Calculus Formulas: Cheat Sheet

Calculus Formulas is a clear calculus cheat sheet for high school and university: more than 250 formulas in 57 topics, from limits and derivatives to integrals, series and differential equations.
Every derivative formula and integral formula is typeset cleanly, explained in plain language and followed by worked examples. It all works offline.

Each topic page lists the key calculus formulas, says when to use them and shows them in action with worked examples. Practice questions with tap-to-reveal answers help you check what you have learned, and short tips point out common mistakes.

What you will learn

• Precalculus Essentials: algebra toolkit, functions and graphs, trigonometry basics, trigonometric identities, exponentials and logarithms
• Limits and Continuity: what a limit means, limit laws, evaluating limits, limits at infinity and asymptotes, continuity and the Intermediate Value Theorem
• Derivatives: the definition of the derivative, differentiation rules (power, product, quotient and chain rule), a table of derivatives, implicit and logarithmic differentiation
• Applications of Derivatives: tangent lines and linear approximation, related rates, maxima and minima, the Mean Value Theorem, curve sketching, optimisation, L'Hôpital's rule, Newton's method
• Integrals: Riemann sums and the definite integral, the Fundamental Theorem of Calculus, a table of integrals, integration by substitution, integration by parts, trigonometric integrals, trigonometric substitution, partial fractions, improper integrals, numerical integration
• Applications of Integrals: area between curves, volume by disks and washers, cylindrical shells, arc length and surface area, average value of a function, work, mass and centre of mass
• Sequences and Series: infinite series, convergence tests, power series, Taylor and Maclaurin series, and a table of Maclaurin series
• Parametric and Polar: parametric equations, polar coordinates, calculus in polar coordinates
• Multivariable Calculus: vectors in space, partial derivatives, gradient and directional derivatives, extrema of functions of two variables, double and triple integrals
• Differential Equations: slope fields, separable equations, Euler's method, first-order linear equations, growth, decay and logistic models, second-order linear equations

Features
• More than 250 calculus formulas in 57 topics and 10 sections
• Tables of derivatives, integrals and Maclaurin series
• 142 worked examples with every step shown
• 109 practice questions with tap-to-reveal answers
• 34 original drawings: secant and tangent lines, Riemann sums, area between curves, disk and shell methods, Taylor polynomials, polar curves, slope fields and more
• Search all topics from the home screen
• Dark mode
• Works offline, no account needed
• Available in 8 languages: English, Español, Português, Français, Deutsch, العربية, हिन्दी and Bahasa Indonesia

Who it is for
• High school students taking calculus; useful when revising for AP Calculus AB and BC
• College and university students in Calculus I, II and III
• Engineering, science and economics students who need a quick derivative or integral formula
• Teachers and tutors who want a reliable calculus formula sheet with clear drawings

Calculus Formulas is an independent study aid. Content is checked against the OpenStax Calculus textbooks (Volumes 1 to 3). It is not affiliated with any exam board, textbook publisher or university.

Recent changes:
Improved Arabic display: maths, codes and English names in tables now read in the right order.