List of Maths formulas

Top 50 Basic Maths Formulas

Mastering fundamental maths formulas is essential for quick calculations and problem-solving in exams like CBSE, ICSE, JEE, NEET, and competitive tests. Below is a list of the top 50 basic maths formulas covering Algebra, Geometry, Trigonometry, and Arithmetic:

1. Arithmetic Formulas
Sum of n natural numbers: S = n(n+1)/2

Sum of squares of n natural numbers: S = n(n+1)(2n+1)/6

Sum of cubes of n natural numbers: S = [n(n+1)/2]²

Percentage formula: (Value/Total Value) × 100

Profit & Loss: Profit = Selling Price - Cost Price

Simple Interest: SI = (P × R × T) / 100

Compound Interest: A = P(1 + R/100)ⁿ

Average: Sum of Observations / Total Number of Observations

Speed, Distance, Time: Speed = Distance / Time

Probability: P(E) = Favorable Outcomes / Total Outcomes

2. Algebra Formulas
(a+b)² = a² + 2ab + b²

(a-b)² = a² - 2ab + b²

a² - b² = (a-b)(a+b)

(a+b)³ = a³ + 3a²b + 3ab² + b³

(a-b)³ = a³ - 3a²b + 3ab² - b³

Quadratic equation formula: x = (-b ± √(b² - 4ac)) / 2a

Logarithm formula: log(ab) = log a + log b

Logarithm base change: logₐb = logₓb / logₓa

Laws of exponents: aᵐ × aⁿ = a^(m+n)

Laws of exponents: (aᵐ)ⁿ = a^(m×n)

3. Geometry Formulas
Area of a triangle: (1/2) × base × height

Pythagoras theorem: c² = a² + b²

Perimeter of a rectangle: 2(l + b)

Area of a rectangle: l × b

Area of a square: s²

Perimeter of a square: 4s

Area of a circle: πr²

Circumference of a circle: 2πr

Volume of a cube: s³

The volume of a cylinder: πr²h

4. Trigonometry Formulas
sin²θ + cos²θ = 1

1 + tan²θ = sec²θ

1 + cot²θ = csc²θ

sin(90° - θ) = cosθ

cos(90° - θ) = sinθ

tan(90° - θ) = cotθ

sec(90° - θ) = cscθ

csc(90° - θ) = secθ

tanθ = sinθ / cosθ

cotθ = cosθ / sinθ

5. Mensuration Formulas
The volume of a sphere: (4/3)πr³

The surface area of a sphere: 4πr²

The volume of a cone: (1/3)πr²h

The curved surface area of a cone: πrl

The total surface area of a cylinder: 2πr(h + r)

Volume of a cuboid: l × b × h

The diagonal of a rectangle: √(l² + b²)

The diagonal of a cube: √3 × s

Area of a parallelogram: base × height

Area of a trapezium: (1/2) × (sum of parallel sides) × height

How Maths Formulas can help in faster Revision

Mathematics formulas are essential tools that can significantly enhance the efficiency of revision. Here are several ways in which they contribute to faster and more effective studying:

1. Condensed Information: Formulas concisely encapsulate complex concepts and relationships, which can help students recall information more quickly. Instead of memorizing lengthy explanations, students can focus on remembering key formulas.
2. Framework for Problem Solving: Understanding and memorizing relevant formulas gives students a structured approach to tackling problems. This framework allows students to recognize what information is needed and how to apply it, speeding up their thought process.
3. Patterns and Relationships: Mathematics often involves recognizing patterns. By reviewing Maths formulas, students can see how different concepts are interconnected, which can help them understand the underlying principles better and apply their knowledge in different contexts.
4. Practice Problems: Utilizing formulas allows for targeted practice. By focusing on specific types of problems related to particular formulas, students can quickly build proficiency in those areas, leading to efficiency in revision.
5. Memory Aids: Formulas can serve as mnemonic devices. Students can create acronyms or visualize equations in memorable ways to aid retention. For example, the order of operations can be remembered using “PEMDAS” (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
6. Self-Assessment: Formulas provide a straightforward way to check understanding. Students can create flashcards with formulas on one side and example problems or explanations on the other. This allows for quicker self-assessment and reinforcement of knowledge.
7. Conceptual Understanding: Revising formulas can lead to deeper comprehension than rote memorization. When students understand the derivation and application of a formula, they are more likely to remember it and apply it correctly. Solving Reasoning Questions in Maths will also improve learning. 
8. Reviewing Key Topics: Students can focus on high-yield concepts during revision sessions by compiling a list of essential formulas relevant to specific topics or chapters. This targeted approach helps to maximize study time.
9. Visual Aids: Creating visual representations of formulas, such as diagrams, graphs, or charts, can enhance understanding and retention. Visual learning is often quicker and more effective for many students.
10. Group Study: Discussing formulas and their applications in a group study setting can help reinforce knowledge. Teaching peers about specific formulas also strengthens understanding and helps with recall during exams.

What are the best ways to Remember Math formulas?

Remembering math formulas can be challenging, but you can employ several effective strategies to enhance your memory retention. Here are some of the best ways to remember math formulas:

1. Understand the Concepts: Instead of simply memorizing formulas, take time to understand the underlying concepts. Knowing why a formula works helps you recall it better and apply it correctly in different contexts.
2. Derivation Practice: Deriving formulas from basic principles helps solidify your understanding. When you can derive a formula on your own, it's easier to remember because you understand the logic behind it.
3. Visual Learning: Create visual aids like charts, graphs, or diagrams that represent the formulas. Visualizing formulas can help you remember their structure and the relationships between different variables.
4. Use Mnemonics: Create catchy phrases or acronyms to help you remember complex formulas. Mnemonics simplify the information and make it easier to recall. you could create a story or a mnemonic based on the elements of the formula. which helps you in RMO. 
5. Flashcards: Use flashcards to write down formulas on one side and their applications or derivations on the other. Regularly reviewing these flashcards helps reinforce memory through active recall.
6. Practice Regularly: Solve problems that require the use of the formulas you’re trying to memorize. The more you use a formula, the more familiar it will become, reinforcing your memory with practical application.
7. Group Study: Studying with peers can provide new insights and different methods of remembering formulas. Teaching someone else a formula can reinforce your knowledge and understanding.
8. Chunking: Break down complex formulas into smaller, manageable parts. Memorizing smaller chunks can make it easier to recall the entire formula as you can piece it together.
9. Association: Associate formulas with real-life applications or examples. Create connections between what the formula represents and practical scenarios to make the formula more memorable.
10. Repetition: Consistent and spaced repetition is key for long-term retention. Regularly reviewing formulas over time helps transfer them from short-term to long-term memory.
11. Mind Maps: Create mind maps that illustrate relationships between different formulas. This visual representation can help you see how different formulas connect, aiding in overall recall.
12. Application Stories: Create a narrative or story around the formula. This might involve imagining a scenario where the formula is applied, which can make it more relatable and easier to remember.
13. Test Yourself: Use practice exams or problems that require you to recall and use the formulas. Self-testing helps reinforce what you've learned and highlights areas that need more focus.

Tips are tricks to create Short notes on Maths formula

Creating short notes for math formulas can help simplify your study process and enhance your memory retention. Here are some tips and tricks for making effective short notes:

1. Categorization: Group related formulas together by topic (e.g., algebra, geometry, calculus). This organization helps you find relevant formulas quickly and you can see how different formulas relate to one another.
2. Use Symbols and Abbreviations: Instead of writing full words, use commonly accepted symbols and abbreviations (e.g., "Δ" for change, "∑" for sum) to save space and make the notes easier to read.
3. Highlight Key Variables: Use color coding to highlight important variables in formulas. For instance, you could use one color for constants and another for variables to help make them stand out.
4. Include Units: Whenever possible, note the units associated with each formula, especially in physics or applied mathematics. This will help clarify how to use the formula correctly.
5. Visual Aids: Incorporate small diagrams, charts, or graphs where applicable. For example, a brief diagram of the Pythagorean theorem can help visualize the relationship between the sides of a right triangle.
6. Simplified Language: Write explanations in simple language, including "What it is" (the formula name) and "When to use it" (application). This clarity can help you recall both the formula and its use.
7. Use Examples: Include a small example of the formula in action. This can help contextualize the formula, making it easier to remember.
8. Formula Derivations: When applicable, include brief derivations or reasoning behind the formula next to it. A few key steps can jog your memory when recalling how to use the formula.
9. Mind Maps: Create mind maps that summarize formulas and their relationships. This visual layout can help you see connections and improve recall.
10. Grid/Tabular Format: Use tables to organize formulas, particularly for comparison purposes, such as equations for various geometric shapes, which can make them easier to read and understand.
11. Use Flashcards: Create digital or physical flashcards with formulas on one side and definitions/applications on the other. This format allows for quick reviews and spaced repetition.
12. Summarize Formulas: For complex formulas, break them down into simpler components and write a summary. For instance, for the area of a circle, you could note that it’s found by (A = πr^2) and summarize it as "Area = Pi times radius squared."
13. Review Regularly: Set a specific timeframe to review these notes (e.g., weekly) to reinforce memory and understanding periodically.
14. Be Concise: Aim for brevity; keep your notes to one page or less if possible. This encourages focusing on the most critical information and prevents overwhelm.
15. Personal Touch: Use your wording and style. Personal notes often resonate more with you and can help with retention because they reflect your understanding of the material.

Maths Formulas – Essential Guide for Quick Learning & Exam Success

Math formulas play a crucial role in solving numerical problems quickly and accurately. Whether you are a CBSE, ICSE, JEE, NEET, or competitive exam aspirant, having a strong command of mathematical formulas helps in better problem-solving and conceptual understanding. From Algebra, Geometry, Trigonometry, Calculus, and Statistics, every branch of mathematics relies on key formulas to simplify complex calculations.

Understanding basic arithmetic formulas like percentages, profit and loss, simple and compound interest, and averages ensures a strong foundation for real-world applications. Algebraic identities such as (a + b)² = a² + 2ab + b² or the quadratic equation formula help in simplifying expressions and solving equations efficiently. Trigonometric formulas, including sin²θ + cos²θ = 1 and tanθ = sinθ / cosθ, are essential for angle-based calculations. Geometry and mensuration formulas like the area of a circle (πr²) and volume of a cylinder (πr²h) are crucial for solving shape and measurement-related problems.

By regularly practicing and applying these formulas, students can enhance their problem-solving speed and accuracy in exams. A well-organized collection of maths formulas is a must-have for every student aiming for high scores. Master these formulas and boost your confidence in mathematics!