How many times have you found yourself sitting in a math class asking: **“When is calculus actually used for in real life?” **That’s exactly what I thought when I was in high school. Now that I’m at University taking Calculus, I really want to know how it’s useful in real life.

I did some research and found out many different functional uses that Calculus has had since its discovery. Today, you can find Calculus within all manner of sciences such as chemistry, physics, computer science, and engineering, and even business and economics.

**What Is Calculus Used For?**

**Calculus is used for optimization, summation, and predicting trends through modeling change over time. For example, a manufacturer could use Calculus to optimize production costs. Another example is meteorologists using Calculus to predict the weather patterns.**

### Calculus Uses In Business

**In Business, Calculus is mainly used for optimization. This includes maximizing profits, minimizing cost, and maximizing or minimizing production. Also, Calculus can be used to calculate the rate of change in cost or the marginal revenue for an interest-bearing account.**

Let’s look at an example of a factory that manufactures and sells * dress-shirts*. This factory is capable of producing 60,000 dress-shirts per week. However, they want to optimize their production rate in order to

*minimize their production costs.*How many dress-shirts should they produce weekly?

Let C(x) represent the production cost defined by the following function:

The first thing we want to do is solve for the derivative. Simple enough:

Next, set the derivative equal to zero and solve for x:

And there we have it! Since there’s no possible way for the factory to make a negative amount of dress-shirts, the optimal number produced is positive. We can see this when we graph the original cost function, C(x). The critical point is the positive x-intercept which as we calculated earlier from C'(x), is *50,000.*

### Calculus Uses In Engineering

**In Engineering, Calculus is mainly used for optimization and summation. This includes the famous Navier-Stokes equations which describe the physical phenomena produced by aircraft. These equations are very useful to Aerospace Engineers. **

The Navier-Stokes equations describe the motions of fluid-like substances, such as liquids and gases. This is why they’re so useful in the engineering of ** aircraft**.

However, the Navier-Stokes equations are actually much more versatile, having applications in modeling the motion of stars, weather, pollution, ocean currents, and blood flow.

If the equation above looks like an alien language, then you’re not alone. Few people can look at the above and understand the implications, let alone what each of the characters represents and how they relate to each other. Each character represents the following:

* ρ* = Density of the fluid

** v** = Velocity of the fluid

*D**v** / Dt* = The derivative of ‘** v**‘ with respect to time, ‘

*t*‘

**∇** (Del) = Gradient of the Vector Field

= (tensor) Surface forces on fluid

= Additional body forces

These equations are typically taught in Calculus 3 (Vector / Multivariable Calculus) and beyond. However, the Navier-Stokes equations aren’t completely solved. The *Navier-Stokes existence of smoothness equation* is part of the Millenium Prize Problems: 7 unsolved problems that will earn any person $1,000,000 if they solve just one of them.

Read more about the Navier-Stokes equations and the Millenial prize problems here:

**Wikipedia: Millenium Prize Problems**

### How Is Calculus Used In Physics

**The applications of Calculus in Physics are abundant. This is because time is virtually always a factor in physics and because modeling change is the primary function of Calculus. The applications include all matter of kinematics, electrodynamics, fluid dynamics, and more.**

Let’s look at a basic example of Calculus in kinematics using * go-carts*.

You’re driving a high-speed go-cart, racing your friend. When you cross the finish line (in 1st place), you hit the brakes and decelerate constantly at 16 feet per second squared. Your go-cart travels 200 feet after you hit the brakes before it finally stops. How fast were you going when you first braked?

First, it’s important to note that there are three functions all dependent on time ‘t’ in this equation: *position, velocity, and acceleration*. These three functions are related, as they are the derivatives and antiderivatives of each other.

** Acceleration** (is the derivative of)

**(is the derivative of)**

*Velocity*

*Position*And the reverse is true, also.

** Position** (is the antiderivative of)

**(is the antiderivative of)**

*Velocity*

*Acceleration*Now let’s define these functions and set up our equation.

Let ** s(t)** =

*Position*Let

**=**

*v(t)*

*Velocity*Let

**=**

*a(t)*

*Acceleration*Braking Begins | Braking Ends |

Time ‘t’ = 0 | Time ‘t’ = n |

Position s(0) = 0 | Position s(n) = 200 |

Velocity v(0) = ? | Velocity v(n) = 0 |

Acceleration a(0) = -16 | Acceleration a(n) = -16 |

Since we know the ** Acceleration** function

**= -16 (we’re decelerating so the acceleration is negative), we can take the antiderivative to find the**

*a(t)***function**

*Velocity***.**

*v(t)*Now, let’s take the antiderivative of our * Velocity* function to get our

*function.*

**Position**If we consider that at time t=0, the position is 0, we can see that the constant ‘D’ is equal to 0. This leaves us with the following functions for ** Position** and

**.**

*Velocity*Now let’s solve for ‘n’ (the time it takes to come to a complete stop). We’ll do this by plugging ‘n’ into our equation for our time value and using substitution with these two equations.

From here, it’s very simple to plug ‘n’ into our other highlighted equation for ‘C’ to reach our final answer. It took * 5 seconds to stop* and our go-cart was originally going

*80 feet per second.*As trivial as calculating the speed of a go-cart might seem, the same mathematical principals can be applied to something more substantial, such as calculating the landing path of a rocket.

Also, as complicated as this calculation may seem, it’s actually very basic. This calculation can be solved by many first-year University students.

### How Is Calculus Used In Chemistry

**In Chemistry, Calculus is used for modeling reactions, calculating radioactive decay rate, transferring heat, and much more. This includes and extends beyond thermodynamics, electrochemistry, analytical chemistry, and quantum chemistry.**

Let’s see how Calculus is used in finding the ** radioactive decay rate** of Uranium 238.

We’ll start by looking at a simple formula:

This formula states that, whether I have a *large* or a *small* sample of radioactive matter, it will decay at a rate proportional to its size. Because of this, the decay rate actually changes as time goes on and the sample shrinks. This is why Calculus is so useful in determining the decay rate at any given time.

= The number of atoms decaying per second in a given sample

= Number of atoms (size of the sample)

= The decay constant, specific to each radioactive element (Uranium-238 = )

Now, knowing the decay constant and using a little calculus, we can come up with our formula to solve for decay rate at any given time. Let’s take our first formula and move our ‘N’ term to one side.

Next, we’ll integrate over a general interval and evaluate said integral.

Then, we’ll combine the left side of the equation using log rules.

Cancel out the natural log (ln).

Finally, multiply both sides by

There we have it! We’ve arrived at the formula for radioactive decay, which we could very easily use to solve the half-life of our sample.

### Calculus In Computer Science

**In Computer Science, Calculus is used for machine learning, data mining, scientific computing, image processing, and creating the graphics and physics engines for video games, including the 3D visuals for simulations. Calculus is also used in a wide array of software programs that require it. **

Once you reach Calculus 3, you learn about 3D models using multiple variable equations. One way Computer Science students utilize these models is through ** game development**.

In video game development, Calculus comes into play in major ways:

- 3D graphics and illumination
- Physics engines

As the Physics applications were discussed earlier with the go-cart example, let’s look at the application in 3D graphics and illumination. More specifically, let’s look at spherical harmonics.

** Spherical harmonical functions **are solutions to the Laplace formula when restricted to a sphere.

#### How is Calculus used in developing video games?

By using and manipulating Laplace formulas, developers can create a 3D mapping of virtual environments and their textured surfaces. Models are also used to apply appropriate shadows, illumination, and refraction to represent the physical world and the objects that move through it.

Read more about Spherical Harmonics and how they’re used in developing games from Peter-Pike Sloans scholarly article here:

**Peter-Pike Sloan: Stupid Spherical Harmonics (SH) Tricks**

#### Watch this **short video** to learn more about developing games:

## FAQs

### How is calculus used in real life with example? ›

Calculus is used **to improve the architecture not only of buildings but also of important infrastructures such as bridges**. In Electrical Engineering, Calculus (Integration) is used to determine the exact length of power cable needed to connect two substations, which are miles away from each other.

### How is calculus used in industry? ›

In Business, Calculus is **mainly used for optimization**. This includes maximizing profits, minimizing cost, and maximizing or minimizing production. Also, Calculus can be used to calculate the rate of change in cost or the marginal revenue for an interest-bearing account.

### How is calculus used in comp sci? ›

Calculus is used in an array of computer science areas, including **creating graphs or visuals, simulations, problem-solving applications, coding in applications, creating statistic solvers, and the design and analysis of algorithms**.

### What's calculus used for? ›

Applications of integral calculus include **computations involving area, volume, arc length, center of mass, work, and pressure**. More advanced applications include power series and Fourier series. Calculus is also used to gain a more precise understanding of the nature of space, time, and motion.

### What is calculus 3 used for in real life? ›

If a quantity or a system is changing. We can use a mathematical modeling of calculus to analyze a

### What is the use of calculus in real life Quora? ›

Calculus is the one of the main subjects which is widely used in various fields. It is the core of applied mathematics. Calculus is the language of engineers, scientists, and economists. **Most common applications are in engineering, computer science, finance, economics, etc.**

### What is an example of calculus? ›

Integral calculus is the process of calculating the area underneath a graph of a function. An example is **calculating the distance a car travels**: if one knows the speed of the car at different points in time and draw a graph of this speed, then the distance the car travels will be the area under the graph.

### How is calculus used in sports? ›

Athletes, trainers, and coaches often use calculus **to gain benefits over their counterparts**. Calculus can also be used to calculate the projectile motion of baseball's trajectory, speed of baseball when hit, and predict if runners can make it to the next base on time, given their running Speed.

### How important is calculus in business? ›

Benefits. Calculus, by determining marginal revenues and costs, **can help business managers maximize their profits and measure the rate of increase in profit that results from each increase in production**. As long as marginal revenue exceeds marginal cost, the firm increases its profits.

### Do you need calculus for business? ›

For many aspiring business students, the most harrowing component of the entire experience is the math coursework. **The business degree track requires students to take calculus**, often a dreaded and difficult experience for many.

### How is calculus used in engineering examples? ›

Many examples of the use of calculus are found in mechanical engineering, such as **computing the surface area of complex objects to determine frictional forces, designing a pump according to flow rate and head, and calculating the power provided by a battery system**.

### Why do CS majors need calculus? ›

In short, a computer scientist major learns calculus, not because it is necessary for software engineering, which does not require a CS degree at all, but **because of what Computer Scientists can potentially do: Software pioneering, refinement, and computational theory**.

### Do you need calculus for CS? ›

Computer science is a broad field, so if you're looking to get your computer science degree, the kind of math you'll need to know will depend on your specific program and career path. But generally speaking, **most degree programs require a basic understanding of calculus, algebra, discrete mathematics, and statistics**.

### Do you need calculus for cyber security? ›

**Calculus is typically not a required course for cybersecurity majors at any level**. Most cybersecurity programs will require one or two math courses to be completed for graduation, however, in most cases, those courses are non-calculus courses.

### What are the 3 main topics in calculus? ›

**The Three Calculus Concepts You Need to Know**

- 1) Limits. Limits are a fundamental part of calculus and are among the first things that students learn about in a calculus class. ...
- 2) Derivatives. Derivatives are similar to the algebraic concept of slope. ...
- 3) Integrals.

### Why is it called calculus? ›

Isaac Newton and Gottfried Leibniz are both credited with the invention of modern calculus in the 17th century. In Latin, calculus means “pebble.” **Because the Romans used pebbles to do addition and subtraction on a counting board, the word became associated with computation.**

### What kind of jobs use calculus? ›

**12 jobs that use calculus**

- Animator.
- Chemical engineer.
- Environmental engineer.
- Mathematician.
- Electrical engineer.
- Operations research engineer.
- Aerospace engineer.
- Software developer.

### Is calculus 3 used in engineering? ›

The answer is **yes.** **They need to take at least three calculus courses, including Calculus 3**. It's also the foundation for many hardware courses. If you're interested in computer engineering and want to know how Calculus 3 in particular and math, in general, affect this technological field, this post is for you.

### How is calculus used in music? ›

Music is said to represent the dynamics of human emotion. The dynamics and tension created by music fluctuates, as do human emotions while we are listening. Calculus can be a powerful tool in **showing these fluctuations and dynamic changes, as well as showing us how well the volume is balanced**.

### Why is calculus important in engineering? ›

In many science and technology programs, Calculus is among the first courses taught. It is considered one of the most important early courses in engineering, **allowing students to subsequently study and model real problems in ways that can be applied to their professional lives**.

### Is calculus used in finance? ›

**Stochastic calculus plays a large role in financial forecasting**, and it is notably implemented in options pricing models such as the Black-Scholes model and the binomial model.

### Is calculus used in biology? ›

**Calculus is important for understanding dynamical systems in biology** and, therefore, is often a required course for life science students. However, many life science students do not understand the utility value of mathematics to biology.

### What are the 4 concepts of calculus? ›

**The main concepts of calculus are :**

- Limits.
- Differential calculus (Differentiation).
- Integral calculus (Integration).
- Multivariable calculus (Function theory).

### What are the 3 tools of calculus? ›

In calculus, we use three main tools for analyzing and describing the behavior of functions: **limits, derivatives, and integrals**. Students will use these tools to solve application problems in a variety of settings ranging from physics and biology to business and economics.

### What are two types of calculus? ›

Calculus is the mathematics of change and motion. There are two types, **differential calculus, finding the rate of change of a function and, integral calculus**, finding the function when its rate of change is given.

### Why is math so important in sports? ›

**Most sports incorporate a certain amount of math in the rules, the way the game is played, and strategies for winning**. Whether it's angles, calculating scores, or figuring out how to distribute players on a field, math comes in handy.

### Where is maths used in sports? ›

Math is used in sports for everything, from **calculating scores to average points, scoring goals, winning scores, creating leaderboards, developing strategies, and calculating probability**. How can Math Assist Children in Improving Their Sports Performance?

### Where integration is used in real life? ›

In real life, integrations are used in various fields such as **engineering, where engineers use integrals to find the shape of building**. In Physics, used in the centre of gravity etc. In the field of graphical representation, where three-dimensional models are demonstrated.

### Do you need calculus for marketing? ›

At a minimum, marketers need to do reporting, which is based on math. They should also be measuring their money, which again is math. **There are a wide variety of math skills that marketers should have.** **These include statistics, geometry, economics, finance and even calculus.**

### How much calculus is used in engineering? ›

Most engineering degree plans require **three semesters** of calculus.

### Do I need calculus for economics? ›

Because the study of economics involves a substantial amount of quantitative analysis, **Economics majors are required to complete a course in calculus prior to beginning the courses of the major**.

### Who needs to take calculus? ›

Introductory calculus is required of **students majoring in the natural sciences, including biology, chemistry and physics**. Students planning on attending medical school, dental school or veterinary school also take calculus, regardless of major.

### Is calculus used in accounting? ›

Accounting isn't hard-core math. It's basic addition, subtraction, multiplication, and division. Possibly some light, entry-level algebra, but that's it. **You don't have to understand calculus**.

### How difficult is calculus? ›

**Calculus is not the hardest type of math**. While calculus may be the hardest type of math offered in high school and most college programs; it is far from being the hardest when compared to all the types of math available. Courses such as analysis, topology, and differential geometry are all harder than calculus.

### How is calculus used in electrical engineering? ›

Calculus is used by engineers **to determine rates of change or rates by which factors, such as acceleration or weight, change**.

### Is calculus used in software engineering? ›

Yes. If you look at a list of required coursework for a degree in software engineering, you'll typically see **Calculus I-III**, Differential Equations, Discrete Mathematics, Linear Algebra, and other advanced math classes.

### How is calculus used in video games? ›

Initially the calculus of physics engines in video games was delegated to **detecting collisions between in-game objects (such as player characters, rocks, and dust particles) and enacting appropriate responses**.

### Why do computer engineers learn calculus? ›

Computers can take massive amounts of data in the form of variables and absolutes and process that data into calculations, predictions, and emulations. As fascinating as they may seem, however, computers are calculators. **Calculus is the finding and properties of derivatives and integrals of functions**.

### Why does computer science need math? ›

Math is an essential component of computer science which **underpins computing and programming concepts**. Without it, you would find it challenging to make sense of abstract language, algorithms, data structures or differential equations. All of which are necessary to fully appreciate how computers work.

### Why do doctors need calculus? ›

Calculus. Calculus is the study of unknown variables in relation to a system over time. It can **help doctors understand the chemical reactions that occur in the body over time as well as the body's evolving relationship to different medical devices**.

### How many years is calculus in computer science? ›

Calculus Prerequisites

Requirements vary across programs, but many require students to take **three semesters** of calculus. Calculus is an advanced mathematics course that teaches students about rates of change and it is essential to the study of computer science.

### Is computer science heavy in math? ›

You will have to learn subjects like Calculus, Algebraic Methods, Trigonometry, Probability and Statistics. However, some aspects of Computer Science are more math heavy than others. This can influence your future career choice, as you explore each avenue and discover the areas which you enjoy.

### How hard is computer science? ›

The short answer is “yes.” Search any list of majors to study, and you'll likely find that computer science tops the list as **one of the most challenging disciplines to learn**. Compared to other fields of study, pursuing a career in computer science requires both technical and analytical skill sets.

### Is cyber security math heavy? ›

**Most entry-level and mid-level cybersecurity positions like cybersecurity analyst aren't math intensive**. There's a lot of graphs and data analysis, but the required math isn't particularly advanced. If you can handle basic programming and problem solving, you can thrive.

### Is cyber security a hard degree? ›

Cyber security degrees **tend to be more challenging than non-research type majors**, such as programs in the humanities or business, but are usually not as difficult as degrees in research or lab intensive areas, such as science and engineering.

### What kind of math is used in cyber security? ›

Binary math is the language of computer systems. The smallest layer of information in computer programming is known as a "bit," equal to a 0 or 1. Data is stored in strings called bytes or unique combinations of these bits. This binary math is the heart of all computer programming.

### What is the hardest topic in calculus? ›

In terms of issues affecting most students I believe **the concept of a variable and that of a function** are still the most difficult concepts for calculus 1 students, even though the concepts are introduced in precalculus. Writing a full and correct mathematical sentence is a topic most students struggle with.

### What is the basic formula of calculus? ›

Fundamental Theorem of Calculus:

**∫baf(x)dx=F(b)−F(a)** ∫ a b f ( x ) d x = F ( b ) − F ( a ) where F is any antiderivative of f.

### How many types of calculus are there? ›

Calculus Mathematics is broadly classified into **two** different such: Differential Calculus. Integral Calculus.

### When was calculus first used? ›

Calculus, as it is practiced today, was invented in the 17th century by British scientist Isaac Newton (1642 to 1726) and German scientist Gottfried Leibnitz (1646 to 1716), who independently developed the principles of calculus in the traditions of geometry and symbolic mathematics, respectively.

### Who founded calculus? ›

Today it is generally believed that calculus was discovered independently in the late 17th century by two great mathematicians: **Isaac Newton and Gottfried Leibniz**.

### What is concept of calculus? ›

calculus, branch of mathematics concerned with the calculation of instantaneous rates of change (differential calculus) and the summation of infinitely many small factors to determine some whole (integral calculus).

### How is calculus used in airplanes? ›

The calculus of variations has become increasingly popular in applied aerodynamics **through the study of the optimum shapes of aircraft and missile components and flight mechanics through the study of the optimum trajectories of aircraft, missiles, and spaceships**.

### How is calculus used in architecture? ›

Architects also use integral calculus **to calculate the amount of materials needed for construction and the type of support systems required to prevent constructions from collapsing**. Even the Eiffel tower was constructed with calculus in mind, focusing exclusively on wind resistance.

### What job uses the most math? ›

**Career Paths for Math-Lovers**

- Computer Programmer: $84,280. ...
- Medical Scientist: $84,810. ...
- Financial Analyst: $85,660. ...
- Statistician: $88,190. ...
- Actuary: $102,880. ...
- Economist: $104,340. ...
- Software Developer: $105,590. ...
- Data Scientist: $121,500.

### What kind of jobs use calculus? ›

**12 jobs that use calculus**

- Animator.
- Chemical engineer.
- Environmental engineer.
- Mathematician.
- Electrical engineer.
- Operations research engineer.
- Aerospace engineer.
- Software developer.

### How integration is used in real life? ›

In real life, integrations are used **in various fields such as engineering, where engineers use integrals to find the shape of building**. In Physics, used in the centre of gravity etc. In the field of graphical representation, where three-dimensional models are demonstrated. Was this answer helpful?

### Why is calculus so hard? ›

Most of the reasons students have difficulty learning calculus is because **they don't study daily after lessons, can't focus in class, have gaps in their math knowledge, and think learning calculus is a waste of time**. Here are the steps you can take to make calculus a breeze: Stay curious. Ask questions.

### What are the 4 concepts of calculus? ›

**The main concepts of calculus are :**

- Limits.
- Differential calculus (Differentiation).
- Integral calculus (Integration).
- Multivariable calculus (Function theory).

### How much calculus is used in engineering? ›

Most engineering degree plans require **three semesters** of calculus.

### How is calculus used in electrical engineering? ›

Calculus is used by engineers **to determine rates of change or rates by which factors, such as acceleration or weight, change**.

### Where is derivative used in real life? ›

Application of Derivatives in Real Life

**To check the temperature variation**. To determine the speed or distance covered such as miles per hour, kilometre per hour etc. Derivatives are used to derive many equations in Physics. In the study of Seismology like to find the range of magnitudes of the earthquake.

### What are examples of functions in real life? ›

**10 Real World Examples of Functions and Relations**

- The Relationship between Age and Height. ...
- A Semester in School. ...
- Temperature and Location. ...
- The Cost of Fuel. ...
- The Cost of Taking a Taxi. ...
- Money Won from a Lottery Ticket. ...
- The Number of Sodas in a Vending Machine. ...
- Places you can drive with Two Gallons of Fuel.

### Why is differential calculus important? ›

Differential calculus **makes it possible to compute the limits of a function in many cases when this is not feasible by the simplest limit theorems** (cf. Indefinite limits and expressions, evaluations of). Differential calculus is extensively applied in many fields of mathematics, in particular in geometry.

### Which math is hardest? ›

Today's mathematicians would probably agree that the **Riemann Hypothesis** is the most significant open problem in all of math. It's one of the seven Millennium Prize Problems, with $1 million reward for its solution.

### Who needs to know calculus? ›

Introductory calculus is required of **students majoring in the natural sciences, including biology, chemistry and physics**. Students planning on attending medical school, dental school or veterinary school also take calculus, regardless of major.

### How long does it take to learn calculus? ›

Self-studying probably takes half again as long as learning in a class, so **375 hours at a high-school pace or 180 hours at a college pace**. If you want to extend this to basic college calculus, add another 90 hours + 180 hours of homework/studying or 405 hours of self-study.