How Hard is Calculus Really? (Everything You Need to Know!)

One of the most common questions I get from math students is how hard is calculus? The word itself sounds a bit scary and unfamiliar, so it is natural to have concerns about the level of difficulty!

If you are here reading this, the odds are you are a math student that is about to study calculus. My goal is to share everything you need to know about this wonderful math topic so that you know just what you are getting yourself into!

As a teacher with many years of high school math teaching experience, I have helped thousands of students understand calculus. This means I have heard many, many different opinions about how hard calculus is. I also have a lot of experience helping students prepare their mathematical mindset so that they can be as successful as possible in their studies of calculus!

But, just how hard is calculus really? Well, let’s dig in so that you can find out for yourself!

How Hard is Calculus Actually? It Depends…

If you ask anyone just how hard is calculus, the odds are you are going to get a different answer depending on who you ask. But why is this? Isn’t math supposed to always have just one right answer? 

As it turns out, there are a few reasons why people have different opinions on how hard calculus is. Let’s dig into these so you can understand why this question can be hard to answer!

Calculus Looks Different Everywhere You Go

Like all math subjects (and non-math subjects!), the difficulty and depth of what you study will vary depending on a few factors. This includes the course and level you are studying at, and where in the world you are studying calculus! 

It goes without saying that calculus at the high school level will be much less challenging than a college level subject or AP calculus courses. More specifically, a course that focuses on integral calculus or multivariable calculus will be much more demanding than a course focusing solely on differential calculus.

Many university or college business programs require students to study business calculus. This is a much lighter course than, say, a course focusing on partial differential equations (sounds scary, right!?).

In addition, the calculus subject matter that you study will depend on where you are located in the world. In some locations, the concepts covered in advanced level calculus would be covered in regular calculus courses elsewhere. A course like Calculus II covers material that I have seen some students only begin to explore in college calculus.

The variability in what is covered can make it difficult to come up with one single answer that explains just how hard calculus is.

Weak or Solid Foundations?

Regardless of the calculus course you are studying, or where in the world you are studying it, one thing is for sure: how hard you find calculus will depend heavily on whether or not you have solid foundations!

In my experience as a teacher, students who struggle with basic algebra, linear relations, trigonometric functions, and have weak problem-solving skills tend to find calculus one of the most difficult subjects. This is because many foundational concepts of calculus depend heavily on these topics and skills. So take a look at your math experiences as far back as middle school and up to the 10th grade to find clues about your readiness for calculus. 

If you have weak foundations in math, does this mean that you are doomed to fail calculus? Of course not! There is always something you can do to brush up on your foundations. 

Consider using Math By The Pixel‘s video resources or taking a few online courses to help you fill in any gaps in your understanding!

Hard Work or Hardly Working?

Having said that, foundations aren’t everything! If you have been around Math By The Pixel for a while, you will know that I am a strong believer in using a growth mindset in mathematics. When I was a classroom teacher, I was known for showing my weakest math students how they could improve by changing the way they see challenges. The mindset you have about math, failure, and your own ability to do anything you put your mind to will all impact how hard you believe calculus to be.

Have you ever considered what your mathematical mindset is? Take a moment to think about your relationship with math. Do you put in the hard work even when things get tough? Or, do new concepts and complex concepts cause you to shy away from the challenge? Do you give up at the first sign of failure when you don’t receive a passing score? 

In simple terms, the work ethic you have will determine whether you think calculus truly is the hardest class there is, or just another obstacle that you know you are capable of conquering. 

Why is Calculus Hard?

In general, many of my students have found calculus to be the hardest class they study in their high school classes. There are some exceptions to this, but many students agree that calculus is a challenge.

So just why is calculus so hard? There are a few reasons most students and teachers will agree on.

Gaps in Prerequisite Knowledge

If you are asking why is calculus is so hard, there are a few reasons you could be struggling with the topic. But the most common reason is that you may have gaps in your prerequisite knowledge.

As I mentioned above, having solid foundations is essential to find success in any calculus class. To develop a very strong understanding of calculus, students need to understand the topics that it is built off of.

In calculus, many of the mathematics topics from middle school are built upon and explored in much more detail. So if students lack a strong background in these areas, it makes sense that they will struggle when it comes to building upon them.

For example, applying the first derivative test requires knowledge of factoring trinomials, a concept introduced earlier in studies of algebra. A gap in factoring knowledge would mean that using the first derivative test would be a struggle.

Even a relatively simple concept such as rate of change can present a challenge to students who are tasked with extending this understanding to differential calculus and the first principles definition, for example.

Gaps in prerequisite knowledge is one of the most common reasons why students struggle with the new material covered in high school calculus.

New Concepts and Critical Thinking

As far as math classes go, calculus provides many opportunities for critical thinking and making connections between new concepts and the real world. Many students are not used to the depth of critical thinking that calculus requires, which can present a challenge.

The subject of calculus also requires much more abstract thinking than many math students are accustomed to. The new concepts that are studied in high school calculus are often very abstract and hard to visualize. This can discourage students who are new to this level of thinking.

For example, the entire concept of an infinite series is so new and unfamiliar to many students that they struggle to visualize it in any meaningful way. And that is without even considering something complex like the divergence test for series!

Complicated Formulas and Rules

Calculus is famous for using complicated looking formulas. Take a look at the first principles definition of the derivative for example! There are so many new symbols that students can become quickly overwhelmed.

There are also so many rules that make it difficult to know when to apply a specific strategy over another. For example, knowing when to apply the chain rule vs the product rule is a common source of confusion I have seen in my own classes that I have taught. There are also many different ways to arrive at an answer, which only further adds to the confusion.

Complicated Problems

Depending on the type of problem you are solving, you could see a solution that ends up taking up more than a single page! This is actually quite common in integral calculus problems where complex substitutions are required.

The sheer length of a solution can be enough to scare off many math students. For me, this is what makes calculus my favorite math subject!

Despite calculus being a very applicable branch of mathematics, real-life applications of calculus don’t always feel familiar to students when they first encounter them. Practice problems that involve word problems and real world scenarios are common sources of confusion for many calculus students.

So, Just How Hard Is Calculus Actually?

A quote from one of my former students summarizes my thoughts about how hard calculus is rather nicely. He said: “for me, calculus was the most difficult math course because it was a major change in the way I thought about math.”

This quote is true in every way. Calculus requires you to build upon strong foundations in a new way. It also challenges students to apply more abstract thinking for the first time. And lastly, calculus requires students to persist in the face of challenging new material and more advanced mathematics than anything they have seen before.

When I am asked how hard calculus really is, I always tell my students that calculus is a ‘mature’ math subject. This means that you should be comfortable with and aware of your math skills. You should also be able to adjust your work ethic depending on how you are feeling about the new concepts that you are learning. It is not a course that you can usually achieve a passing score in with little effort.

If you find that calculus is hard, don’t forget to use the resources you have to help you! I would not have excelled in my senior year without the help of my study groups. Having the support of a good teacher and strong study groups will help you persevere through calculus’ most difficult challenges.

Check out this list of the best books to learn calculus for more support, and take some time to review this ultimate guide to calculus word problems.

You can also watch the calculus playlist on the Math By The Pixel YouTube channel if you are looking for more in depth instruction.

Remember, with the right attitude, you get to control how hard calculus is!

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