Formulas

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Formulas are short rules that help you solve maths and science problems quickly and correctly. Knowing the right formula and when to use it saves time in school exams and competitive tests. This page gives a clear overview of the most important formulas from Class 6 to 12, how to learn them and how to avoid common mistakes.

Why Learning Formulas Properly Matters

Many students memorise formulas without understanding them and forget them under exam pressure. A better method is to learn what each symbol means, where the formula comes from and in which type of question it is used. Practise with examples and keep a formula sheet for quick revision. This builds both speed and confidence.

Algebra Formulas

Formula Name / use
(a + b)² = a² + 2ab + b² Square of a sum
(a − b)² = a² − 2ab + b² Square of a difference
a² − b² = (a + b)(a − b) Difference of squares
(a + b)³ = a³ + 3a²b + 3ab² + b³ Cube of a sum
a³ + b³ = (a + b)(a² − ab + b²) Sum of cubes
a³ − b³ = (a − b)(a² + ab + b²) Difference of cubes
x = [−b ± √(b² − 4ac)] / 2a Quadratic formula for ax² + bx + c = 0

Use these identities to expand, factorise and simplify expressions quickly. Always check the signs when applying them.

Geometry and Mensuration Formulas

Shape Area Perimeter / Circumference / Volume
Rectangle l × b 2(l + b)
Square a² 4a
Triangle ½ × base × height Sum of three sides
Circle πr² 2πr
Cuboid Surface area = 2(lb + bh + hl) Volume = l × b × h
Cube Surface area = 6a² Volume = a³
Cylinder Curved surface area = 2πrh Volume = πr²h
Cone Curved surface area = πrl Volume = ⅓πr²h
Sphere Surface area = 4πr² Volume = ⁴⁄₃πr³

Remember to write units: cm² or m² for area and cm³ or m³ for volume.

Trigonometry Formulas

Formula Use
sin²θ + cos²θ = 1 Basic identity
1 + tan²θ = sec²θ Identity with tan and sec
1 + cot²θ = cosec²θ Identity with cot and cosec
tan θ = sin θ / cos θ Ratio relation
sin 30° = ½, cos 60° = ½, tan 45° = 1 Standard values

Learn the table of values for 0°, 30°, 45°, 60° and 90°. These come in many board exam questions.

Coordinate Geometry Formulas

Formula Use
Distance = √[(x₂ − x₁)² + (y₂ − y₁)²] Distance between two points
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2) Midpoint of a line segment
Section formula (internal) = ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)) Point dividing a line in ratio m : n
Area of triangle = ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)| Area from three vertices
Slope m = (y₂ − y₁)/(x₂ − x₁) Slope of a line

Arithmetic Progression, Percentages and Interest

Topic Formula
nth term of AP aₙ = a + (n − 1)d
Sum of n terms of AP Sₙ = n/2 [2a + (n − 1)d]
Percentage (Part / Whole) × 100
Profit percentage (Profit / Cost price) × 100
Simple interest SI = (P × R × T) / 100
Compound interest amount A = P (1 + R/100)ⁿ

When using these formulas, write the given values first, check units and time periods, and then calculate carefully.

Statistics and Probability

  • Mean = Sum of all observations / Number of observations
  • Median is the middle value when data is arranged in order
  • Mode is the value that occurs most often
  • Probability of an event = Number of favourable outcomes / Total number of outcomes
  • Probability of an event lies between 0 and 1

Physics Formulas for School Students

Concept Formula Unit
Speed Distance / Time m/s
Acceleration (v − u) / t m/s²
Equations of motion v = u + at, s = ut + ½at², v² = u² + 2as —
Force F = m × a Newton (N)
Work W = F × s Joule (J)
Power P = W / t Watt (W)
Kinetic energy ½mv² Joule (J)
Potential energy mgh Joule (J)
Density Mass / Volume kg/m³
Pressure Force / Area Pascal (Pa)
Ohm’s law V = I × R Volt (V)
Electric power P = V × I Watt (W)

Always write the units in your answer and convert units if needed before substituting values. For more, explore our physics category.

Chemistry Formulas and Concepts

Topic Formula or idea
Number of moles Mass / Molar mass
Molarity Moles of solute / Volume of solution in litres
Atomic number Number of protons
Mass number Protons + Neutrons
pH −log [H⁺]
Balanced equation Atoms on both sides must be equal

In Chemistry, formulas are often paired with rules, such as valency and balancing equations. Learn symbols and valencies of common elements and practise writing chemical formulas for compounds. Visit our chemistry category for notes.

How to Learn and Revise Formulas

  1. Write formulas on cards with the name on one side and the formula on the other.
  2. Revise a small set every day instead of everything on one day.
  3. Use a notebook where you write each formula with one solved example.
  4. Group formulas by chapter and keep them in a single formula sheet.
  5. Test yourself by writing formulas from memory once a week.

Solved Examples: Using Formulas Step by Step

Example 1: Area of a circle

Find the area of a circle with radius 7 cm. Formula: Area = πr². Substitute: Area = 22/7 × 7 × 7 = 154 cm². The answer is 154 square centimetres.

Example 2: Factorise using the difference of squares

Factorise x² − 25. Use a² − b² = (a + b)(a − b). Here a = x and b = 5. So x² − 25 = (x + 5)(x − 5).

Example 3: Force from mass and acceleration

A body of mass 5 kg has an acceleration of 3 m/s². Force = m × a = 5 × 3 = 15 N.

Example 4: Simple interest

Find the simple interest on ₹2,000 at 5% per year for 3 years. SI = (P × R × T)/100 = (2000 × 5 × 3)/100 = ₹300.

Formulas for Competitive Exams

Competitive exams such as JEE, NEET and government exams use many of these basic formulas along with more advanced ones. The key difference is speed and application. Practise mixed questions, learn short methods only after you know the standard method, and avoid depending on tricks without understanding.

Common Mistakes With Formulas

Mistake How to fix it
Using the wrong formula Identify the type of problem and write the matching formula first
Sign errors in algebra Write each step and check signs carefully
Mixing units Convert all values to the same unit before using the formula
Forgetting brackets Use brackets when substituting negative or fractional values
Memorising without practice Solve at least 5 questions on every formula you learn

Quick Revision Plan Before Exams

  • One week before: go through the formula sheet for each chapter and solve one mixed set daily.
  • Three days before: revise the formulas you often forget and solve previous year questions.
  • One day before: read the formula sheet once and sleep well.
  • On exam day: write important formulas on the rough sheet as soon as the paper starts, if the rules allow.

For calculators and step-by-step solutions, see our calculators and NCERT solutions pages.

Commonly Used Constants and Values

Quantity Value (approx.)
π 22/7 or 3.14
Speed of light 3 × 10⁸ m/s
Acceleration due to gravity (g) 9.8 m/s² (often taken as 10 m/s² in problems)
Avogadro number 6.022 × 10²³ per mole
√2, √3 1.414, 1.732

Use the value given in the question. If none is given, follow the textbook or exam instructions.

Tips for Parents and Teachers

Encourage students to explain formulas in their own words and to apply them to real-life situations, such as calculating the area of a room or the cost of a loan. Make formula revision a short daily habit instead of a long weekend task. Praise understanding, not just correct answers. If a child struggles, go back to the concept and use simple examples before moving on.

Keep this page bookmarked and return to it before every test. Regular revision turns formulas from something to fear into tools you can use with confidence.

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FAQs on Formulas

How can I remember formulas easily?

Understand the meaning of each formula, write it daily, use a formula sheet, and solve different questions with it.

Are formulas allowed in the exam hall?

Generally no. You must remember formulas for school and most competitive exams, unless the exam instructions say otherwise.

What are the most important formulas for Class 10 maths?

Algebraic identities, quadratic formula, arithmetic progression formulas, trigonometric identities, mensuration formulas, coordinate geometry and probability are important.

How do I use the quadratic formula?

Write the equation in the form ax² + bx + c = 0, find a, b and c, and substitute them in x = [−b ± √(b² − 4ac)] / 2a.

What is the formula for the area of a circle?

Area = πr², where r is the radius. Use π = 22/7 or 3.14 as instructed.

What is the difference between area and volume?

Area measures the surface of a flat shape in square units, while volume measures the space inside a solid in cubic units.

What is a formula sheet?

It is a short list of formulas for a subject or chapter that you use for quick revision.

Which physics formulas should I know first?

Start with speed, velocity, acceleration, equations of motion, force, work, power, energy, density and pressure.

How can I avoid mistakes while applying formulas?

Write the formula, list the given values, substitute carefully with units and check the final answer for reasonableness.

Where can I find more formulas?

Use our maths, physics and chemistry categories and NCERT textbooks for detailed formulas and examples.

Should I memorise or derive formulas?

Try to understand the derivation so you remember it, then memorise it for speed. Both approaches help.

Can calculators help with formulas?

Calculators help with calculations, but you still need to know the formula and understand the problem.