert a Roman Numeral to a Number

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Last week in the Chandoo.org Forums a user asked a question

How do I convert a Roman Numeral to a Number eg: MMMCCCLVII to 3357

User Xlstime presented the solution of:

=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)

Today we are going to look at how and why that simple formula works

As always at Formula Forensics you can follow along using a sample file: Download Sample File

Solution

Excel has a Roman function wherein =Roman(3357, 0) will return MMMCCCLVII

I knew there was no such reverse Roman function prior to Excel 2013 and so my initial thought was to look at a VBA Solution.

See notes on the Arabic Excel function at the end of the post.

However Xlstime presented =MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)

How does this work?

lets start by pulling it apart from the inside out

=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)

The Indirect Function simply takes its inputs and converts them to a Range, in this case 1:3999.

We will study why 3999 later

=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)

The next function working out is Row()

Excel will convert the function ROW(INDIRECT(“1:3999”)) to an array of Row Numbers

={1;2;3;4;5;6;7;8;9;10;11; …. 3995;3996;3997;3998;3999}

You can see this if you goto cell D7 in the Sample File, press F2 and then F9

I limited the numbers to 300 as Excel cannot display more than 8,192 digits

Stepping out one more function:

=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)

The Roman() function converts its inputs into Roman Numbers

eg: Roman(58) will return LVIII

But as we are feeding it an array of numbers from 1 to 3999 Excel handles all these and converts them to an Array of Roman Numbers

Goto  D9 in the sample file =ROMAN(ROW(INDIRECT(“1:300”))) press F2 and then F9

Excel returns an array of roman numbers

={“I”;”II”;”III”;”IV”;”V”;”VI”;”VII”;”VIII”; … “CCXCVI”;”CCXCVII”;”CCXCVIII”;”CCXCIX”;”CCC”}

We have limited the example to 300 as Excel cannot display more than 8,192 characters when processing  a Function using F9.

 

Stepping out one more function

=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)

The Excel Index() function is taking the Array of Roman Numerals and Converting it into a single Column array

This isn’t technically needed but it simplifies the solution

If you goto cell D11 in the sample file =INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0) press F2 and then F9

Excel returns an array of roman numbers

={“I”;”II”;”III”;”IV”;”V”;”VI”;”VII”;”VIII”; … “CCXCVI”;”CCXCVII”;”CCXCVIII”;”CCXCIX”;”CCC”}

This is exactly the same as the previous output from the Roman() function above, Except that it is now a Single Vertical Array.  This is important for the next function.

 

Stepping out one more function

=MATCH(A2,INDEX(ROMAN(ROW(INDIRECT(“1:3999”))),0),0)

We can see here that the Array of Roman Numerals is now being fed into a Match() function.

Match uses the Syntax =Match(Lookup value, Lookup Array, Match Type)

Match returns the position of the Lookup value within the array

So in our example

The Lookup value is A2 or our Roman Numeral MMMCCCLVII

The Lookup Array is an array of Roman Numerals from 1 to 3999

={“I”;”II”;”III”;”IV”;”V”;”VI”;”VII”;”VIII”; … “MMMCMXCV”; “MMMCMXCVI”; “MMMCMXCVII”; “MMMCMXCVIII”; “MMMCMXCIX”}

and the Match Type is 0 or an exact Match

So the Match function will lookup the value MMMCCCLVII in the array and find it in position number 3357, which happens to correspond to the Number of the Roman Numeral and Return 3357 as the result.

Why are we limited to 3999 numbers.

The Excel Roman() function is limited to numbers up to 3999

roman01

Why 3999?

Because in Roman Numerals there is no Letter for 5,000 and 4,000 would be shown as M before the Letter for 5,000.

 

Why did we need the Index() function?

If you goto D17 in the sample file you will see the formula:

=MATCH(A2,ROMAN(ROW(INDIRECT(“1:3999”))),0)

It is the same formula as above but without the Index() function

You will see that it is returning a #VALUE! error

If you edit the formula with F2 and then press F9 to process the function you will see it now shows 3357

What s happening here?

Pressing F9 is the same as Array Entering the Function

so if you edit the function pressing F2 and now Array Enter the function by pressing Ctrl+Shift+Enter, excel now returns 3357

The Index() function puts a wrapper around the array for processing by the Match() function and so Array Entering is avoided.

Most array formulas that require Ctrl+Shift+Enter can be rewritten incorporating an INDEX wrapper and will not require the Ctrl+Shift+Enter confirmation.

The Excel Arabic Function

In 2013, Microsoft introduced the Arabic function to Excel

To use simply use =Arabic(A2) or =Arabic(“MMMCCCLVII”)

You can read about the Syntax of the function in the Excel Help.

roman03roman04

Download

You can download a copy of the above file and follow along, Download Sample File.

 

A Challenge

Can you solve the problem another way ?

Post your solutions in the comments below.

 

Other Posts in this Series

The Formula Forensics Series contains a wealth of useful solutions and information specifically about how Normal Formula and specifically Array Formula work.

You can learn more about how to pull Excel Formulas apart in the following posts: http://chandoo.org/wp/formula-forensics-homepage/

If you have a formula and you want to understand how it works contact Hui and it may be featured in future posts.

 

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41 Responses to “How to use Excel Data Model & Relationships”

  1. Ashish Youngy says:

    Data is Excel 2013 behaves so much like a OLAP cube when using with PivotTables. And this is actually wow. Consider learning not just DAX but MDX too 🙂 Happy Excel

    @Chandoo.. Have a nice and safe time in US. Best Wishes. And when they are publishing your interview in Entrepreneur 🙂

  2. Buzz says:

    I have been using PowerPivot in Excel 2010. My understanding was (via PowerPivot Pro blog) that Power Pivot would NOT be available in Excel 2013 in all versions; my recollection is that it was only going to be available in certain enterprise subscription editions. Thus, for individual users, it will no longer be available? For that reason I have moved some of my projects to Tableau, and do not expect to upgrade to Excel 2013.
    Can you confirm the availability of Power Pivot for all Excel 2013 users , or will it be restricted and unavailable for some users?

  3. Oz says:

    Just this weekend I upgraded from Home Premium to Professional Plus and spent time with Power View and PowerPivot.

    Up to that point I never saw myself in VLOOKUP Hell, and it may not be going away any time soon. I'm surprised to discover how many of my clients are still on Excel 2003. And then I have Mac users who don't have a lot of this great stuff available to them at all.

    These are great features and I'm going to dive into the Data Models. Unfortunately, I suspect, for me, the practical use may be limited to blogposts because I can't teach Power View in my workshops or send a client a spreadsheet that has a Power View in it.

    • thundom says:

      Hi OZ,

      I think the Microsoft would only upgrade the excel to a certain level instead of making it so powerful that it might threat their BI product. You know these "powerful" stuff can be easily done with a entry level crystal reports version.

      Glad to listen to ur opinion on it.

      I spent quite some time and energy on Excel and used it a lot, but now I am focusing energy on BI software like crystal reports.

    • thundom says:

      We both know that based on the technology today. All the time we spend on the Macro and advanced function of Excel can be done easily with other softwares which costs only hundreds of bucks.

      • Hui... says:

        @Thondom
        I don't think Excel tries to be the solver of all problems
        It is a generic tool
        Which for about 95% of people will do what they want 95% of the time
        There will always be specifics where specific custom software will do better than Excel
        It is the commonness of Excel which means that I can send a model to you and it will work , most of the time, that is its strength, of course combined with its flexility in being able to be adapted to suit most needs

        • thundom says:

          Hi Hui,
          You are right.

          But,

          for the business and individual, who spend too much resource on Excel to meet their BI requirements and other processing requests.

          Should they open their eyes to other ways to do it, in this age? Especially for many people try too much time to process stuff with thousands lines of macro programming.

          It is just as when human being created gun fire, the martial arts would not be that effective.

          Ppl need to be prodent when they choose their solution.

          • Hi guys, I just came across your conversation. I have an example of BI vs. Excel stuff. Here in Russia there is an ERP-system called "1C". It became a defacto standart for accounting, planning and BI / analytics. It is positioned as a flexible and powerful system and it really is.
            But its reporting abilities aren't user-friendly (or maybe just not me-friendly).
            Many reports require programming and all those SQL things, so that is common for a company to have a couple of programmers who develop and code those reports.
            So the common solution is to export data to Excel and then process it to be more suitable for further analysis or reporting.
            Well, it's obviously not a rule of thumb that special BI software can outperform Excel in day-to-day routine.

  4. Tris says:

    Hi Chandoo, thanks for publishing great Excel information. Pardon the ignorance as I havent used Data Model nor PowerPivot. But having seen your video clip on PowerPivot, how does Data Model differ from PowerPivot - the "process" seems familiar? Have a great day! And Excel to new heights! Regards,

  5. Nolberto says:

    Excellent posting, some pride themselves for having sheets with thousands of formulas or complicated formulas, but in the end the important thing is to work as little as possible.

    • Oz says:

      @Nolberto let's not gloat yet. Some people are forced to have thousands of complicated formulas when they don't have the fancy tools. I'm sad for the 2003 users who have to use SUMPRODUCT when the rest of us have SUMIFS available.

      In the end, I think the important thing is clean, trustworthy data--however you arrive at it. People survived more than 300 years with slide rules and paper. No PowerPivot for the Wright Brothers.

  6. koi says:

    hi chandoo,

    i added 2 column into sales, 1st column vlookup customer ID to CUST sheet to get the male or female, then 2nd column vlookup Product ID to Product sheet to get the product name, then after that i make pivot table out of sales sheet.

    but then the result is really different from yours

    the purposes is just try to do the vlookup vs add to data model to see if they get same result

    thanks

  7. koi says:

    ups sorry, didnt see that you're filtering using slicer..then it is good now the result are same with less effort 🙂

    thanks

  8. SPrasad says:

    Hi Chandoo, .I am interested to know whether we can build a star schema or snow flake data models through relations in Excel? (trying to correlate with Qlikview)

    • Chandoo says:

      Hi there,

      You can create a Star schema for sure. Snow-flake is possible too. As long as all relationships are one to many (or one to one) anything is possible.

      • Nestavaro says:

        What if customer.profession change its value after sometime?
        Supposed we have monthly data for Sales. What if one customer is a doctor in Feb, then a pilot in October, for example?

        How to build data model for such that situation?

        Thank you.

  9. Raghavendra Shanbog says:

    Hello ,
    I find this option similar to that of MS Access.
    In MS Access as well we have relationship concept and once you create a relationship, you can start creating number of queries based on that.
    But MS Access is not so user friendly and basically its database. Good that we are getting those options/functions in Excel.
    Thanks for sharing this info.

    Regards,
    Raghavendra Shanbog

  10. What is star schema and snow flake.??? Can we have next article on that if it is useful for us???

  11. Roberto says:

    Hi there, can anyone help? I tried testing this out in Excel using two tables. When I go to the Data tab the Relationships button does not appear at all. I am using Microsoft version 14.0.4760.1000, Microsoft Office Professional Plus 2010. Does this version have this capability? Or is there an add-in required?

  12. […] even a layperson can perform if they have the almighty Excel 2010 and PowerPivot installed. Or Excel 2013′s Data Model, which lets you mash up data from Excel Tables and serve them up directly as PivotTables with not a […]

  13. Chandeep Chhabra says:

    Chandoo/Hui,

    The dates grouping feature does not seem to work in Data Model. Is that true or am I making a mistake somewhere?

  14. Jay says:

    I don't think this is really for "lookups"...

    Try creating a pivot with sale ID and customer name in row fields. It will give you ALL customer names per sale ID.

    You'd need to use RELATED function in a new column in powerpivot if you want something equivalent to "vlookup"

  15. Aslam says:

    Please explain the difference between data model and power pivot, the functions of both of them are different and similar
    thanks

  16. […] Handling large volumes of data in Excel—Since Excel 2013, the “Data Model” feature in Excel has provided support for larger volumes of data than the 1M row limit per worksheet. Data Model also embraces the Tables, Columns, Relationships representation as first-class objects, as well as delivering pre-built commonly used business scenarios like year-over-year growth or working with organizational hierarchies. For several customers, the headroom Data Model is sufficient for dealing with their own large data volumes. In addition to the product documentation, several of our MVPs have provided great content on Power Pivot and the Data Model. Here are a couple of articles from Rob Collie and Chandoo. […]

  17. Bernadette Savage says:

    I need to use a slicer to allow a user to select vendor by name. In the background, I need to obtain the vendor ID to link to multiple datasets where the name may not be spelled consistently. Any advice?

  18. Andrea says:

    I've tried this in Excel 2016. It works great.
    I can even create Cube Formulas on the Data model after I've inserted the pivot table.
    Just for the fun of it, I tried to see if I could do Cube Formulas without creating the pivot table in advance. I can define Cube members, but it seems as if the measure part is playing tricks on me.

    I can't get a Cube Value for Chocolates sold to Male customers.
    With the Pivot created the formula looks like this (and works fine)
    =CUBEVALUE("ThisWorkbookDataModel";"[Customer].[Gender].&[Male]";"[Product].[Category].&[Chocolates]";"[Measures].[Sum of Quantity]")

    Does anyone know how I can solve this, or am I asking the impossible?

  19. Kwabena Anaafi says:

    I want to see the video on this topic

  20. nestavaro says:

    What if customer.profession change its value after sometime?
    Supposed we have monthly data for Sales. What if one customer is a doctor in Feb, then a pilot in October, for example?

    How to build data model for such that situation?

    Thank you.

    • Chandoo says:

      In such case, you need to make relationships based on two columns. This kind of feature is not supported in Excel. You can use Power Query to merge tables based on multiple columns and return a consolidated giant table to Excel for reporting.

  21. nestavaro says:

    Is it able in MS Access?
    I have never used access before.

  22. faisal says:

    thanks chandooo your article is very helpfull for troubling peoples' especially in office environment under boss pressure.

  23. Ron says:

    Here is an introduction to PowerPivot.

    The link above is broken

  24. Venkatesh says:

    Hi. This has really taken my interest.. I have huge data tables to work with...and I use vlookup to fetch certain data. I have different data in different sheets...

    Like customer sales (customer code, product code,qty, piece rate, total amount, branch code) data in one sheet
    Branch details in another (branch code, branch address, state , region)
    Customer Geographical Data in third sheet (region, region name)
    Product details in fourth sheet (product code, product description and related)

    Now I use a vlookup to get branch name, state and product name respectively into my main sheet.

    Now what I want is

    customer code, product code,qty, piece rate, total amount, branch code) data in one sheet, branch address, state , region, region name, product description

    Can't his be done thru data model... I tried but it's not working... Eitherway, I will gonthru thr session on e again and give a try... Any help, is appreciated. Thankyou

  25. Achyutanand Khuntia says:

    Dear All,

    i am striving to do reverse relationship in Power pivot ,

    example : -

    1 - Data sheet
    2. - Source data

    step to stops - import first data sheet in power piovt and then source data , made relationship with both sheet , after created relationship i am able to do put related formula in source data sheet only (=releted('Source data'[Amount]), if i go to put formula in data sheet , parameter of Source data are not visible ,

    could someone educate me how can i do , and utilize related formula in data sheet.

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