What is Calculus?
Are you ready to tackle one of the most advanced subjects in high school math? Meet UPchieve—your free, online tutoring platform! Sign up today and get help mastering calculus concepts.
Introduction to Calculus
When starting a challenging subject like calculus, it’s important to have a solid understanding of everything you’ve learned in algebra, geometry, and pre-calculus. UPchieve is here to help you whether you need to freshen up your math skills or prepare for your AP Calculus exam.
Today, we’re breaking down the basics of calculus. By the end of this blog, you’ll know the answer to “What is calculus?” and have a foundation for tackling its most important concepts.
What is the Definition of Calculus?
Calculus is defined as “a branch of mathematics that studies continuous change using concepts like limits, derivatives, and integrals.”
In simpler terms, calculus helps us understand how things change over time or how quantities accumulate. It’s like tracking how fast a car is going at one specific moment (not over time, but right now) or figuring out how much space is under a curved graph.
There are two main branches of calculus:
Differential Calculus: Focuses on how things change, like how fast something is moving or growing.
Integral Calculus: Focuses on total accumulation, like finding the total area under a curve.
If you think of calculus as a video game, differential calculus is like figuring out how fast your character is moving, while integral calculus is like tracking how far you’ve gone in total.
The Two Main Type of Calculus
As we briefly mentioned above, Calculus is divided into two main categories, but each type introduces its own important concepts.
Differential Calculus
Differential calculus is all about understanding change. Imagine you're tracking how fast a car is going right now, not the average speed. That’s what a derivative measures — the instantaneous rate of change.
Key Concepts: Derivatives, rates of change, slopes of curves.
Real-World Examples:
Calculating how fast a car is moving at an exact moment.
Predicting how fast your savings account balance will grow.
Measuring the speed of a growing population in biology.
Integral Calculus
Integral calculus is the opposite of differential calculus. It’s about understanding total accumulation—like figuring out how much water has filled up a glass over time. It helps you find the total area under a curve, which comes in handy for everything from physics to economics.
Key Concepts: Integrals, areas under curves, accumulation.
Real-World Applications: Physics (area under velocity curves), economics (total cost/revenue), and statistics (calculating probabilities). For example:
Calculating the total distance a car has driven.
Finding the total amount of liquid in a tank after it’s been filled.
Measuring revenue over time for a business.
Both of these concepts are essential for more advanced math, physics, and engineering. You’ll also see them a lot in AP Calculus. If you're preparing for the AP Calculus AB exam, check out our guide on How to Ace the AP Calculus AB Exam for tips, strategies, and key concepts to focus on.
What Grades and Ages Need to Learn Calculus?
Calculus is typically taught in the 11th or 12th grade, but it depends on your school’s curriculum. If you’re on an advanced track, you might see calculus earlier, especially if you’re taking AP Calculus AB or AP Calculus BC.
How UPchieve Can Help with Calculus
Let’s be real—calculus can be overwhelming. But guess what? You don’t have to figure it out alone. UPchieve provides free, 24/7 online tutoring for students who need support. Whether you’re working on a tricky homework problem or trying to review for an exam, we’ve got your back.
Here’s what makes UPchieve different:
24/7 Availability: Connect with a tutor anytime—even at midnight before your big test.
1:1 Support: You’ll work directly with a tutor who can explain things step-by-step.
Interactive Whiteboard: Visualize tough concepts with a shared whiteboard.
Completely Free: It’s 100% free for low-income students, as part of our nonprofit mission.
If you’re looking for personalized support from a tutor, check out our online calculus tutor page to learn more about how you can get expert help on demand.
We know it’s frustrating when limits don’t "make sense" or when derivatives feel like a mystery. UPchieve tutors are here to make calculus feel more manageable. Get started today for free!
FAQs: How to Get Free Calculus Tutoring
How do I sign up for free calculus tutoring?
It’s easy! Here’s how it works:
Create a free UPchieve account.
Connect with a tutor in under 10 minutes.
Work with your tutor in a live chat or whiteboard to solve calculus problems together.
No appointment required! Just instant help.
How much does UPchieve calculus tutoring cost?
UPchieve tutoring is 100% free. We’re a nonprofit, so our goal is to make education accessible for low-income students. There are no fees, subscriptions, or payments—ever.
When can I get help with calculus?
Anytime! UPchieve offers 24/7 tutoring, which means you can get support at 2 pm, 10 pm, or even 2 am if you’re cramming for a big exam.
Can I get help with AP Calculus?
Absolutely! Our tutors are trained to support students in AP Calculus AB and AP Calculus BC. We know those classes are tough, and we’re here to help you succeed. If you’re looking for extra AP support, check out our blog post on How to Ace the AP Calculus AB Exam for helpful tips.
Can I get help with calculus homework?
Yes! Our tutors can walk you through tough homework problems and help you understand each step, so you’re ready for future assignments. They won’t just give you the answers—they’ll help you understand why the answers work.
What topics can I get help with?
UPchieve tutors can help with every major topic in calculus, including:
Limits
Derivatives
Chain Rule
Product Rule
Integrals
Area Under a Curve
Optimization Problems
If you have a specific topic in mind, we can help!
Can I get help with test preparation for calculus?
Yes! Our tutors will help you prepare for class tests, final exams, and standardized exams like the AP Calculus AB/BC tests. You’ll get test-taking strategies, practice problems, and expert guidance.
Can I work with a calculus tutor near me?
UPchieve tutoring is online, so it doesn’t matter where you live. Connect with a tutor from anywhere in the U.S., right from your phone or laptop.
Can I get live help for AP Calculus?
Yes! Our live tutors can support you in real time as you review AP Calculus material. If you’re looking for specialized AP tutoring, check out our online calculus tutor page to learn more.
How fast can I get help?
It takes under 5-10 minutes to connect with a live tutor. No appointments required, and no waiting lists. Just go to UPchieve and get support when you need it most.