There are 3 super common math mistakes even engineers make. Thankfully though, these mistakes are avoidable with some due diligence.
I’m going to discuss each of the mistakes, which you’ll find are common even among high schoolers. Then in detail, I’ll go over three fast ways to catch any math mistake in engineering.
The 3 most common math mistakes
By understanding the reasons behind math mistakes, you can more easily avoid them. Let’s make a driving analogy.
Say I tell you to avoid large potholes, pieces of plywood, and reckless drivers on Highway X. In return, you’ll have your eyes glued to the road on Highway X to avoid accidents. Now sure, you still may get into an incident, but statistically, the chance is far less.
#1 Careless math errors
You may have a heavy workload and you’re racing to get things done fast. Or maybe, you’re just having a bad day. Regardless, you don’t pay close attention and you do the following:
- Enter wrong values into a calculator or software application
- Not carefully follow a step-by-step math process, thus miss a step
- Copy problem parameters wrong from the start into a workspace
- Write down wrong numbers
- Forget negative signs
- Forget or misplace units
- Use bad handwriting leading to all the above errors
What to do to avoid careless math errors?
- Take your time in problem-solving.
- If you’re not in the right mindset to do math problems, then hold off until later.
- Highlight the important parts of your math problems, like problem parameters. This helps ensure you use the right values.
- Write out each of your math steps and define your variables. Take a look at my current limiting reactor sizing calculation.
- Review your work from start to finish.
#2 Computational math errors
Say you don’t fully understand what a problem is asking. So, you mistakenly add, subtract, divide, or multiply.
In engineering, most problems aren’t straightforward. Sometimes variables are missing, and other times you won’t know what you’re solving for. This then becomes a source of confusion.
What to do to avoid computational math errors?
- Take your time to review and understand all parts of the problems you solve.
- Reason in your head why you make certain arithmetic decisions. If you only go through the motions, you’ll more likely make a mistake.
- Ask for a second set of eyes to review your problem, if you can’t puzzle it out.
#3 Conceptual math errors
This is the most common reason for errors in engineering. Because unlike in the classroom, you don’t have equations you’re told to use by your professor. In the real world, YOU make the decision over the analytical approach and equation choice. And not surprisingly, the choice is never clear-cut.
So, if you misunderstand concepts or use poor logic, you can make endless mistakes. What’s worse, you’ll think you’ve done everything right too. Because you haven’t made any careless or conceptual errors.
What to do to avoid conceptual math errors?
- Learn concepts from their root. This way you don’t blindly plug numbers into equations.
- Relate textbook equations to the real world for better understanding. Hands-on skills for engineers are super important!
- Use first principles thinking to dissect problems.
3 fast ways to catch common math mistakes in engineering
Through a lot of practice, I’ve learned how to catch math mistakes fast. I can quickly scan a math problem and say, “oh, hey, there’s an error!”
To do this scan efficiently and effectively, I use the following three techniques:
- Real-world test
- Consistency test
- Accuracy test
Important Note: practice doing hand calculations. Or at the very least, learn how your software calculates values. This way you’ll better understand the underlying concepts of equations.
Because today, we over-rely on computers. We’ve lost touch with a lot of basic engineering and math methods. As a result, it’s difficult to tell if a calculation is right or wrong.
#1 Real-world test
Check the units of your calculated values. Right off the bat, you’ll know if you made a mistake or not.
For example, say you’re solving total power consumption for an electric generator. You’ll know to solve for the “kVA” unit for apparent power. But if your calculated value is in “kW,” you’ll instantly know you missed a step.
Why, because all induction machines need reactive power (kVAR) to operate. It’s for the magnetization of the generator’s magnetic field. So, you expect to see a kVA value, which would include both the kW and kVAR power components.
In short, checking units are super easy. It’s a GREAT way to catch math mistakes. Check out the following added unit tips:
TIP #1: dimensionless values
Values inside a log, trigonometric function, and exponents need to be dimensionless. This doesn’t mean each standalone term needs to be dimensionless. BUT, the combination of the terms needs to be dimensionless.
For example, you can take the log of 100, but not of 100 feet.
TIP #2: arithmetic with units
You can only add and subtract quantities with the same units. For example, you can’t add 100 pounds to 200 kilograms. But, you can convert one unit to the other and then add the values together.
TIP #3: matching perfect square units
Values inside a square root, cube root, and so on need to have matching perfect square units.
For example, imagine a free-falling object on Earth. The equation is and the variables are the following:
v= velocity (length/time)
g = acceleration of gravity (length/time)
h = height an object falls from (length)
Both g and h don’t have perfect square units. BUT, when you multiply them together, look what happens:
(length/time) x (length) = length/time
We now have our perfect square. So now, when you take the square root, you get the following =
#2 Consistency test
In the real world, devices and equipment need to operate per their designed specs. Imagine the following:
- If you flip on the light switch, you expect a light to turn on.
- If you hit the start button on a motor control panel, you expect a motor to start.
What I’m getting at is, do your calculated results look logical to you? In other words, are you seeing what you expect to see?
For the consistency test, use the following tips:
TIP #1: real-world check
Check if your results seem reasonable to you. For example, you calculate the power consumption of a running motor is negative. So, you clearly have a bust in your calculation, as you can’t have negative power consumption.
Of course, though, the negative power may also represent power flowing in the opposing direction from positive power. In this case, check if your value is consistent with all your other values.
TIP #2: analyzing variables
Check to see how your overall output changes as your variables change. For example, using Ohm’s Law, V = IR, if resistance increases, does the electric current then decrease? It should!
Picture Ohm’s law in the form of a pipe. The more the pipe clogs, the greater the water resistance becomes. So water flow, or electric current, decreases.
TIP #3: real-world implications
Think of the real-world implications of your calculations. For example, assume you’re doing a voltage drop calculation. You then calculate no voltage drop on a 10,000-foot conductor run.
This result makes no absolute sense as every conductor has a resistance. So, you have a bust in your calculation. And no, no one is installing superconductors in the field.
TIP #4: comparison of terms
Think of an equation, where you subtract two terms. What would then happen if you set both terms equal to each other?
For example, your power system draws reactive power for your induction loads. While your capacitor delivers reactive power to your power source. So if > , your power system overall consumes reactive power. This is why you have a lagging power factor.
But if = , it means your power system no longer consumes vars. So your power system is now operating at unity power factor. Your capacitor is compensating for the consumed reactive power from your induction loads.
This level of understanding is important with each equation you use, to limit mistakes.
#3 Accuracy test
These days, you can find a lot of information on various equipment online. For example, say you want to know the amount of current consumed by a 10 HP motor running at full load. You can find actual factory-tested information in a motor manufacturer’s catalog. But also, you can find generally listed values in the National Electrical Code (NEC).
So, when YOU calculate a motor’s current draw, compare your value to trusted values. If your value is off by a factor of 2, you’ll instantly know something is wrong. EVEN if your math passed the consistency and real-world logic tests.
Now of course, if you’re working on the bleeding edge of tech, you won’t have many reliable sources to use. Still, though, you can compare to similar past calculated values. Because the source of new-age engineering is past technologies.
For example, SpaceX leads the new-age effort with rocket technology. BUT, they still sit on the shoulders of NASA and other existing technologies. In fact, surprising to most, SpaceX wasn’t the first to build reusable rockets. The DC-X built by McDonnell Douglas and later supplied to NASA was the first reusable rocket. The point is, SpaceX had a lot of data to compare and contrast with when they started building rockets.
Common math mistakes in engineering wrap up
Even the best of engineers make math mistakes. But by applying the safety nets we discussed, your engineering work will instantly improve. Because even single decimal point errors can cause catastrophic failures.
Even more, if you have the tools to improve your work, and you don’t use them, it’s bad engineering!
What common math mistakes do you often see in engineering? What methods do you use to avoid math mistakes in your work?
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Koosha started Engineer Calcs in 2020 to help people better understand the engineering and construction industry, and to discuss various science and engineering-related topics to make people think. He has been working in the engineering and tech industry in California for over 15 years now and is a licensed professional electrical engineer, and also has various entrepreneurial pursuits.
Koosha has an extensive background in the design and specification of electrical systems with areas of expertise including power generation, transmission, distribution, instrumentation and controls, and water distribution and pumping as well as alternative energy (wind, solar, geothermal, and storage).
Koosha is most interested in engineering innovations, the cosmos, our history and future, sports, and fitness.