Sample Calculations for your Lab Report

Is your professor making you include sample calculations in your lab report?  This lesson will show you how to make great sample calculations and explain why your professor wants you to do them.

Why are Sample Calculations Important?

Sample calculations are important in a lab report for two reasons.

First, they help you make sure that your calculations are correct.  This is very helpful if you are using a spreadsheet to quickly do repetitive calculations.

Second, they help you show your professor that you understand the calculations.

What Calculations Should I Include?

You only need to place one sample calculation for each type of calculation into your report.  You don’t have to show multiple versions of the same repeated calculation.

I sometimes see multiple versions of the same equation in my student’s lab reports. I can imagine them sitting there and doing each individual one with their calculator.

Use your spreadsheet to perform the repetitive calculations. Think of the spreadsheet as a “super” calculator. Use your sample calculation to make sure that the first one is correct.

Where Should I Do My Sample Calculations?

You should write your sample calculations in your lab “notebook”.  

It is a good idea to recopy these calculations neatly before photographing or screenshotting them to place them into your lab report.

How Can I Prepare My Calculations?

You can write the calculations on paper or digitally on a tablet.  I wrote the sample calculation in this video using Microsoft OneNote.  I would then copy and paste it into my word processor.  

If you are so inclined, you can type them in a word processor.  If you do this, use the “insert equation” options to do so. Don’t type equations as normal text. They will be difficult to read. I’ll include a guide for using word processor equations in a future lesson.

Example of a Sample Calculation

The sample calculation I’m making is based on a lab where different masses were hung from a spring and oscillated. 

A full sample calculation. The details are in the following images.

We determined the frequency and the plotted the frequency squared as a function of the mass. After doing some algebra, we find that the model equation is a straight line.  The fraction in parentheses turns out to be the slope of the line.

We use this slope to determine “g”, the acceleration due to gravity.

Key Parts of Sample Calculations

A sample calculation should include several key parts. I’ll list them here, and then go into details.

  1. A title describing the calculation.
  2. The starting equation.
  3. Any necessary algebra.
  4. The numbers that are inserted, along with their units.
  5. Any appropriate middle steps.
  6. The unrounded answer.
  7. The unit algebra
  8. The final answer, fixed for significant digits, along with its units.

Title

The title should consist of two or three words describing the calculation.

Title of the sample calculation:  Finding g from the slope.

Base Equation

The starting equation is the definitional or “base” equation.  This would be the type of equation that you would find in a textbook or lab handout.

Slope equals g divided by parentheses 4 times el squared times mu end parentheses.

Algebra

Next, perform any algebra steps necessary to solve this equation for the variable of interest.  Don’t put any numbers into the equation, unless it is a zero that helps simplify the algebra.  You can combine any very simple steps, but try to make it clear what the steps are.

g equals four times el squared times mu times the slope.

Insert the Numbers and Their Units

Once you have solved for the variable of interest, put the values into the equation.  Include any units.  If any of the units cancel, put a slash through them.

g equals 4 times (1.5 m) squared times 9.63 times ten to the negative four kg per meter times 1134.7 hertz squared divided by kg.

Do the Math

Now perform the math necessary to solve the equation.  If you’ve simplified the equation well, you should be able to place the numbers directly into your calculator.  I use the Desmos scientific calculator to do my calculations. It might be helpful to show intermediate steps, especially if part of the equation is a useful value.

Take Care of the Units

Do any algebra on the units.   If any of the units cancel, put a slash through them.  Group units that will eventually be combined.  Be careful of any powers of ten that are involved.

Preliminary Final Result

g equals 9.8344 m times 1/s squared.  one factor of mass has been canceled and the units of kg have been canceled.

Write down the final result with a few extra significant digits.  Include the simplified units.  For example, you might end up with something like N m.  Keep it this way for this penultimate step.

Final Result

Finally, write down the answer, fixed for significant digits. Combine any units where appropriate.  For example, the units N m could be combined into J for joules.

g equals 9.83 m per second squared

Putting the Sample Calculation into Your Lab Report

Once you have a good copy of your sample calculation, take a picture or screenshot of it.  Place this picture into your lab report in the appropriate spot.  

One Photo Per Calculation

Don’t include a photograph of a full page of sample calculations.  Each sample calculation should be its own image.  Crop things down to only include one sample calculation at a time.  Make sure that the image is readable.  It should be of decent size and not stretched in any direction.

Notes on Neatness

It is helpful to write your equations on lined paper. This isn’t visible in my calculation because I hid the lines before taking a screenshot in Microsoft OneNote.

Note that I tried to align the equals signs in my equations. This isn’t always possible, especially if the left-hand side of the equation starts out containing a lot of symbols. Once you’ve simplified down, though, try to keep the equals signs aligned.