In short: This is a complete list of every important formula from the new CBSE Class 9 Science textbook Exploration (2026-27). Physics formulas cover motion, force, work, energy, power, pressure, and Archimedes' principle. Chemistry formulas cover the mole concept, atomic mass, and valency. Biology does not have formulas in the traditional sense, but we have listed the key numerical facts you are expected to know. Every formula includes its SI unit, a worked example, and the chapter it comes from.
The new Exploration textbook integrates Physics, Chemistry, Biology, and Earth Science into 13 chapters. The theory paper is worth 80 marks with 20 marks for internal assessment. If you are using formula lists from the old separate Physics-Chemistry-Biology NCERT books, they may not map correctly to the new chapter structure.
For a complete chapter-wise strategy covering all 13 chapters, read our Class 9 Science Complete Guide.
Physics Formulas from Exploration
Physics dominates the numerical-solving part of the Class 9 Science paper. Most 3-mark and 5-mark numericals come from motion, force, and work-energy chapters.
Motion Formulas
These are the three equations of uniformly accelerated motion. You must know all three — exams typically give you any two known values and ask you to find the third.
| Formula | Name | When to Use |
|---|---|---|
| v = u + at | First equation of motion | When displacement (s) is not involved |
| s = ut + ½at² | Second equation of motion | When final velocity (v) is not involved |
| v² = u² + 2as | Third equation of motion | When time (t) is not involved |
Variables and Units
| Symbol | Meaning | SI Unit |
|---|---|---|
| u | Initial velocity | m/s |
| v | Final velocity | m/s |
| a | Acceleration | m/s² |
| t | Time | s (seconds) |
| s | Displacement | m (metres) |
Example: A car starts from rest (u = 0) and accelerates at 2 m/s² for 5 seconds. Find the final velocity and distance covered.
v = u + at = 0 + 2 × 5 = 10 m/s
s = ut + ½at² = 0 + ½ × 2 × 25 = 25 m
Tip: "Starts from rest" means u = 0. "Comes to rest" means v = 0. These two phrases account for about half of all motion numericals.
Additional Motion Formulas
| Formula | Meaning |
|---|---|
| Speed = Distance / Time | Average speed (scalar) |
| Velocity = Displacement / Time | Average velocity (vector) |
| Acceleration = (v − u) / t | Rate of change of velocity |
Force and Newton's Laws
| Formula | Meaning | Unit |
|---|---|---|
| F = ma | Newton's Second Law: Force = mass × acceleration | Newton (N) |
| W = mg | Weight = mass × gravitational acceleration | Newton (N) |
| p = mv | Momentum = mass × velocity | kg·m/s |
| F × t = Δ(mv) | Impulse = Change in momentum | N·s or kg·m/s |
- g = acceleration due to gravity = 9.8 m/s² (use 10 m/s² if the question says "take g = 10")
- 1 Newton = the force needed to accelerate 1 kg by 1 m/s²
Example: A 5 kg object is pushed with 20 N of force. Find its acceleration.
F = ma → a = F/m = 20/5 = 4 m/s²
Tip: Always check your units. If mass is in grams, convert to kg first. If speed is in km/h, convert to m/s by dividing by 3.6.
Newton's Third Law: For every action, there is an equal and opposite reaction. (No formula, but expect a 2-3 mark explanation question.)
Law of Conservation of Momentum: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ (total momentum before collision = total momentum after collision)
Work, Energy, and Power
| Formula | Meaning | Unit |
|---|---|---|
| W = F × s | Work = Force × displacement (in the direction of force) | Joule (J) |
| W = Fs cos θ | Work when force and displacement are at angle θ | Joule (J) |
| KE = ½mv² | Kinetic Energy | Joule (J) |
| PE = mgh | Gravitational Potential Energy | Joule (J) |
| P = W/t | Power = Work done / Time taken | Watt (W) |
| 1 kWh = 3.6 × 10⁶ J | Commercial unit of energy | kWh |
Example: A 2 kg ball is at a height of 10 m. PE = mgh = 2 × 10 × 10 = 200 J. If it falls freely, using conservation of energy: v = √(2gh) = √200 ≈ 14.14 m/s.
Tip: The work-energy theorem says net work done on an object equals its change in kinetic energy. This connects the force chapter to the energy chapter.
Pressure and Fluids
| Formula | Meaning | Unit |
|---|---|---|
| P = F/A | Pressure = Force / Area | Pascal (Pa) or N/m² |
| P = ρgh | Pressure due to a liquid column | Pascal (Pa) |
| Buoyant Force = ρ_fluid × V_displaced × g | Archimedes' Principle | Newton (N) |
- ρ (rho) = density of the fluid (kg/m³)
- V_displaced = volume of fluid displaced by the object
Example: A block is submerged in water (ρ = 1000 kg/m³). The volume of water displaced is 0.002 m³. Find the buoyant force.
F_b = 1000 × 0.002 × 10 = 20 N
Tip: An object floats when buoyant force ≥ weight. An object sinks when weight > buoyant force. This is Archimedes' principle in one line.
Sound Formulas
| Formula | Meaning | Unit |
|---|---|---|
| v = fλ | Speed of sound = frequency × wavelength | m/s |
| v = d/t | Speed = distance / time (for echo problems) | m/s |
| Echo: 2d = v × t | Distance to reflecting surface = (speed × time) / 2 | m |
- Speed of sound in air at 20°C ≈ 343 m/s (or use 340 m/s)
- Minimum distance for echo = 17.2 m (sound must travel 34.4 m total in 0.1 s)
Example: A person claps near a cliff and hears the echo after 3 seconds. Speed of sound = 340 m/s. How far is the cliff?
2d = v × t → d = (340 × 3)/2 = 510 m
Chemistry Formulas from Exploration
Chemistry in Class 9 has fewer computational formulas than Physics, but the mole concept and atomic mass calculations are critical.
Mole Concept and Atomic Mass
| Formula | Meaning |
|---|---|
| Number of moles = Given mass / Molar mass | n = m/M |
| Number of particles = n × Nₐ | Nₐ = Avogadro's number = 6.022 × 10²³ |
| Molar mass of compound = sum of atomic masses of all atoms | E.g., H₂O = 2(1) + 16 = 18 g/mol |
Example: How many moles are in 36 g of water (H₂O)?
Molar mass of H₂O = 2 × 1 + 16 = 18 g/mol
n = 36/18 = 2 moles
Example: How many molecules is that?
Number of molecules = 2 × 6.022 × 10²³ = 1.2044 × 10²⁴
Valency Rules
Valency is not a "formula" in the traditional sense, but you need to know these numbers:
| Element/Group | Valency |
|---|---|
| Hydrogen (H) | 1 |
| Oxygen (O) | 2 |
| Nitrogen (N) | 3 |
| Carbon (C) | 4 |
| Sodium (Na), Potassium (K) | 1 |
| Magnesium (Mg), Calcium (Ca) | 2 |
| Aluminium (Al) | 3 |
| Iron (Fe) | 2 or 3 |
| Chlorine (Cl) | 1 |
| Sulphate (SO₄) | 2 |
| Nitrate (NO₃) | 1 |
| Carbonate (CO₃) | 2 |
Tip: To write a chemical formula using valency, cross-multiply the valencies. Example: Aluminium oxide → Al has valency 3, O has valency 2 → Al₂O₃.
Concentration Formula
Mass percentage = (Mass of solute / Mass of solution) × 100
Example: 10 g of salt in 90 g of water → Mass percentage = (10/100) × 100 = 10%
Key Atomic Masses to Remember
| Element | Symbol | Atomic Mass |
|---|---|---|
| Hydrogen | H | 1 |
| Carbon | C | 12 |
| Nitrogen | N | 14 |
| Oxygen | O | 16 |
| Sodium | Na | 23 |
| Magnesium | Mg | 24 |
| Aluminium | Al | 27 |
| Sulphur | S | 32 |
| Chlorine | Cl | 35.5 |
| Potassium | K | 39 |
| Calcium | Ca | 40 |
| Iron | Fe | 56 |
| Copper | Cu | 63.5 |
| Zinc | Zn | 65 |
Tip: Memorize at least the first 10 in this list. They appear in almost every mole concept problem.
Practice any chapter on Padhaao
AI tutor for CBSE, ICSE & 15 state boards · 10 learning modes · 3 free chapters daily
Biology — Key Numerical Facts from Exploration
Biology does not have formulas like Physics or Chemistry, but there are specific numbers and facts that examiners test. Here are the ones you should know:
| Fact | Value |
|---|---|
| Number of chromosomes in humans | 46 (23 pairs) |
| Number of bones in the human body (adult) | 206 |
| Normal body temperature | 37°C or 98.6°F |
| pH of human blood | 7.35 – 7.45 (slightly alkaline) |
| pH of stomach acid (HCl) | ~1.5 – 2.0 |
| pH of pure water | 7 (neutral) |
| Number of chambers in the human heart | 4 |
| Normal pulse rate (adult) | 72 beats per minute |
| Number of cranial nerves | 12 pairs |
| Number of spinal nerves | 31 pairs |
| Cell organelle that produces energy | Mitochondria ("powerhouse of the cell") |
| Cell organelle for protein synthesis | Ribosomes |
| Plant cell-specific structures | Cell wall, chloroplast, large central vacuole |
Tip: These are not "formulas" to derive — they are facts to memorize. Use flashcards or write them down 3 times each.
Physics vs Chemistry Formulas — Comparison Table
This table helps you see at a glance where each formula comes from and what type of problems it appears in.
| Topic | Physics Formulas | Chemistry Formulas |
|---|---|---|
| Core chapter | Motion, Force, Work-Energy | Atoms, Molecules, Mole Concept |
| Number of key formulas | ~20 | ~5-6 |
| Type of problems | Numericals (calculate values) | Calculations + conceptual (write formulas) |
| Units matter? | Yes — always include SI units | Yes — g/mol, particles, etc. |
| Common exam format | 3-mark and 5-mark numericals | 2-mark formula writing + 3-mark calculations |
| Biggest scoring area | Motion equations (v = u + at, etc.) | Mole concept problems |
| Most common mistake | Forgetting to convert units | Wrong molar mass calculation |
| Formula sheet length | 1.5 pages | 0.5 pages |
| Requires derivation? | Sometimes (Newton's second law) | Rarely |
Physics requires more practice because it has more formulas and more numerical problem types. Chemistry has fewer formulas but requires you to remember atomic masses and valency rules, which is a memory challenge.
How to Approach Science Numericals in Exams
Step 1: Read the question and list the given values with units.
Write: u = 0 m/s, a = 3 m/s², t = 5 s, v = ?
Step 2: Identify the formula.
We need v and we have u, a, t → use v = u + at
Step 3: Substitute and solve.
v = 0 + 3 × 5 = 15 m/s
Step 4: Write the answer with the correct unit.
v = 15 m/s
Examiners give separate marks for each step. Even if your final answer is wrong, you get marks for correctly listing given values and writing the right formula. Never skip a step.
Which Formulas Are Most Important for Class 9 Science Exams?
Based on marks distribution and question frequency:
| Priority | Formula | Reason |
|---|---|---|
| 🔴 Must know | Three equations of motion | Asked every year, 3-5 mark numericals |
| 🔴 Must know | F = ma | Core Newton's law numerical |
| 🔴 Must know | W = Fs, KE = ½mv², PE = mgh | Work-energy chapter is high weightage |
| 🔴 Must know | n = m/M (mole concept) | The central Chemistry calculation |
| 🟡 Important | P = W/t (Power) | Often combined with work problems |
| 🟡 Important | v = fλ (Sound) | 2-3 mark numerical |
| 🟡 Important | Buoyant force formula | Application-based question |
| 🟡 Important | Valency and chemical formula writing | Conceptual but carries marks |
| 🟢 Good to know | Echo formula (2d = vt) | Simple but not always asked |
| 🟢 Good to know | Concentration formula | Straightforward calculation |
Frequently Asked Questions
How many formulas are there in Class 9 Science for 2026-27?
Across Physics and Chemistry in Exploration, there are about 25-30 key formulas. Physics contributes roughly 20 and Chemistry about 5-6. Biology has zero formulas but around 15-20 key numerical facts.
Are the formulas in the new Exploration textbook different from the old NCERT?
The formulas themselves are the same — physics and chemistry formulas do not change. What has changed is the chapter organization. Always cross-check your formula list against the current syllabus.
Do I need to learn formula derivations for Class 9 Science?
For the annual exam, you should know the derivation of the three equations of motion and F = ma from Newton's second law. These are commonly asked as 3-5 mark questions. Other derivations are less commonly asked but good to understand conceptually.
Which carries more marks in Class 9 Science — Physics or Chemistry?
The Exploration textbook does not separate Physics and Chemistry distinctly. However, physics chapters (motion, force, work-energy, sound) have more numericals and therefore more calculation-heavy marks. Both are important — you cannot skip either.
How should I revise Science formulas before the exam?
Make a single-page formula sheet: Physics on front, Chemistry on back. Include variable meanings and units. Revise daily for the last 10 days. In the exam, write key formulas on the rough sheet in the first 5 minutes.
Is Biology easier than Physics and Chemistry in Class 9?
Biology has no numericals, which makes it different, not easier. It requires precise definitions, diagram labels, and process knowledge. The advantage is no calculations to go wrong — if you know the content, you score full marks.
Practice Science Numericals with Padhaao
Knowing a formula and being able to use it under exam pressure are different skills. Padhaao gives you chapter-wise numerical practice from Exploration, with AI-powered step-by-step guidance when you are stuck. Build the problem-solving confidence that formula lists alone cannot give you.
Want the full chapter with solved examples?
10 learning modes. Board-specific content. 3 free chapters every day.
Try it free