Class 10 All Formulas - Maths, Science, SST Complete 2027
Complete Class 10 formula sheet for 2027 board exams — Maths (Real Numbers, Polynomials, Quadratic formula, AP, Coordinate Geometry, Trigonometry tables and identities, Surface Area/Volume, Statistics, Probability), Science Physics (equations of motion, Ohm's law, lens/mirror formula), Chemistry (pH, reactions), Biology (diagrams list), and SST (important dates, map locations, Constitutional articles, economic indicators). Print this page — your complete revision sheet.
In short: This is the MEGA formula page for Class 10 — covering Maths, Science (Physics, Chemistry, Biology), and Social Science. Every formula, identity, equation, diagram reference, important date, and key fact you need for the 2027 board exam is here in one place. Maths covers Real Numbers through Probability. Science covers equations of motion, Ohm's law, lens/mirror formula, chemical equations, and more. SST covers important dates, map locations, Constitutional articles, and economic indicators. Print this page — it is your complete revision sheet.
Maths Formulas
Real Numbers
Formula
Expression
HCF × LCM relationship
HCF(a, b) × LCM(a, b) = a × b
Euclid's Division Lemma
a = bq + r, where 0 ≤ r < b
Fundamental Theorem of Arithmetic
Every composite number can be expressed as a product of primes uniquely
Polynomials
Formula
Expression
Sum of zeroes (quadratic)
α + β = -b/a
Product of zeroes (quadratic)
αβ = c/a
Sum of zeroes (cubic)
α + β + γ = -b/a
Sum of product of zeroes taken two at a time (cubic)
Memory trick for sin values: Write 0, 1, 2, 3, 4 → divide each by 4 → take square root. So sin 0° = √(0/4) = 0, sin 30° = √(1/4) = 1/2, sin 45° = √(2/4) = 1/√2, sin 60° = √(3/4) = √3/2, sin 90° = √(4/4) = 1. For cos, reverse the order.
Trigonometric Identities
Identity
Expression
Fundamental identity 1
sin²θ + cos²θ = 1
Fundamental identity 2
1 + tan²θ = sec²θ
Fundamental identity 3
1 + cot²θ = cosec²θ
Complementary angles
sin(90° - θ) = cos θ
Complementary angles
cos(90° - θ) = sin θ
Complementary angles
tan(90° - θ) = cot θ
Reciprocal
sin θ = 1/cosec θ
Reciprocal
cos θ = 1/sec θ
Reciprocal
tan θ = sin θ/cos θ
Surface Area and Volume (All 6 Shapes)
Shape
Lateral/Curved Surface Area
Total Surface Area
Volume
Cube (side a)
4a²
6a²
a³
Cuboid (l, b, h)
2h(l + b)
2(lb + bh + hl)
lbh
Cylinder (r, h)
2πrh
2πr(r + h)
πr²h
Cone (r, h, l)
πrl
πr(r + l)
(1/3)πr²h
Sphere (r)
4πr²
4πr²
(4/3)πr³
Hemisphere (r)
2πr²
3πr²
(2/3)πr³
Frustum (r₁, r₂, h, l)
π(r₁ + r₂)l
π(r₁ + r₂)l + πr₁² + πr₂²
(πh/3)(r₁² + r₂² + r₁r₂)
Slant height formulas:
Cone: l = √(r² + h²)
Frustum: l = √[h² + (r₁ - r₂)²]
Areas Related to Circles
Formula
Expression
Area of circle
πr²
Circumference
2πr
Area of sector
(θ/360°) × πr²
Length of arc
(θ/360°) × 2πr
Area of segment
Area of sector - Area of triangle
Statistics
Measure
Formula
Mean (Direct method)
x̄ = Σfᵢxᵢ / Σfᵢ
Mean (Assumed Mean)
x̄ = a + (Σfᵢdᵢ / Σfᵢ), where dᵢ = xᵢ - a
Mean (Step Deviation)
x̄ = a + (Σfᵢuᵢ / Σfᵢ) × h, where uᵢ = (xᵢ - a)/h
Median
l + [(n/2 - cf)/f] × h
Mode
l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)] × h
Empirical relationship
Mode = 3 Median - 2 Mean
Where: l = lower limit of modal/median class, f = frequency, cf = cumulative frequency, h = class size
Probability
Formula
Expression
Classical probability
P(E) = Number of favourable outcomes / Total outcomes
Complementary event
P(not E) = 1 - P(E)
Impossible event
P(E) = 0
Sure event
P(E) = 1
Range
0 ≤ P(E) ≤ 1
Common probability scenarios:
Experiment
Total Outcomes
Common Questions
One coin
2 (H, T)
P(Head) = 1/2
Two coins
4 (HH, HT, TH, TT)
P(at least one Head) = 3/4
One die
6 (1-6)
P(even) = 3/6 = 1/2
Two dice
36
P(sum = 7) = 6/36 = 1/6
Deck of cards
52
P(ace) = 4/52 = 1/13
Science Formulas — Physics
Equations of Motion (Kinematics)
Formula
Expression
Variables
First equation
v = u + at
v = final velocity, u = initial velocity, a = acceleration, t = time
Second equation
s = ut + ½at²
s = displacement
Third equation
v² = u² + 2as
No time variable
Distance in nth second
sₙ = u + a(2n - 1)/2
sₙ = distance in nth second
Force and Newton's Laws
Formula
Expression
Newton's Second Law
F = ma
Weight
W = mg (g = 9.8 m/s² ≈ 10 m/s²)
Momentum
p = mv
Impulse
F × t = mv - mu (change in momentum)
Newton's Third Law
F₁₂ = -F₂₁ (action = reaction)
Conservation of momentum
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Work, Energy, and Power
Formula
Expression
Work done
W = F × d × cos θ
Kinetic energy
KE = ½mv²
Potential energy
PE = mgh
Work-energy theorem
W = ΔKE = ½mv² - ½mu²
Power
P = W/t = F × v
1 horsepower
746 W
1 kWh
3.6 × 10⁶ J
Electricity
Formula
Expression
Ohm's Law
V = IR
Resistance
R = ρl/A (ρ = resistivity, l = length, A = cross-section area)
Series resistance
R_total = R₁ + R₂ + R₃ + ...
Parallel resistance
1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...
Electric power
P = VI = I²R = V²/R
Electric energy
E = P × t = VIt
Heat generated
H = I²Rt (Joule's law)
1 unit of electricity
1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J
Light — Reflection and Refraction
Formula
Expression
Mirror formula
1/v + 1/u = 1/f
Magnification (mirror)
m = -v/u = h'/h
Lens formula
1/v - 1/u = 1/f
Magnification (lens)
m = v/u = h'/h
Power of lens
P = 1/f (in metres), unit = Dioptre (D)
Snell's Law
n₁ sin i = n₂ sin r
Refractive index
n = speed in vacuum / speed in medium = c/v
Relation: focal length and radius
f = R/2
Sign Convention (New Cartesian):
All distances measured from the optical centre/pole
Distances in the direction of incident light = positive
Distances against the direction of incident light = negative
Heights above the principal axis = positive
Heights below the principal axis = negative
Magnetic Effects
Formula
Expression
Force on current-carrying conductor
F = BIl (B = magnetic field, I = current, l = length)
Fleming's Left Hand Rule
Thumb = Force, Index = Field, Middle = Current
Fleming's Right Hand Rule
Thumb = Motion, Index = Field, Middle = Current (for generators)
Transformer ratio
V₁/V₂ = N₁/N₂ (primary/secondary)
Science Formulas — Chemistry
Chemical Reactions Quick Reference
Reaction Type
Example
Combination
2Mg + O₂ → 2MgO
Decomposition
2FeSO₄ → Fe₂O₃ + SO₂ + SO₃
Displacement
Fe + CuSO₄ → FeSO₄ + Cu
Double displacement
Na₂SO₄ + BaCl₂ → BaSO₄ + 2NaCl
Neutralisation
HCl + NaOH → NaCl + H₂O
Oxidation
Addition of oxygen / removal of hydrogen
Reduction
Removal of oxygen / addition of hydrogen
Acids, Bases, and Salts
Concept
Formula/Fact
pH formula
pH = -log[H⁺]
Neutral pH
pH = 7
Acidic
pH < 7
Basic
pH > 7
Strong acid examples
HCl, H₂SO₄, HNO₃
Strong base examples
NaOH, KOH, Ca(OH)₂
Baking soda
NaHCO₃ (Sodium hydrogen carbonate)
Washing soda
Na₂CO₃·10H₂O (Sodium carbonate decahydrate)
Plaster of Paris
CaSO₄·½H₂O
Bleaching powder
CaOCl₂ (Calcium oxychloride)
Metals and Non-metals Key Reactions
Reaction
Equation
Metal + Oxygen
2Cu + O₂ → 2CuO
Metal + Water
2Na + 2H₂O → 2NaOH + H₂
Metal + Acid
Zn + H₂SO₄ → ZnSO₄ + H₂
Metal + Salt solution
Fe + CuSO₄ → FeSO₄ + Cu
Reactivity Series (decreasing order): K > Na > Ca > Mg > Al > Zn > Fe > Ni > Sn > Pb > H > Cu > Hg > Ag > Au > Pt
Carbon Compounds
Functional Group
Formula
Example
Alcohol
-OH
CH₃OH (Methanol), C₂H₅OH (Ethanol)
Aldehyde
-CHO
CH₃CHO (Ethanal)
Ketone
-CO-
CH₃COCH₃ (Propanone)
Carboxylic acid
-COOH
CH₃COOH (Ethanoic acid)
Alkane (saturated)
CₙH₂ₙ₊₂
CH₄, C₂H₆
Alkene (unsaturated)
CₙH₂ₙ
C₂H₄, C₃H₆
Alkyne (unsaturated)
CₙH₂ₙ₋₂
C₂H₂, C₃H₄
Periodic Classification Key Facts
Property
Across Period (L → R)
Down Group (T → B)
Atomic size
Decreases
Increases
Metallic character
Decreases
Increases
Electronegativity
Increases
Decreases
Valency
1→4→1 (increases then decreases)
Remains same
Ionisation energy
Increases
Decreases
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Social Science — Constitutional Articles for Civics
Article
Provision
Article 14
Equality before law
Article 15
Prohibition of discrimination
Article 17
Abolition of untouchability
Article 19
Right to freedom of speech and expression
Article 21
Right to life and personal liberty
Article 21A
Right to education (6-14 years)
Article 25
Freedom of religion
Article 32
Right to constitutional remedies
Article 243
Panchayati Raj provisions
Article 356
President's Rule in states
Article 370
Special status of J&K (now abrogated)
Social Science — Economic Indicators for Economics
Indicator
India's Approximate Value (2025-26)
Significance
Per capita income
~₹1,72,000/year
Measure of average income
GDP growth rate
~6.5-7%
Economic growth measure
Poverty line (rural)
₹32/day (Tendulkar)
Below this = Below Poverty Line
Poverty line (urban)
₹47/day (Tendulkar)
Urban poverty threshold
Literacy rate
~77%
Percentage who can read/write
Sex ratio
~943 females per 1000 males
Gender indicator
HDI rank
~134 out of 193
Human Development Index
Primary sector contribution to GDP
~17%
Agriculture's GDP share
Secondary sector contribution
~26%
Manufacturing's GDP share
Tertiary sector contribution
~57%
Services' GDP share
Organised sector employment
~10%
Only 10% in formal sector
Unorganised sector employment
~90%
90% in informal sector
Frequently Asked Questions
How should I use this formula page for revision?
Print this page or save it on your phone. During the last 2 weeks before exams, go through it once daily for 30-40 minutes. Focus on Maths formulas and Physics formulas first since they carry the most numerical marks. For Science, cross-check that you know every formula in the Electricity and Light sections. For SST, review the dates and map locations 3-4 times.
Which Maths formulas are most important?
The quadratic formula (x = (-b ± √(b² - 4ac))/2a), AP formulas (nth term and sum), trigonometric ratios table, and surface area/volume formulas for all 6 shapes are the most tested. Integration of these formulas into word problems is where marks are earned. Know the formula AND practice applying it.
Which Physics formulas carry the most marks?
Ohm's Law (V = IR), mirror formula (1/v + 1/u = 1/f), lens formula (1/v - 1/u = 1/f), power (P = VI = I²R = V²/R), and equations of motion (v = u + at, s = ut + ½at², v² = u² + 2as) are the top scoring formulas. Electricity and Light chapters together carry 15-17 marks in numericals.
Is this formula sheet valid for all boards (CBSE, UP Board, Bihar Board)?
Yes. Since all major boards follow NCERT textbooks, the formulas are identical across CBSE, UP Board, Bihar Board, and most state boards. The only difference is in exam patterns and mark distribution, not in the formulas themselves.
Should I memorise all the SST dates and articles?
Focus on the 15 most important dates for History and the top 10 Constitutional articles listed above. These cover the most frequently asked questions. For Geography map work, practice marking the locations on actual blank maps — visual memory is stronger than text memorisation.
How many formulas do I need to know for Class 10?
Approximately 80-100 formulas across Maths and Science. This page covers all of them. For Maths, the AP and Trigonometry sections have the most formulas. For Science, Electricity has the most formulas. Do not try to memorise all at once — learn them chapter by chapter as you study, then use this page for revision.
Start Practicing on Padhaao
Padhaao covers every Class 10 chapter with interactive formula practice, step-by-step numerical solving, and chapter-wise quizzes across 10 learning modes. Use this formula sheet alongside Padhaao's practice sessions for maximum retention and board exam readiness.
