Calculus
Learn Calculus for Free
Calculus is the study of change, motion and accumulation. It provides tools for understanding how quantities vary and is used across science, engineering, economics, computer graphics and many real-world systems.
This page introduces the main ideas in calculus and links to free, accessible learning resources including games, worksheets and practice materials.
Start Learning Calculus
Introduction to Calculus
A beginner overview explaining what calculus is, why it matters, and how limits, derivatives and integrals fit together.
Understanding Limits
Introduces limits, how they describe behaviour near a point and why they form the foundation of calculus.
Derivatives (Basics)
Explains what a derivative represents, simple rules for differentiation and how derivatives describe rates of change.
Integrals (Basics)
Covers the idea of integration, areas under curves and the relationship between derivatives and integrals.
Functions and Graphs
Introduces functions, domains, ranges and how graphs represent relationships.
Intermediate Calculus
Advanced Differentiation
Covers product, quotient and chain rules, plus derivatives of trigonometric, exponential and logarithmic functions.
Applications of Derivatives
Explores tangent lines, optimisation, rates of change and graph analysis using derivatives.
Advanced Integration
Introduces substitution, integration by parts, partial fractions and definite integrals.
Applications of Integrals
Includes area between curves, volumes of solids of revolution and solving basic differential equations.
Sequences and Series
Explains sequence behaviour, convergence and introductory series concepts.
Advanced Calculus
Multivariable Calculus
Introduces functions of several variables, partial derivatives and multiple integrals.
Vector Calculus
Covers vector fields, line integrals, divergence, curl and major theorems.
Differential Equations
Explains first-order and higher-order differential equations and where they appear in real contexts.
Fourier Series & Transforms
Introduces breaking functions into frequency components and basic transform ideas.
Calculus Resources
Calculus Games
Interactive tools and games that help reinforce core calculus skills.
Calculus Worksheets
Downloadable worksheets, generators and printable practice problems.
Optional Next Steps
These pages deepen understanding once you’re comfortable with the fundamentals:
- Practical Applications of Calculus – Examples in physics, engineering, economics and biology.
- Calculus in Careers – How calculus appears in real professions.
- Advanced Problem Solving – Challenging problems and explanations.