How much math do engineers use?

How much math do engineers use? Not a lot. Engineers typically use basic algebra and trigonometry. While computers do the complex math.

The math engineers do use, comes in the following forms:  

  • Solving problems by hand using math
  • Using software tools baked in with math
  • Reviewing and trying to understand math calculations done by others
  • Visualizing solutions to problems, through mathematical relationships

Now, to better understand the math used in engineering, we’ll answer 7 related questions.

#1 What type of math do I do by hand as a design engineer?

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

Math types I use in engineeringAmount of math types I use in engineering
Algebra65%
Trigonometry20%
Calculus5%
Statistics5%
Geometry5%

#2 When do engineers use math?

It depends on the type of engineer you are, and what you do. For example, engineers working in the field, normally don’t use much math. While design engineers, commonly use math as they design things to work in the real world.

The following is when I most often use math:  

  • Calculating the short circuit magnitude
  • Cable sizing
  • Battery sizing
  • Creating power relay settings
  • Transformer sizing
  • Equipment sizing

So, for every one of my projects, I always do some level of math. Whether by hand or in my head. The following are some 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

In some instances, I use a string of equations together. For example, when I calculate battery sizes for substations.

#3 How much calculus do engineers use?

The application of calculus is found in all areas of engineering. Whenever you study the rate of change of something, you’re using calculus.

Your computer software will do most of the heavy lifting for you though. The few times I have used calculus is when I calculated the following:

  • Battery capacity
  • Transmission energy consumption
  • Electric field strength

Most important, understand calculus theory, even if you never do a calculus problem. Because the theoretical side of engineering comes from calculus.

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

And if you deeply understand the concept of derivatives and integrals, you’ll become a better designer. Because you’ll better understand the physical world around you.

#4 What’s the level of math used by engineers versus all working Americans?

Compared to all working Americans, engineers use a lot of math.

Below is Michael Handel’s data from his STAMP survey, to infer and compare. The table shows the percentage of types of math Americans use most at work. And I bet the more advanced math is more often used by engineers.

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

Not surprisingly, most Americans use basic arithmetic. But, so do most engineers. The difference is, engineers also need to understand high-level math.

#5 How have advances in computer software impacted engineering?

Like with everything in the world today, computer software has overtaken engineering. Computers now solve the problems, which once were painstakingly done by hand. This includes management, design, and testing work.

In return, engineers have become much more efficient in their work. On the same token though, some have become lazy.

Just a half-century ago, you had to wisely plan to execute a single design option. Because calculations were all meticulously done by hand. Still, engineers were amazingly able to design the following:

  • Aircraft
  • Electric utilities
  • Bridges
  • Buildings

Today, you can instantly generate countless design scenarios, while analyzing endless data. Yet, some engineers blindly trust their software without making any checks. They don’t even understand the math behind their software outputs. This is a recipe for engineering failures.

#6 Does understanding difficult math concepts make you a better engineer?

Absolutely!

Math is the building block of engineering principles. With a strong understanding of math, you can do the following:

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

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

  • Bad inputs generating bad outputs
  • Mistakes in the software

The only way to spot such errors, is to have a deep understanding behind the engineering. You need to grasp the mathematical relationships between variables in formulas. This way, you can perform a reality check on your output results.

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 do so, because I understand the math behind electricity and transformers.

Without math, I’d struggle to form a pragmatic conclusion. In fact, I’ve read many articles on the impact of CMEs on Earth. Many of the authors never use math and as a result, their conclusions are wrong. It goes without saying, math is the blueprint for the physical world.

#7 How math helps you think outside of the box? 

With unique designs, the variables you need may not exist in existing software. Engineering software typically only includes models, which are commonly used.

With edge-case designs though, 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. Hand calculations won’t cut it. 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 moon. Not surprisingly, the software used to analyze Earth drilling, won’t cut it.

The faraway planet has too many distinct variables. Think of variances in gravitational strength, atmosphere thickness, and extreme temperatures. 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. So, you’re left with options #1 and #2.

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

“How much math do engineers use?” wrap up

Engineers don’t use as much math as you may have expected. Also, it’s not the type of math you were thinking. The math done by hand is mostly basic algebra and trigonometry. 

But, if you understand and can apply high-level math concepts, you’ll set yourself apart from your peers. You’ll enhance your creativity, and be on your way to becoming a 10x engineer

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

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