Physics or calculus which is harder? (solved)

In this topic, we will discover which is harder, physics or calculus?

Also, discovers the hardest subject that students study in physics and the hardest one that studies in calculus?

So if you want to know more about the relationship between physics and calculus, keep reading because we will prove to you that you have wrong ideas to correct

Which is harder, physics or calculus?

Physics is way harder than calculus simply because physics includes calculus and other complex math subjects. In addition, physics has some highly complex models like thermodynamics and quantum mechanics. Both these models use calculus.

So calculus is included in physics. Thus it is hard to put physics and calculus into comparison simply because physics contains a lot of calculus.

In addition, the physics used in calculus is harder than abstract math, not just the math calculus is different from physic calculus. But the analysis that you need to make before writing your first calculus equation.

In physics, calculus is used in many physics applications such:

  • Electricity
  • heat
  • light
  • harmonics
  • acoustics
  • astronomy
  • dynamics

What do students study in physics?

were going to list the hardest subjects that physicists student study in their physic program

1 – Quantum mechanics

quantum mechanics is one of the hardest subjects of physics. It is not chemistry or classic physics. It is completely different.

Quantum mechanics studies the behavior of atoms, photons, and electrons by using a quantum mechanical equation like this in the image below.

File:SchrodingerEquation.svg - Wikimedia Commons

You might fear these weird symbols if you haven’t seen them before or heard about quantum mechanics. But to be honest, in physics, quantum mechanics is a domain that requires a lot of math, especially calculus like derivatives and integrals.

2 – vibrations and waves

Physicists study a specific module called vibration and waves, in which mechanical systems vibrate and interchange the energy. for example, you will study:

  • how pendulum work
  • study spring and calculate their forces
  • the relation between energy and Mass
  • how you can break a glass of wine just with a sound ( reasoning phenomena)

The module is heavy in math like calculus and especially differential equations. In other words, you will make a lot of derivatives.

3 – Thermodynamics

thermodynamics is a field that studies energy and its relation between temperature and volumes. In other words, it is a domain that makes combustion machines like plane engines or cars work.

In general, you will study :

  • how the energy is exchanged from object to other
  • The entropy ( which is the science of chaos)
  • you will study how particles behave in different temperatures and volumes

In other words, you will deal a lot with volumes and liquids. This domain is closer to chemistry.

4 – Fluid dynamics

Fluid dynamics is a physic domain that studies the behavior of fluids like oil and water. To clarify, you will study:

  • the pressure on the pipes
  • how boats or submarines move in the water
  • the equations that relate between Masse and volume
  • know what the density is and how it relates to masse and volume
  • Know what is energy in fluid dynamics systems

A fluid dynamic system is known for applying a lot of calculus, especially equation differential, making it the hardest subject in the physics major field.

5 – Solid state physics 

solid state physics is a domain that studies fixed objects like buildings, bridges, or any non-mobile object. In other words, it is a domain that protects buildings and bridges from collapsing.

You will study in detail molecules and particles. In addition, to learning and applying newton theorems like forces and friction of objects.

What do students study in calculus?

The 3 principals components that students study about calculus that for sure are used in physics too are:

  • limits
  • derivative
  • integral

step1 learning limits

To not dig into details limits is a pillar subject in calculus. In other words, it is a mathematical method that helps to determine the state of functions. To explain, let’s talk about an example.

Trigonometry or calculus

Now we have a pool and want to fill it with water. But the water debit at night is bigger than a day. So we want to determine how much time we need to fill this pool during the night compared to the day.

To determine the difference, we need, in this case, to use the limit function. We don’t want to go into technical details but just need to keep your approach of how much limit interested in math and calculus.

You could watch this adorable video about how calculus is used in real life.

step 2 derivative

The derivative is a second part that students learn in calculus. To simplify, the derivative is the ability to study the change of functions. Or, in other words, how things are evaluated in the environment.

It is hard to explain derivatives for people who haven’t studied yet. But the example that will notice will be helpful to give a close idea about derivatives.

 calculus in travel

let’s say we have a plane and we need to cross a distance between new york and Paris, which is 5834 km and the plane speed is 1000km/h. So how of time need a plane takes to cross this distance?

It is easy. The response is 1000/5834 = 5.834 hours.

But if we say that the plane speed is not constant in the first 2000 km, the speed of the plane is 800km/h, and the rest is 1000km.

So how much time will it take for a plane to get to Paris?

So as we can see, things are different. You can’t calculate it easily. In this case, we need to use derivatives. We won’t tell you how to do that but just make the message clear.

step 3 integral

The last and most important thing is integral in mathematics. Integral is used in many applications. But in most cases, it is used to calculate surface and volumes.

let’s say we have this geometry forme

calculate the air

if someone asks you to calculate the air of this geometry, you won’t be able to do that. Because there is no specific rule that can calculate the air of this shape.

In this case, integral play its role. The integral use a technic of splitting each part of geometry and calculating it individually. calculus is used to calculate:

  • airplane wings
  • cartridges surfaces or volumes
  • any complex surface that can be measured in traditional ways

Algebra-based physics vs calculus-based physics

Algebra-based physics is that study and focuses on algebra topics, including matrices, vectors, and trigonometry. While calculus-based physics narrows down to topics like derivatives, limits, and integrals.

Using based physic algebra only in some physics applications like dynamics will not allow you to solve or study how an object can move in the air. So calculus is also important to implement.

To explain more, let’s say that we have this person who needs to jump between rockss, as is noticed in the image below.

If someone asks you if this person can jump and reach another side, how will you do that?

Calculus-based students and algebra ones study this subject differently.

In algebra-based physic, where students don’t study calculus, they have to give you this equation to solve this issue.

Whereas if you study calculus physics, you need to prove this relation or equation. As a result, they start to form the ground ( first newton and the second law of newton) to attend to this equation.

As a result, it allows them to understand kinematics principles more than algebra-based physics classes deeply.

So it is better to take both or combined algebra and calculus-based courses to understand physics deeply. Because there are no alternatives in some applications like quantum mechanics and thermodynamics, you will be forced to use calculus.


Calculus and physics are one thing. Without calculus, we would not have physics. Calculus collaborates hugely to explain many physical phenomena we live in our lives.

As a recommendation, the first thing that students should do is learn calculus and understand it well, then go ahead and apply it in physics.

you can read this article 13 interesting reasons why the US focuses on calculus


Yassin ajanif is a physics graduate and electromechanical engineer width more than 5 years in the field. My goal and my team are to share our experience to help you succeed in your career as a stem major. we talk about all tips, problems, and struggle STEM students face in their career and how to overcome them.