Free Printable Math Formula Sheets (PDF)

Get your free, printable math formula sheet pdf here. We offer a calculus formula sheet, a derivative and integral table, and a trig identities sheet. Also find a unit circle chart, an algebra formula sheet, a geometry formula sheet, and a statistics formula sheet with a full z-table. Each sheet is A4. It fits on one page. The statistics sheet adds two z-table pages. Print them well in black and white. They are free to print and share for study.

Every sheet below was written and typeset by CalculusCalc. They aren’t scans or copies of a textbook, so you can download, print and share them for study with no sign-up. Each formula links back to a guide on this site that explains where it comes from and shows worked examples, and most have a step-by-step calculator so you can check your answers.

Calculus

The one-page calculus formula sheet covers the derivative rules, the common integrals, the Fundamental Theorem of Calculus and the key series. Use it for a quick review before a test.

This sheet is ideal for students who have already learned the core concepts of Calculus I and II. You can use it to refresh your memory on fundamental theorems like the Mean Value Theorem or the Integral Test for series convergence. It helps you quickly recall a forgotten rule during problem-solving or identify areas where your memory is weak before an exam. Do not rely on it to learn new concepts; use it as a powerful recall tool.

The derivative and integral table goes further. It lists every standard derivative and antiderivative side by side, the product, quotient and chain rules, the special inverse-trig and logarithm integrals, and the core techniques (substitution, integration by parts and the Fundamental Theorem).

This table is more comprehensive than the general calculus sheet, serving as a deep reference for specific differentiation and integration problems. When you encounter complex functions, this table helps you break them down into known forms. It is particularly useful when you need to confirm the correct application of a rule or technique, such as integration by parts, where remembering the exact setup (∫u dv = uv - ∫v du) is crucial. Use it to verify your steps on homework or practice problems, ensuring you apply the correct formulas for inverse trigonometric and logarithmic functions.

Learn the formulas: derivative rules, integration formulas, chain rule, integration by parts. Check your work with the derivative calculator and the integral calculator.

Trigonometry

The trig identities formula sheet has the reciprocal, quotient, Pythagorean, sum and difference, double-angle, half-angle, power-reducing, even-odd, cofunction and product-to-sum identities. It also has the laws of sines and cosines, and a table of exact values at the special angles.

Trigonometry is fundamental to precalculus and calculus, where you often need to simplify expressions or solve equations using identities. This sheet organizes the vast array of identities into logical categories, making it easy to find the specific one you need. For example, if you are integrating a trigonometric function, you might need a power-reducing identity to transform it into an integrable form. When solving triangles, the laws of sines and cosines are essential. Use this sheet to avoid common errors like misremembering the sign in a sum-and-difference identity or using the wrong form of a double-angle identity.

The unit circle chart shows all 16 special angles in degrees and radians, each labelled with its exact ( (costheta, sintheta) ) coordinates, plus the memory tricks that make it easy to rebuild from scratch.

The unit circle is a cornerstone for understanding trigonometric functions and their values at key angles. This chart not only provides the exact values but also illustrates the symmetry and patterns that exist. You can use the memory tricks to reconstruct the circle’s values on your own, strengthening your understanding rather than just memorizing. This is invaluable when you need to evaluate trigonometric functions without a calculator or when working with inverse trigonometric functions. It also clarifies the relationship between angles in degrees and radians, a common source of confusion for many students.

Learn the ideas: trig identities, the unit circle, trigonometric functions, special right triangles, law of sines and cosines.

Algebra

The algebra formula sheet covers exponent and logarithm rules, factoring patterns, the quadratic formula and discriminant, slope and the forms of a line, arithmetic and geometric sequences, and percentage and interest formulas.

Algebra is the language of higher mathematics, and a strong foundation is crucial. This sheet compiles the most frequently used algebraic formulas and rules, helping you quickly recall how to manipulate expressions and solve equations. For instance, when simplifying complex fractions, you might need to remember exponent rules. When solving for roots, the quadratic formula is indispensable. It also includes practical formulas for sequences and financial calculations, which are often overlooked but vital in many contexts. Use this sheet to reinforce your foundational skills, ensuring you don’t stumble on basic algebra when tackling more advanced problems in calculus or statistics.

Learn the ideas: exponent rules, logarithm rules, quadratic formula, slope formula, sequences.

Geometry

The geometry formula sheet has the area and perimeter of every common 2D shape, the volume and surface area of every common solid, right-triangle facts including the Pythagorean theorem, angle facts, and coordinate geometry (distance, midpoint and the circle equation).

Geometry provides the spatial reasoning skills necessary for many STEM fields. This formula sheet is a comprehensive guide to the measurements and properties of shapes and solids. Whether you need to calculate the area of a complex figure by breaking it into simpler shapes or determine the volume of a three-dimensional object, this sheet has the necessary formulas. It also includes coordinate geometry, which links algebra and geometry, allowing you to represent shapes algebraically. When solving problems involving distance between points or the equation of a circle, this sheet prevents common errors like mixing up formulas or forgetting a key component of the Pythagorean theorem. It’s an excellent resource for anyone reviewing for standardized tests or working on problems that require spatial understanding.

Learn the ideas: area formulas, volume formulas, Pythagorean theorem. Calculators: area, volume, circle.

Statistics

The statistics formula sheet covers measures of center and spread (mean, median, mode, range, variance, standard deviation, IQR), the normal distribution with z-scores, the empirical rule and key critical values, probability rules, permutations and combinations, the binomial formula and expected value. The second and third pages are a full standard normal table, with negative and positive z-values, giving the area to the left of z to four decimal places.

Statistics helps you make sense of data, a skill valuable in countless fields. This sheet provides essential formulas for descriptive statistics, probability, and inferential statistics. You will find it useful when calculating standard deviation or variance, using the binomial distribution for discrete probabilities, or interpreting data with z-scores and the empirical rule. The included z-table is particularly important for working with normal distributions, allowing you to find probabilities associated with specific z-values. Be careful not to confuse the formulas for population vs. sample standard deviation, or permutations vs. combinations. This sheet helps you distinguish between them and apply the correct formula for your specific data set.

Learn the ideas: mean, median and mode, standard deviation, z-scores. Calculators: standard deviation, z-score.

How to use a math formula sheet pdf well

A formula sheet is a powerful study aid, but only if you use it effectively. Avoid common pitfalls like relying on it too much or using it as a substitute for understanding. Here are concrete steps to maximize its benefit:

• Make it yours. Print the sheet, then annotate it: circle the formulas you keep forgetting, add a worked example next to each one, and note the conditions (for example, the ratio test is inconclusive when the limit is 1). You might write short, memorable cues next to complex formulas. For instance, next to the chain rule, you could write “derivative of the outside, times derivative of the inside.”
• Don’t just memorise. A sheet is a reminder, not an explanation. If you can’t say why a formula holds or when to use it, read the linked guide. Understanding the derivation or the conceptual basis of a formula helps you apply it correctly in varied problem contexts. Simply knowing the formula without understanding its purpose often leads to misapplication.
• Practise without it. Before an exam, work problems with the sheet face down and only check it when you’re stuck. That shows you what you still need to learn. This method helps you identify specific formulas or concepts that are still weak in your memory. Once you’ve identified a weak spot, return to the sheet and your notes to reinforce that particular area.
• Check your exam rules. Some exams provide their own formula booklet and don’t allow your own sheet. Practise with the official one so you know where things are. Familiarize yourself with its layout and content to avoid wasting precious exam time searching for formulas you could have located easily with prior practice.

Who benefits most from these sheets?

While helpful for many, these sheets are not a replacement for comprehensive learning. They are less suitable for:

• Beginners: If you are learning a topic for the first time, a formula sheet alone will not provide the necessary conceptual understanding or worked examples to grasp the material.
• Students needing in-depth explanations: The sheets list formulas but do not explain their derivations or the nuances of their application.
• Those seeking problem-solving strategies: The sheets focus on formulas, not methods for approaching different types of math problems.

Free textbooks and NCERT books

For full textbooks, see our guide to free calculus textbooks. It lists open-licensed books (OpenStax, Active Calculus, APEX Calculus, Strang’s Calculus) that you can legally download in full. Students in India can find the official links to the NCERT Class 11 and 12 maths textbooks in NCERT maths books.

Frequently asked questions

Are these formula sheets really free?

Yes. They’re free to download, print and share for study. Please don’t sell them or re-upload them as your own.

Can I print them in black and white?

Yes. Colour is used only for the section headings, so the sheets read clearly in greyscale. They’re sized for A4 and also print on US Letter with “fit to page”.

Is there a z-table PDF?

Yes. The statistics formula sheet includes a full standard normal table on its second and third pages, covering z from −3.49 to 3.49.

Which formula sheet do I need for calculus?

For a one-page review, use the calculus formula sheet. For a full list of derivatives and integrals, use the derivative and integral table. Most calculus students also want the trig identities sheet and the unit circle chart.

How can I suggest a new formula sheet?

We welcome suggestions for new formula sheets or improvements to existing ones. Please use the contact form on our website to send us your ideas.

Further reading

• OpenStax Calculus Volume 1 — a free, openly licensed textbook whose appendices include tables of integrals and derivatives.
• Paul’s Online Math Notes: Calculus I — free notes from Lamar University, with downloadable cheat sheets for algebra, trig and calculus.

These formula sheets are most beneficial for students who have already engaged with the subject matter and are looking for a concise review tool. They suit:

• Test-takers: Use them for quick revision of key formulas right before an exam.
• Homework-doers: Refer to them when you get stuck on a specific formula during practice problems.
• Reviewers: Students returning to a subject after a break can use them to refresh their memory.
• Problem-solvers: When a problem requires a multi-step solution, the sheets help you keep all necessary formulas at hand.

Who these sheets might not suit as a primary resource

While helpful for many, these sheets are not a replacement for comprehensive learning. They are less suitable for:

• Beginners: If you are learning a topic for the first time, a formula sheet alone will not provide the necessary conceptual understanding or worked examples to grasp the material.
• Students needing in-depth explanations: The sheets list formulas but do not explain their derivations or the nuances of their application.
• Those seeking problem-solving strategies: The sheets focus on formulas, not methods for approaching different types of math problems.

Free textbooks and NCERT books

For full textbooks, see our guide to free calculus textbooks. It lists open-licensed books (OpenStax, Active Calculus, APEX Calculus, Strang’s Calculus) that you can legally download in full. Students in India can find the official links to the NCERT Class 11 and 12 maths textbooks in NCERT maths books.

Frequently asked questions

Are these formula sheets really free?

Yes. They’re free to download, print and share for study. Please don’t sell them or re-upload them as your own.

Can I print them in black and white?

Yes. Colour is used only for the section headings, so the sheets read clearly in greyscale. They’re sized for A4 and also print on US Letter with “fit to page”.

Is there a z-table PDF?

Yes. The statistics formula sheet includes a full standard normal table on its second and third pages, covering z from −3.49 to 3.49.

Which formula sheet do I need for calculus?

For a one-page review, use the calculus formula sheet. For a full list of derivatives and integrals, use the derivative and integral table. Most calculus students also want the trig identities sheet and the unit circle chart.

How can I suggest a new formula sheet?

We welcome suggestions for new formula sheets or improvements to existing ones. Please use the contact form on our website to send us your ideas.

Further reading

• OpenStax Calculus Volume 1 — a free, openly licensed textbook whose appendices include tables of integrals and derivatives.
• Paul’s Online Math Notes: Calculus I — free notes from Lamar University, with downloadable cheat sheets for algebra, trig and calculus.