Math Formula Sheet by Course: Algebra, Geometry, Trigonometry, and Calculus

Overview

This math formula sheet is organized by course so you can find the formulas you are most likely to use in classwork, homework, and exams. It is not meant to replace understanding. It is meant to support it. If you already know the underlying concept, a well-built formula sheet saves time and reduces small errors. If you do not yet understand the concept, the sheet can still help you spot patterns and identify what to learn next.

Use this guide as a living reference. Add your teacher’s preferred notation, circle the formulas that appear most often in your assignments, and write one short reminder next to each formula about when it should be used. That last step matters. Many students do not lose points because they forgot a formula completely. They lose points because they used the wrong one for the situation.

Below, you will find the core formula groups for algebra, geometry, trigonometry, and calculus, followed by a topic map and study advice. The goal is to make this article useful whether you are building your first formula sheet or refining one you already use in live study sessions, virtual tutoring, or online study help.

Algebra formulas

Algebra is where most students first learn to translate words, graphs, and patterns into equations. A strong algebra formula sheet should focus on operations, equation forms, exponents, factoring, and functions.

• Slope of a line: m = (y2 - y1) / (x2 - x1)
• Slope-intercept form: y = mx + b
• Point-slope form: y - y1 = m(x - x1)
• Standard form of a line: Ax + By = C
• Quadratic formula: x = [-b ± √(b² - 4ac)] / 2a
• Vertex form of a quadratic: y = a(x - h)² + k
• Factored form of a quadratic: y = a(x - r1)(x - r2)
• Exponent rules: a^m · a^n = a^(m+n), a^m / a^n = a^(m-n), (a^m)^n = a^(mn), a^-n = 1 / a^n
• Radical rule: √(ab) = √a · √b for nonnegative values in standard classroom settings
• Distance formula: d = √[(x2 - x1)² + (y2 - y1)²]
• Midpoint formula: ((x1 + x2)/2, (y1 + y2)/2)
• Arithmetic sequence: an = a1 + (n - 1)d
• Geometric sequence: an = a1(r)^(n - 1)

What to write in the margin: note that slope is about rate of change, the discriminant b² - 4ac tells you how many real solutions a quadratic has, and vertex form is often the quickest way to identify a parabola’s turning point.

Geometry formulas

Geometry formulas are easiest to remember when they are grouped by shape and purpose: perimeter, area, surface area, volume, and angle relationships.

• Perimeter of a rectangle: P = 2l + 2w
• Area of a rectangle: A = lw
• Area of a triangle: A = (1/2)bh
• Area of a parallelogram: A = bh
• Area of a trapezoid: A = (1/2)(b1 + b2)h
• Area of a circle: A = πr²
• Circumference of a circle: C = 2πr
• Pythagorean theorem: a² + b² = c²
• Sum of interior angles of an n-gon: (n - 2)180°
• Volume of a rectangular prism: V = lwh
• Volume of a cylinder: V = πr²h
• Volume of a sphere: V = (4/3)πr³
• Volume of a cone: V = (1/3)πr²h
• Surface area of a cylinder: SA = 2πr² + 2πrh
• Surface area of a sphere: SA = 4πr²

What to write in the margin: mark whether a formula uses radius or diameter, whether the question asks for area or perimeter, and whether a three-dimensional problem wants volume or surface area. Many geometry mistakes happen because students solve the wrong quantity correctly.

Trigonometry formulas

Trigonometry becomes easier when you connect triangle definitions, identities, and graph behavior. On your trigonometry formulas sheet, keep right-triangle ratios separate from identities and from laws used for non-right triangles.

• Sine: sin θ = opposite / hypotenuse
• Cosine: cos θ = adjacent / hypotenuse
• Tangent: tan θ = opposite / adjacent
• Reciprocal ratios: csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ
• Pythagorean identity: sin² θ + cos² θ = 1
• Tangent identity: tan θ = sin θ / cos θ
• Law of sines: a/sin A = b/sin B = c/sin C
• Law of cosines: c² = a² + b² - 2ab cos C
• Unit circle coordinates: (cos θ, sin θ)
• Degree-radian conversion: 180° = π radians
• Arc length: s = rθ, where θ is in radians
• Sector area: A = (1/2)r²θ, where θ is in radians

What to write in the margin: identify whether the problem uses a right triangle, a unit circle angle, or a non-right triangle. Also note whether your calculator is set to degrees or radians before you begin. That one setting can change an otherwise correct process into a wrong answer.

Calculus formula sheet

A calculus formula sheet should be less about memorizing long lists and more about tracking common derivative, integral, and limit patterns. If your class allows a reference sheet, keep it compact enough that you can actually use it under pressure.

• Power rule for derivatives: d/dx [x^n] = nx^(n-1)
• Constant rule: d/dx [c] = 0
• Constant multiple rule: d/dx [cf(x)] = c f'(x)
• Sum rule: d/dx [f(x) + g(x)] = f'(x) + g'(x)
• Product rule: (fg)' = f'g + fg'
• Quotient rule: (f/g)' = (f'g - fg') / g²
• Chain rule: d/dx [f(g(x))] = f'(g(x)) · g'(x)
• Derivative of e^x: d/dx [e^x] = e^x
• Derivative of ln x: d/dx [ln x] = 1/x
• Derivative of sin x: cos x
• Derivative of cos x: -sin x
• Derivative of tan x: sec² x
• Power rule for integrals: ∫x^n dx = x^(n+1)/(n+1) + C, for n ≠ -1
• Integral of 1/x: ∫(1/x) dx = ln|x| + C
• Integral of e^x: ∫e^x dx = e^x + C
• Integral of sin x: ∫sin x dx = -cos x + C
• Integral of cos x: ∫cos x dx = sin x + C
• Average rate of change: [f(b) - f(a)] / (b - a)
• Definition of derivative: f'(x) = lim h→0 [f(x+h) - f(x)] / h

What to write in the margin: label which formulas give a derivative, which give an antiderivative, and which require conditions such as n ≠ -1. Also remind yourself to include + C for indefinite integrals. That small detail is easy to miss on homework and exams.

Topic map

If you want this hub to be genuinely useful, do not think of formulas as isolated facts. Think of them as a map of recurring problem types.

• Algebra: linear equations, quadratics, exponents, radicals, functions, sequences, graph interpretation
• Geometry: shapes, measurement, angle relationships, similarity, circles, area and volume, coordinate geometry
• Trigonometry: right triangles, unit circle values, identities, graphs, inverse trig basics, laws of sines and cosines
• Calculus: limits, derivatives, applications of derivatives, antiderivatives, definite integrals, accumulation, motion

There is also overlap across courses. The distance formula comes from the Pythagorean theorem. Trigonometry builds on geometry. Calculus uses algebra constantly. This is why a single math formula sheet can become a strong long-term study tool for students if it is organized well.

A practical layout is to divide your sheet into three columns for each course:

1. Formula — the symbolic expression exactly as you need it.
2. Use it when — a short plain-language trigger such as “given two points” or “finding area of a circle.”
3. Watch out for — a frequent error such as “do not forget square root” or “angle must be in radians.”

This structure works especially well in live study sessions, on-demand study tutorials, and math homework help online because it encourages explanation, not just copying.

Related subtopics

A formula sheet becomes more valuable when you pair it with related study habits and course-specific review methods.

1. Problem recognition

Before choosing a formula, identify the problem type. Ask: am I solving for a side, an angle, a rate, an intercept, an area, or a derivative? Students often know the formula but misread the task. Build this habit by writing the target quantity at the top of each problem before you calculate anything.

2. Units and notation

Units matter in geometry and applied problems. Notation matters in algebra and calculus. For example, function notation, exponent placement, and parentheses can change the meaning of an entire line. If your teacher uses a certain format, mirror it on your sheet.

3. Graph connections

Whenever possible, attach a visual idea to a formula. A quadratic formula belongs with a parabola. Sine and cosine belong with the unit circle and wave graphs. Derivatives belong with slope and rate of change. This helps formulas stick longer than memorization alone.

4. Test prep use cases

This hub is also useful for broader test prep resources. Standardized math sections often reward speed, pattern recognition, and checking. A compact formula review can support a SAT study guide, ACT practice help, AP exam review, or GED study resources, especially when you pair it with timed sets. If you are preparing across subjects, it can help to keep your math review separate from reading and writing materials so your study plan stays focused. For schedule-based exam planning, readers may also find SAT Test Dates and Registration Deadlines 2026-2027, PSAT Test Dates, Score Release Windows, and What They Mean, and AP Exam Dates 2026: Full Schedule by Subject helpful companions to a study calendar.

5. Study tools and support options

If you struggle to build your own sheet, use study tools for students that help you summarize class notes, turn text into audio review, or organize examples by topic. A text summarizer for students can help condense chapter notes, while a text to speech study tool or voice notes for studying can make formula review more active. For a practical overview, see Best AI Study Tools for Students Compared by Use Case. If you need broader online study help beyond math, Homework Help Websites Ranked by Subject and Grade Level can help you compare options.

6. Teacher and classroom use

Teachers can adapt this hub into a classroom reference, warm-up sheet, or review handout. It also fits well with teacher test prep resources when planning cumulative reviews. For broader planning support, NGSS and Math Teaching Resources Teachers Can Use This Year offers additional classroom-facing ideas.

How to use this hub

The best formula sheet is the one you can use quickly and confidently. Here is a practical way to turn this article into a working study aid.

1. Start with your current course. If you are in Algebra 2, do not spend most of your time on calculus. Build the section you need now.
2. Copy only high-frequency formulas first. Begin with the formulas that appear repeatedly in homework, quizzes, and review sheets.
3. Add a plain-language trigger. Next to each formula, write when to use it. Example: “quadratic with no easy factoring.”
4. Attach one worked example. You do not need many. One clean example per formula group is usually enough.
5. Color-code by task. You might use one color for solving equations, another for measurement, and another for graph-based questions.
6. Practice retrieval. Cover the formulas and see what you can recall from memory. Then check your sheet.
7. Review mistakes, not just right answers. If you miss a problem, write the correction beside the relevant formula.
8. Update weekly. A formula sheet should change as your class moves into new units.

If you learn best through conversation, use the sheet during live study sessions or virtual tutoring and ask someone to quiz you on the “when to use it” column. That approach is often more effective than rereading alone because it forces you to match formulas to situations.

For students balancing academics with college planning, it can help to separate your math review system from scholarship tasks. If that is relevant to you, studies.live also has planning resources like No Essay Scholarships: Current Opportunities and Deadlines, Scholarships for First-Generation College Students: Updated List, Scholarships for High School Seniors Updated for 2026, and Scholarship Deadlines Calendar 2026: Month-by-Month List for Students. Keeping deadlines organized separately can free up more focused time for math.

When to revisit

Return to this hub whenever your class changes units, your assignments start repeating certain problem types, or you notice the same mistake more than once. Those are signs that your formula sheet needs an update.

In practical terms, revisit this page:

• At the start of a new chapter or unit
• One to two weeks before a major test
• After each graded quiz, to add missed concepts
• When moving from one course to another, such as geometry to trigonometry
• When preparing for cumulative exams or standardized tests
• When new related subtopics emerge in your course, such as conic sections, polar coordinates, or integration techniques

Your next step is simple: build a one-page formula sheet for the course you are taking now, add a short “use it when” note for every formula, and test yourself on application rather than recognition. That small shift turns a static list into a reusable study tool. Over time, this hub can become your year-round math reference, not just a page you visit the night before an exam.