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 fact, in college, you use much more high-level math. Whereas working as an engineer, you normally only use basic algebra and trig.

Then maybe a couple of times a year, you’ll throw in some calculus. Doing high-level math by hand is rare.

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

It’s important to realize though, in engineering, math comes at you in the following ways:

• Solving problems by hand using math

• Using software that’s baked in with a ton of math

• Reviewing and trying to understand math calculations done by others

• Visualizing solutions to problems, supported by math equations

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

The below table is a breakdown of the types of math I use in my work. The majority is algebra.

Let’s now dive into the details of the math used in engineering.

When do engineers use math?

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

For example, engineers working in the field normally don’t use much math at all. That’s totally okay.

But, design engineers naturally use more math. Because you’re designing things to work in the real world. And, math is the framework for ourphysical 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 showed earlier. Now, here are some equations I use almost daily:

[Latexpage]

$S = V \times I$

$Z = R + jX_{L}$

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

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

Then in some instances, I use many equations together. For example, when I calculate battery sizes for substations.

On even rarer equations, I’ll use calculus.

How much calculus do engineers use?

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

What’s more, almost everything in engineering undergoes change. So, you’ll see 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 use calculus is when I calculate:

• The capacity of a battery
• Transmission energy consumption
• Electric field strength

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 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 following concepts to various design elements:

• 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 if you want to be a great engineer.

As a result, you’ll have a better understanding of the physical world around you.

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

The level of math used by engineers versus all working Americans

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

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

Clearly, most Americans use basic arithmetic. Even more, most engineers only use basic arithmetic.

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

Advances made in computer software have changed engineering

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

Most engineers use software to design and test. Keep in mind, all engineering software includes layers of math.

As a result, engineers can more efficiently design cooler things.

On the same token, computers have made some engineers lazy. Some engineers are even dumbfounded on how engineers designed just a half-century ago.

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

Rather, you painstakingly went through each scenario one by one. You carefully did each calculation by hand.

Sounds crazy today, but that’s how engineers designed decades ago. What’s more, they still made the most amazing designs, which include:

• Aircraft
• Electric utilities
• Bridges
• Buildings

In short, computers have simplified math calculations. But, you still need to understand the math. You’ll never become a great engineer without understanding basic 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.

Understanding math concepts

To become a great engineer you need to understand the math behind engineering. Math is the building block of engineering principles.

With this in mind, you do the following when you understand the math behind 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 for accuracy

• Follow and assess the math of other engineers

I always tell people, you can’t blindly accept your program outputs. Consider the following two issues:

• Your inputs were wrong from the start

• The program breaks when variables are set or inputted a certain way

Both of these issues have happened to me before. If I hadn’t reviewed my output results, 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) on our power grid. I was able to properly evaluate the impact because of math. More specifically, the math around electricity and transformers.

I used math to highlight how a powerful CME could destroy power transformers. Without math, I couldn’t have dived into the subject to form a conclusion.

That said, I’ve read many articles on the impact of CMEs on Earth. Many of the authors never use math to support their conclusions. And this is why I wrote my article on the subject.

Important to realize, math is the blueprint to the physical world. Without math, it’s difficult to explain the physical world.

Using math to think outside the box for new designs

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 design something super unique. In these edge cases, you have the following three options:

1. Do hand calculations
2. Write software to 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 option #2.

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 don’t exist on Earth that we’d never consider.

So, we’d need to create a math model and build software around it.

Option #3: forget this option. Any great engineer would never quit. Thus, you’re left with options #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 you need to have.

“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.

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

All in all though, to become a superstar engineer you need great math skills. No exceptions!

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

Engineer Calcs

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.