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

Overview

This article gives you a structured math formula sheet with the formulas students most often need in core secondary and early college math. It is not meant to replace your class notes or textbook, because teachers may use different notation, emphasize different topics, or allow different levels of formula support on tests. Instead, think of it as a clean master list you can adapt.

The most useful way to study formulas is not to memorize a page in isolation. Start by grouping formulas by scenario: solving equations, measuring shapes, analyzing triangles, and working with rates of change or accumulation. That method helps you connect a formula to a type of question.

As you use this guide, keep a short personal checklist beside it:

• What kind of problem is this?
• What quantity am I solving for?
• What information is already given?
• Are the units consistent?
• Does the formula require special conditions, such as a right triangle or radians?

If you are building a broader study system, it can also help to pair formula review with a study planner, flashcards, and a grade tracker. For example, if you are organizing exam prep alongside other classes, you may also want to review a grade planning resource such as Semester Grade Calculator Explained for Percentage, Points, and Weighted Categories or GPA Calculator Guide: How to Calculate Weighted and Unweighted GPA.

Checklist by scenario

Use this section like a subject-by-subject checklist. Before a test or homework session, scan the category you need and mark the formulas you know, the ones you confuse, and the ones you still need to practice with examples.

Algebra formulas list

Algebra often asks you to solve, simplify, factor, compare rates, and model patterns. The formulas below show up repeatedly.

• 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
• Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
• Midpoint formula: ((x1 + x2)/2, (y1 + y2)/2)
• Quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / 2a
• Vertex form of a quadratic: y = a(x - h)^2 + k
• Factored form of a quadratic: y = a(x - r1)(x - r2)
• Difference of squares: a^2 - b^2 = (a - b)(a + b)
• Exponent rules: a^m · a^n = a^(m+n), a^m / a^n = a^(m-n), (a^m)^n = a^(mn)
• Simple interest: I = Prt
• Compound growth model: A = P(1 + r/n)^(nt) when that form is taught in your course

Use these when: you are graphing lines, solving systems, working with quadratics, or modeling growth and decay.

Quick reminder: in the quadratic formula, the discriminant b^2 - 4ac tells you how many real solutions you have.

Geometry formulas cheat sheet

Geometry is usually less about memorizing every formula and more about matching the right formula to the right shape. Always sketch the figure if one is not provided.

• 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 = πr^2
• Circumference of a circle: C = 2πr or C = πd
• Pythagorean theorem: a^2 + b^2 = c^2
• Volume of a rectangular prism: V = lwh
• Volume of a cylinder: V = πr^2h
• Volume of a cone: V = (1/3)πr^2h
• Volume of a sphere: V = (4/3)πr^3
• Surface area of a cylinder: SA = 2πr^2 + 2πrh
• Surface area of a sphere: SA = 4πr^2

Use these when: the problem asks for area, perimeter, volume, surface area, or a missing side length.

Quick reminder: do not mix up area and perimeter, or volume and surface area. Those are among the most common errors in geometry homework.

Trigonometry formulas

Trigonometry becomes easier when you connect formulas to triangle relationships, circle definitions, and graph behavior. Many students remember the basic ratios first, then build from there.

• 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: sin^2 θ + cos^2 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: c^2 = a^2 + b^2 - 2ab cos C
• Arc length: s = rθ when θ is in radians
• Sector area: A = (1/2)r^2θ when θ is in radians
• Degree-radian conversion: 180° = π radians

Use these when: you are solving right triangles, non-right triangles, unit circle questions, or graphing trig functions.

Quick reminder: check whether your calculator is in degree mode or radian mode. A correct formula with the wrong mode still gives a wrong answer.

Calculus formulas

Calculus formulas usually make more sense when tied to a concept: derivatives measure rate of change, and integrals measure accumulation or signed area. If you memorize only symbols, it is easy to forget when to use them.

• Limit notation: lim (x→a) f(x)
• Derivative definition: f'(x) = lim (h→0) [f(x+h) - f(x)] / h
• Power rule: d/dx (x^n) = nx^(n-1)
• Constant rule: d/dx (c) = 0
• Constant multiple rule: d/dx [c f(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') / g^2
• Chain rule: d/dx [f(g(x))] = f'(g(x)) · g'(x)
• Basic antiderivative power rule: ∫ x^n dx = x^(n+1)/(n+1) + C for n ≠ -1
• Definite integral: ∫[a to b] f(x) dx = F(b) - F(a)
• Derivative of e^x: d/dx (e^x) = e^x
• Derivative of ln x: d/dx (ln x) = 1/x

Use these when: you are finding slopes of tangent lines, rates of change, optimization solutions, areas under curves, or accumulation totals.

Quick reminder: for indefinite integrals, do not forget the constant of integration, + C.

Mixed problem checklist

Sometimes the hardest part is not the formula itself but identifying the problem type. Before solving, ask:

• Is the problem asking for a missing value, a graph feature, a measurement, or a rate?
• Is the shape two-dimensional or three-dimensional?
• Is the triangle right or not necessarily right?
• Do I need exact form or a decimal approximation?
• Am I using degrees or radians?
• Do I need a derivative, an antiderivative, or just algebraic simplification before calculus begins?

What to double-check

This section helps you catch mistakes before you turn in homework or submit a test. A quick review here can save points even when your main method is correct.

• Variables and labels: Confirm what each letter stands for. In geometry, r and d are not interchangeable. In algebra, b in y = mx + b is the y-intercept, not a second slope value.
• Parentheses: In formulas like the quadratic formula or point-slope form, missing parentheses changes the result.
• Units: If dimensions are in different units, convert before calculating. If the answer is area or volume, the units should be squared or cubed.
• Calculator mode: For trigonometry, verify degree or radian mode before entering anything.
• Signs: Negative numbers are easy to lose in slope, distance, and derivative work.
• Restrictions: Some formulas apply only in specific cases. The Pythagorean theorem is for right triangles. Arc length formulas often assume radians. Certain derivative shortcuts depend on standard rules being applicable.
• Reasonableness: Ask whether the answer makes sense. A side length should not be negative. A small rectangle should not have a huge perimeter unless dimensions support it.

If you are studying for a cumulative exam, turn these double-check items into flashcards: one side can say the formula, and the other can list the most common trap associated with it.

Common mistakes

Most formula errors are not memory failures. They are recognition and setup failures. Here are the mistakes worth watching for across subjects.

• Using the right formula on the wrong kind of problem. Students often use area formulas when the question asks for perimeter, or the Law of Cosines when a basic right triangle ratio would be simpler.
• Substituting values incorrectly. This happens often in the quadratic formula, midpoint formula, and distance formula. Write the formula first, then substitute carefully.
• Dropping exponent rules. In algebra and calculus, sign errors and exponent slips can undo an otherwise correct solution.
• Ignoring diagram details. Geometry problems sometimes include hidden dimensions, shared sides, or diameters where students assume radii.
• Forgetting special notation. In calculus, omitting + C on indefinite integrals is common. In trigonometry, forgetting the angle unit creates preventable mistakes.
• Memorizing without practice. A formula sheet is useful, but it only becomes reliable when you use each formula in several worked examples.

A practical fix is to annotate your personal formula sheet with one note per formula: “used for,” “watch out for,” and “example type.” That turns a static cheat sheet into a real study resource.

When to revisit

The best formula sheet is not something you read once. It is something you update and return to whenever your class moves into a new unit or your test format changes.

Revisit this guide in the following situations:

• Before a new unit test: review only the formulas for that unit and remove distractions from topics not being tested.
• Before midterms or finals: combine all four subject sections into a single review sheet with starred priorities.
• After getting homework back: add the formulas connected to problems you missed most often.
• When your teacher introduces new notation: rewrite the same formula in the notation used in class so your practice matches your assessments.
• When moving from homework to timed practice: trim your sheet to the formulas you still hesitate on, then practice recalling them without notes.

To make this article actionable, build your own one-page version today:

1. Pick your current subject: algebra, geometry, trigonometry, or calculus.
2. Copy only the formulas your class has actually covered.
3. Add one short example or reminder under each formula.
4. Highlight formulas you confuse with similar ones.
5. Review the sheet for five minutes before practice problems, not after.

If your study routine includes writing-heavy classes too, it helps to keep other repeat-use academic guides nearby, such as MLA Citation Guide 2026: Website, Book, Video, and Article Formats, APA Citation Guide 2026: Books, Websites, Journal Articles, and More, or Word Counter Guide for Essays: How Long Should Your Paper Be?. The same principle applies across subjects: keep one clear reference, revisit it often, and update it when your coursework changes.

A strong math formula sheet is not about collecting the most formulas. It is about keeping the right formulas visible, understandable, and ready when you need them. Bookmark this page, revise your own sheet as your classes change, and use it as a steady review tool rather than a last-second scramble.