Calculus by Khan Academy

About this course

Calculus can feel like a new language at first, but once the key ideas click, it becomes one of the most powerful tools you can use to describe change, motion, growth, and optimization. This free online course guides you from the first intuitions behind limits and rates of change to the kinds of problems used in exams and real applications. You will learn to think clearly about how a function behaves near a point, how small input changes create big effects, and how those ideas connect naturally to slopes, areas, and accumulated quantities.

Instead of treating formulas as things to memorize, the course builds understanding step by step: you strengthen your intuition for limits, connect the derivative to tangent lines and instantaneous velocity, and practice using differentiation rules to handle increasingly complex expressions. Along the way, you develop the ability to interpret graphs using derivative information, identify patterns like concavity and inflection points, and solve optimization and related-rates problems with a structured approach that reduces guesswork.

As you progress, integration appears not as a separate topic but as a natural counterpart to differentiation. You will learn to model accumulation with definite integrals, compute antiderivatives with reliable techniques, and apply integrals to geometry and motion. The course also expands your toolbox with series and polynomial approximations, helping you estimate functions and understand why approximations work so well near a point.

For learners ready to go further, the material opens the door to multivariable calculus and vector calculus ideas such as partial derivatives, gradients, divergence, curl, and multiple integrals, building intuition for surfaces and fields in higher dimensions. With plentiful practice opportunities, this course is designed for students aiming to improve school performance, prepare for standardized assessments, or strengthen the math foundation used in physics, engineering, economics, and data-driven fields.