How Much Math Do Engineers Use?

How much math do engineers use? Not much. Engineers typically rely on basic algebra and trigonometry, leaving the complex math to computers.

Here’s what the math side of engineering generally looks like:

Crunching numbers by hand to solve problems
Using software tools loaded with built-in math
Reviewing and attempting to comprehend calculations done by others
Visualizing solutions to problems through mathematical relationships

To give you a better idea of the math involved in engineering, let’s dive into 7 related questions.

#1 As a design engineer, what kind of math do I work with by hand?

Check out the table below for a breakdown of the math I use in my job. You’ll notice algebra takes the lead.

Math types I use in engineering	Amount of math types I use in engineering
Algebra	65%
Trigonometry	20%
Calculus	5%
Statistics	5%
Geometry	5%

#2 When do engineers need math?

It really depends on the type of engineer you are and what you do. For instance, engineers working in the field usually don’t need much math. On the other hand, design engineers often use math to make sure their creations work in the real world.

Here’s when I typically use math:

Calculating short circuit magnitude
Sizing cables, batteries, transformers, and equipment
Creating power relay settings

For each project, I always do some math, either by hand or in my head. I use these equations almost daily:

$S = V \times I$

$Z = R + jX_{L}$

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

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

Sometimes, I even use a series of equations together, like when calculating battery sizes for substations.

#3 How much calculus do engineers use?

You’ll find calculus applications in all areas of engineering. Whenever you’re studying the rate of change of something, that’s calculus at work.

But don’t sweat it – your computer software does most of the heavy lifting. The few times I’ve used calculus were when calculating:

Battery capacity
Transmission energy consumption
Electric field strength

What’s crucial is understanding calculus theory, even if you never solve a single calculus problem. That’s because engineering theory is rooted in calculus.

Calculus concepts in engineering

I actually use a decent amount of calculus theory in my work, almost on a weekly basis. For instance, I apply these concepts to various design elements:

Exponential growth and decay
Relationships between time and frequency domains

By truly grasping derivatives and integrals, you’ll become a better designer. You’ll gain a deeper understanding of the physical world, which is what engineering is all about!

#4 How does the math level used by engineers compare to that of other working Americans?

Engineers sure do love their math, and boy, do they use a lot of it compared to the average Joe! Let’s take a look at some data from Michael Handel’s STAMP survey to give us a clearer picture. The table below highlights the percentage of different types of math used by Americans in their daily work, and I’m willing to bet engineers are the ones using the more advanced stuff.

Math types used by Americans at work	Amount of math types used by Americans at work
Any math	94%
Add / subtract	86%
Multiply / divide	78%
Fractions	68%
More advanced arithmetic	22%
Algebra (basic)	19%
Geometry / trig	14%
Statistics	11%
Algebra (complex)	9%
Calculus	5%

As you can see, basic arithmetic is the bread and butter for most Americans, engineers included. But here’s the kicker: engineers need to have a good grasp of high-level math too.

#5 How has the rise of computer software impacted engineering?

In today’s fast-paced world, computer software has taken the engineering realm by storm. Long gone are the days of manual problem-solving for tasks like management, design, and testing. Computers have stepped in, making engineers more efficient than ever.

But, you know what they say: with great power comes great responsibility. Some engineers have let the ease of technology make them lazy.

Rewind just fifty years, and you’ll find engineers painstakingly planning and calculating each design option by hand. And yet, they were able to create marvels like aircraft, electric utilities, bridges, and buildings.

Nowadays, countless design scenarios and data analysis are just a click away. But beware: some engineers blindly trust their software, skipping the necessary checks and balances. They may not even understand the math behind the results, and that’s a recipe for an engineering disaster.

#6 Does mastering complex math concepts make you a better engineer?

You betcha!

Math is the backbone of engineering principles. A solid understanding of math allows you to:

Design effectively and confidently
Explain the possibilities and limitations of a project
Evaluate engineering software outputs for accuracy
Assess the math of fellow engineers

I always say, don’t just take your software outputs at face value. Keep an eye out for two major pitfalls:

Garbage in, garbage out: bad inputs leading to bad outputs
Software glitches or mistakes

To catch these issues, you need a deep understanding of engineering concepts and the mathematical relationships between variables in formulas. That way, you can perform a reality check on your output results.

Take, for example, the math behind a coronal mass ejection (CME). I was able to analyze the impact of a powerful CME on our power grid, all thanks to my understanding of the math behind electricity and transformers.

Without math, it’d be a struggle to draw any sensible conclusions. I’ve read plenty of articles discussing CMEs’ effects on Earth, but many authors skip the math and end up with incorrect conclusions. Simply put, math is the blueprint of the physical world.

#7 How does math help you think outside the box?

When dealing with one-of-a-kind designs, you might find that the necessary variables aren’t available in existing software. Most engineering software includes pre-built models for commonly used situations, but what about those edge cases? You’re left with three options:

Do hand calculations
Write software to handle your unique edge case model
Give up on the problem

Option #1 is a solid starting point, but if the software doesn’t already exist, you’ll quickly discover that your problem is super complex, and hand calculations just won’t cut it. Enter option #2.

Option #2 is a popular choice. Let’s say we want to drill into the surface of a distant moon. It’s no shocker that Earth-drilling software won’t do the trick.

This far-off moon has a bunch of unique variables—think differences in gravity, atmospheric thickness, and extreme temperatures. So, we’d have to create a mathematical model and develop software around it.

Option #3? Forget about it! No great engineer would ever quit, leaving you with options #1 and #2.

In a nutshell, a strong math foundation is essential for bringing new ideas to life.