How much math do engineers use?

How much math do engineers use? A lot. Most hand calculations are only basic math. But, great engineers need to understand high-level math concepts.

In college, you do a lot more high-level calculations. Working as an engineer, a lot of the times you’ll just use basic algebra and trig though.

Then maybe a couple of times a year, you’ll throw in some calculus. Higher-level math is much rarer to sit down and do.

A lot of this is thanks to the great advancements made in computer software.

It’s important to realize though, in engineering, math will come at you in several ways:

  • Doing math by hand to solve problems
  • Using software that’s baked in with a ton of math
  • Reviewing and trying to understand math calculations handed to you

How much math do I do by hand as an electrical engineer?

From all the areas of math, I do by hand in my job, the below table is a summarized breakdown for each. You can see how most of the math I do is algebra.

Math types usedPercent
Algebra65
Trigonometry20
Calculus5
Statistics5
Geometry5

With this out of the way, let’s dive more into the math used in engineering. And, why you shouldn’t be afraid to use more math in your work.

When do engineers use math?

It depends on the type of engineer you are. Also, what type of work you do as an engineer.

If you’re a field engineer, you probably won’t use much math at all. And that’s totally okay.

But as a design engineer, you’ll naturally use more math. Because you’re designing things that need to work in the real world. And, math is the framework for our physical world.

To illustrate, here are some things I do hand calculations for:

  • Finding the short circuit magnitude
  • Cable sizing
  • Battery sizing
  • Creating power relay settings
  • Transformer sizing
  • Circuit element sizing

So, for every one of my projects, I always do some level of math by hand. Or, just in my head.

Most times though, I use basic algebra as I broke down in my above table. And here are some of the equations I use almost daily:

S = V \times I

Z = R + jX_{L}

S = \sqrt{3} \times I \times V_{L-L}

\dfrac{N_{P}}{N_{S}} = \dfrac{V_{P}}{V_{S}} = n

Then, in some instances, I go a little deeper. For example, when I calculate the size of substation batteries. I’ve outlined the calculation for it here.

Then on even rarer equations, I’ll use calculus.

How much calculus do engineers use

Calculus is very important in engineering. Whenever you want to study the rate of change of something you use calculus.

And, almost everything in engineering undergoes change. So, you can find the application of calculus in all areas of engineering.

But again, your computer software does a lot of the heavy lifting for you.

The few times I do calculus problems by hand is when I calculate:

  • The capacity of a battery
  • Transmission energy consumption
  • An electric field

All in all, I don’t do much calculus by hand.

But, what’s most important is understanding the concepts behind calculus. You may not be able to solve an equation, but understanding the theory is really key.

Calculus theory used in engineering

I use a good amount of calculus theory in my work. Almost on a weekly basis.

For example, I apply the below concepts to various things:

  • Exponential growth and decay
  • Relationships with time and frequency domain

Just remember, the theoretical side of engineering comes from calculus. So you need to be comfortable with derivatives and integrals.

As a result, you’ll have a better understanding of the physical world. I find this to be very helpful.

I will say though, I’m thankful for computer software. As I’d hate to calculate integrals by hand every day. My work output would slow to a snail’s speed.

Math used by engineers compared to all working Americans

Compared to working Americans, engineers use a lot of math. Let’s look at Michael Handel’s data from his STAMP survey to compare.

The table shows the percentage of the type of math Americans use at work. I bet the more advanced math is probably used by folks in the STEM fields.

Math type used by Americans at workPercentage used at work
Any math94%
Add / subtract86%
Multiply / divide78%
Fractions68%
More advanced arithmetic 22%
Algebra (basic)19%
Geometry / trig14$
Statistics11%
Algebra (complex)9%
Calculus5%

Clearly, most Americans use basic arithmetic. Also, many engineers only use basic arithmetic.

But, most engineers still need to understand high-level math to be great at what they do. Especially since as they say math is the mother of engineering.

Advances in computer software have changed engineering

Like everything in the world today, computer software has also overtaken engineering. Complex equations that were once done by hand are now done by a computer.

Most engineers use software to design and test. And all engineering software programs include a great deal of math.

In return, this has increased efficiency and accuracy in calculations and designs. So, we can design even more cool things.

On the same token, the software has made some engineers lazy. Some engineers even become amazed when they see how designs were done just a half-century ago.

Engineers solved problems step-by-step with paper and pencil. You couldn’t test 10 different scenarios in several minutes.

Rather, you went through each scenario one by one. You carefully carried out each calculation by hand.

It sounds crazy today, but that’s how engineers worked not so long ago. And engineers still designed some of the most amazing things, which include:

  • Aircraft
  • Electric utilities
  • Bridges
  • Buildings

Even though computers have made math easy, you still need to understand it. You’ll never become a great engineer without understanding math concepts.

It’s like a very athletic basketball player. He can jump out of the gym and he’s super fast.

But, if he never masters basketball fundamentals, he’ll never become a superstar player. You can’t have holes in your game.

Math concepts

This is critical. To become a great engineer you need to understand the math behind the engineering. Math is the building block for most engineering principles.

With this in mind, you can then do the following when you get the math concepts:

  • Understand why you need to design in a certain way
  • Explain to others why you can and can’t do something
  • Review outputs from software calculations fo accuracy
  • Follow and assess the math of other engineers

I always tell people, you can’t blindly go with whatever your software outputs. Consider these two issues:

  1. Your inputs were wrong from the start.
  2. The software breaks when variables are set or inputted a certain way.

Both of these issues have happened to me before. If I didn’t review the output results closely, I would’ve had big problems on my hands.

To top it off, I’ve found errors in software code many times. For example, equation parameters were incorrectly programmed in.

The only way to figure this stuff out is to have a deep understanding of math concepts. Also, you need to understand the relationships between variables in formulas.

The math behind a coronal mass ejection

I analyzed the impact of a powerful Coronal Mass Ejection (CME). I was able to properly evaluate the impact because of math. More specifically, the math around electricity and transformers.

This math helped me understand how a powerful CME could destroy transformers. The math formulas highlighted what could go wrong.

Without it, I couldn’t have dived into the details of the subject to come to a conclusion.

Also, I’ve read many articles on this subject. Many authors never used math to support their conclusion. Thus, I always found the conclusions had holes.

You need to always remember that math makes the physical world. So, without math, it’s difficult to find the truth.

In short, math is the key to help you better understand the universe. 

New designs and thinking outside the box

With new designs, the variables you need may not exist in sold software. Engineering software normally only includes models that are commonly used in everyday designs.

So, you can’t buy software to help you design something super unique. In these cases, you have three options:

  1. Do hand calculations
  2. Write software that can handle your edge case model
  3. Give up on the problem

Option #1 is a good start. But if the software doesn’t already exist, you’ll soon realize your problem is very complex. This leads us to the next option.

Option #2 is a common approach. As an example, imagine we want to drill into the surface of a faraway planet.

The software we have today won’t cut it. There are too many variables that exist that on Earth we would never consider.

So, we need to create a math model to then build software around it.

Option #3 just forget this option. Any great engineer would never quickly just quit. So you’re left with option #1 and #2.

In short, you need a strong math background to implement new ideas.

At the end of the day, math is a skill that you can learn.

“How much math do engineers use?” wrap up

Engineers use a lot of math as you may have expected. But, it’s not the type of math you were thinking.

You mostly do basic math by hand, but you need to understand high-level math concepts. All in all though, to become a superstar engineer you need to have great math skills. No exceptions!

This will set you apart from your peers. As many engineers become rusty with their math as they rely too much on software.

So, use this to your advantage. You’ll in return become a better engineer. And, you’ll make yourself more marketable.

How important do you find math skills to be? How often do you use math?

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