Discussion Thread

Avoiding Numerical Mistakes

  • 1.  Avoiding Numerical Mistakes

    Posted 01-18-2020 11:38 AM
    Hi All,

    Maybe this is a simple solution, but ever since beginning my journey at University, I have been affected tremendously by making frequent numerical mistakes in my calculation reports. It gets pretty frustrating because of the need for constant re-work / adjusting values. Though I've tried a lot to eliminate such mistakes, I can't seem to find a solution that works.

    Any suggestions?

    Kind Regards,

    Justin Redman Aff.M.ASCE
    Port of Spain

  • 2.  RE: Avoiding Numerical Mistakes

    Posted 01-19-2020 09:29 AM
    Hi Justin,

    Personally speaking, numerical mistakes usually occur either when I'm not fully focused on what I do or I'm too "confident" to re-check what I've first done.

    To avoid numerical mistakes, I will make sure when I deal with numbers, I'm 100 percent focused and minimalize distractions during this work. Additionally, I will double-check those areas whenever I feel they might have a risk of inaccuracy.

    Hope this could give you a hand and best wishes!

    James Wang, M.ASCE
    Senior Cost Estimator
    Turner & Townsend
    Shenzhen, China

  • 3.  RE: Avoiding Numerical Mistakes

    Posted 01-19-2020 09:30 AM

    Three suggestions are as follows:

    A) Try using spreadsheets, likely Excel is available to you on a work computer.  Be absolutely sure that the spreadsheet is set up correctly, then just enter new and different data for future calculations and the result should be correct.

    How to be sure spreadsheet is set up correctly?  Search back into books used for classes, enter examples from the book into a spreadsheet.  Highlight cells that are data input.  Show intermediate calculation results.   Identify the final solution result.  Check all of this by hand, pencil, & calculator.  Save the spreadsheet for future use, again just changing the input cell values.  Have a colleague at work use, check, & verify the spreadsheet.

    B) If the calculator you have was more than $20 +/- and is programmable, you likely could create a program on your calculator also, just entering a new & different variable value while running the program on the calculator to get the correct result.

    C) Work solutions out by hand, pencil, & calculator, on paper, working slowly & cautiously.  Make long calculations by intermediate steps.  Think critically about each solution step, does it make sense, check & re-check.


    David Devine P.E.,L.S.,M.ASCE
    Fort Wayne IN

  • 4.  RE: Avoiding Numerical Mistakes

    Posted 01-19-2020 05:35 PM
    Today we are so used to using calculators; when I first started out we used slide rules which force you to approximate the result and force you to find the decimal place, since the slide rule only gives you the significant figures.  No does that anymore, but what I do is always estimate what the answer should be.  Just try to approximate the answer by simplifying the numbers to whole numbers and 1 significant figure.  I do this when I do example problems on the board for my students.  I have them use the calculator, but I just make a rough estimate the answer by looking at the numbers.  It takes a little practice.  The calculator result can be compared to the rough estimate and if it  seems "off", redo the calculation.  When dealing with roots and exponents and sines/cosines, radians/degrees you need be extra careful.  Maybe to the calcs twice.  You may be off a little, but you avoid the big mistakes.  Good luck.

    Joseph Reichenberger P.E., F.ASCE
    Professor of Civil Engineering
    Monterey Park CA

  • 5.  RE: Avoiding Numerical Mistakes

    Posted 01-20-2020 09:00 AM
    I like very much the suggestions of Professor Reichenberger and recall that senior engineers I worked under & with soon out of college myself also made such suggestions to me, what is the "ballpark" expectation of the result, no calculation at all, use your mind to come up with a reasonable expected result so that once the calculation is completed, with a calculator, you can assess the reasonableness, did a wrong key get punched/did a value not get entered correctly such as a 100 rather than 10000, order of magnitude issues.

    David Devine P.E.,L.S.,M.ASCE
    Fort Wayne IN

  • 6.  RE: Avoiding Numerical Mistakes

    Posted 01-19-2020 09:33 PM
    Hi Justin,

    There's a strategy that I've been using during my professional and academic life which is to re-calculate everything before I send it to any stakeholder. Another thing that I used to do is based on the numbers I mentally compute the numbers after I end up my task and see if it is approximate to my estimations.

    Jhon Grajales S.M.ASCE
    Bogotá D.C.

  • 7.  RE: Avoiding Numerical Mistakes

    Posted 01-20-2020 08:59 AM
    One little trick I learned a while ago was how to find transposition errors.  That is when you accidentally swap digits in a long number and then use it to run a calculation (ie. you were supposed to enter 1300 but instead entered 3100).  The resulting error will always be divisible by 3 with the solution being a whole number: (72 - 27) / 3 = 15.  Transposition errors of course are but a small subset of possible mathematical errors, and you have to know the number your looking for, however its something that might come in handy for you down the road.

    Aside from this mathematical anomaly, I'd echo the other responses on this board about double checking your results, using computer software such as spreadsheets, and removing distractions while you perform your work (music and headphones works well for me to drown out ancillary noises and other distractions).

    David Coe P.E., M.ASCE
    Charlotte NC

  • 8.  RE: Avoiding Numerical Mistakes

    Posted 01-21-2020 08:24 AM
    Excel is a good suggestion.  It does not handle units very well though.  I would recommend Mathcad or Tedds software if allowed.  They do offer student editions.  These programs handle units easily and allow variables to be changed on the fly.

    Check your work before, during, and after your calculations.  Redoing calculations is part of the process, whether there are errors or iterations.  I suppose it is funny that we hold math to such a strict standard... we would never frown upon a writer who produces a rough draft, edits it, has a proofreader, and produces a final draft, and yet we hold practitioners of math to a high standard that says getting it right the first time is the only acceptable way.  Perhaps it is the way we are taught and tested in school?  The important rule here is to not submit work that has not been at least self-checked.

    Even without software, always include units in your calculations.  If your units do not work out, something is wrong.

    Pay attention to  significant figures.  Do not get bogged down with meaningless decimal places.

    Use variables and algebra in your presentation.  It is easier to change variables than it is numerical values.

    Chad Morrison P.E., M.ASCE
    Professional Engineer
    Greenville RI