Hand Calculations – How To and How Not To – Rev 1

We at PVEng use hand calculations when we do not have a program or spreadsheet or when we want to create a spreadsheet and need verification. Hand calculations are respected more than programs for audits or code submission but in my opinion, they are much more likely to be wrong.

The ideas presented here are designed to reduce the most common causes of hand calculation problems:

  • Sources not referenced and therefore not checkable
  • Calculations not showing intermediate steps -how was the final number reached
  • Inputs not explained Units not shown and wrong (ft vs inches etc.)
  • Results not double checked (numerical mistakes)
  • Results not presentable
  • Results not reviewed

These common problems will be investigated in more depth on the following pages.

Show References


Calculations showing references.

Without references it is not possible to check if the equations are sourced right.

The correct equation is t = PR/(2SE+0.4P) not as shown above. With the references listed it is possible to go back and find this copying problem.

Show Intermediate Steps


Calculations showing intermediate steps.

The illustrated intermediate step allows the reviewer to see what numbers were used for the variables. It is not possible to check what is not known.

Where Do the Numbers Come From?


Calculations showing where the numbers come from.

How was the first answer calculated? What values were used for P,R,S and E -why is the first answer wrong?

Here we are assuming that the reader/reviewer understands what P, R, S and E mean, probably a good assumption. However, it would be a better assumption if the reference for the equation was included. There is no reason to provide further explanation for something that is easily looked up.

Include Units!


Calculations showing inclusion of units.

The equation should read specific gravity, not density. Without the units, it is not verifiable.

Also Consider:

  • Check your calcs! Run the numbers through your calculator one more time can reduce surprises.
  • Work in pencil.
  • Add a sketch or copy an illustration.
  • Get someone else to review your calcs.
  • Use proper paper. Ready for review.


Sample Hand Calculations Ready for Review
Simple hand calculations on appropriate paper ready for review.