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Class 10 Science formula sheet 2026-27: physics, chemistry and biology, with units

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This sheet collects the formulas, units, chemical equations and key numbers of the 2026-27 NCERT Class 10 Science book in one place. Physics comes first (light, the eye, electricity, magnetism), then chemistry (reaction types and the equations worth knowing), then the few relations biology uses. Every line gives the textbook page, so you can go back to the chapter. At the end are 8 worked questions of our own, then three common mistakes.

To print it, use your browser's Print option; the page prints without colours.

The layout, wording and questions on this page are our own, drafted with AI help. Every formula and number was checked against the NCERT chapter page given next to it, and every answer was re-computed by a script, but no practising teacher has reviewed the page yet. If you find a mistake, please tell us.

Page numbers are the printed page numbers of NCERT Science, Textbook for Class X (Reprint 2026-27). The maths twin of this page is our Class 10 Maths formula sheet 2026-27.

Physics, Chapter 9: Light, reflection and refraction

Sign rule first (page 142). Measure every distance from the pole of the mirror (or the optical centre of the lens, page 155). Distances in the direction the light travels, to the right, are positive; distances against it, to the left, are negative. Heights above the principal axis are positive, heights below are negative. So an object in front of a mirror or lens always has a negative u.

FormulaSymbols and unitsPage
R = 2f, so f = R/2R radius of curvature, f focal length, both in cm or m. Holds for mirrors of small aperture137
Mirror formula: 1/v + 1/u = 1/fu object distance, v image distance, f focal length, all from the pole, same unit143
Mirror magnification: m = h′/h = −v/uh object height, h′ image height. m is a plain number with no unit. Negative m: real and inverted; positive m: virtual and erect143
Snell's law: sin i / sin r = constanti angle of incidence, r angle of refraction, for one colour of light and one pair of media148
n₂₁ = v₁ / v₂index of the second medium relative to the first, from the speeds of light in the two media. No unit148
n = c / vabsolute refractive index; c = 3 × 10⁸ m s⁻¹ (speed of light in vacuum, page 148), v speed in the medium149
Lens formula: 1/v − 1/u = 1/ff is positive for a convex lens and negative for a concave lens (page 155). Note the minus sign; the mirror formula has a plus155
Lens magnification: m = h′/h = v/uno minus sign for lenses156
Power: P = 1/ff in metres gives P in dioptres (D); 1 D = 1 m⁻¹. Convex lens: P positive; concave lens: P negative157-158
Lenses in contact: P = P₁ + P₂ + P₃ + …add the powers with their signs158

Values worth recognising (Table 9.3, page 149; the book says you need not memorise them): water 1.33, crown glass 1.52, diamond 2.42. A larger refractive index means an optically denser medium, where light is slower.

More practice on this chapter: Light notes and Light questions with answers.

Physics, Chapter 10: The human eye

Key number or ruleWhat it meansPage
Near point about 25 cmthe closest a young adult can hold a page and still read it easily (also called the least distance of distinct vision)162
Far point at infinityfor a normal eye; so it sees clearly from 25 cm to infinity162
Myopia: far point closer than infinitycorrected with a concave lens (negative power)163
Hypermetropia: near point beyond 25 cmcorrected with a convex lens (positive power)163
Presbyopia, with both defectsoften needs bi-focal lenses, concave in one part and convex in the other163-164

There is no new formula here: an eye prescription is a lens power, so P = 1/f from Chapter 9 does the work. Questions: Human eye questions with answers.

Physics, Chapter 11: Electricity

FormulaSymbols and unitsPage
I = Q/tcurrent in ampere (A), charge in coulomb (C), time in second (s); 1 A = 1 C/1 s172
1 mA = 10⁻³ A, 1 µA = 10⁻⁶ Asmall currents172
Charge of an electron: 1.6 × 10⁻¹⁹ Cso 1 C is the charge of nearly 6 × 10¹⁸ electrons172
V = W/Qpotential difference in volt (V), work in joule (J); 1 V = 1 J C⁻¹. The voltmeter goes in parallel173
Ohm's law: V = IR (so R = V/I and I = V/R)resistance in ohm (Ω); 1 Ω = 1 V / 1 A. Only at a steady temperature176
R = ρl/Aρ resistivity in Ω m, l length in m, A cross-section area in m²178
Series: Rs = R₁ + R₂ + R₃the same current flows through each resistor184
Parallel: 1/Rp = 1/R₁ + 1/R₂ + 1/R₃each resistor gets the same potential difference186
P = VIpower in watt (W)188
Heat: H = VIt = I²Rtheat in joule; Joule's law of heating188-189
P = VI = I²R = V²/Ruse V²/R when the voltage is fixed, I²R when the current is191
1 W = 1 V A; 1 kW h = 3.6 × 10⁶ Jthe kilowatt hour is the "unit" on an electricity bill191

Resistivity values used in problems (Table 11.2, page 179, at 20°C; not for memorising): copper 1.62 × 10⁻⁸ Ω m, aluminium 2.63 × 10⁻⁸ Ω m, tungsten 5.20 × 10⁻⁸ Ω m. Metals and alloys lie between 10⁻⁸ and 10⁻⁶ Ω m.

Converting units is where most marks go: 1 mm² = 10⁻⁶ m², 1 cm = 10⁻² m, 1 hour = 3,600 s. More practice: Electricity notes, Electricity numericals 2026-27 and Electricity questions with answers.

Physics, Chapter 12: Magnetic effects of electric current

This chapter has rules and household numbers rather than formulas.

Rule or numberUsePage
Right-hand thumb rulethe direction of the magnetic field around a straight wire carrying current199
Fleming's left-hand rulethe direction of the force on a current-carrying conductor in a magnetic field, when field and current are at right angles203
220 V between live (red) and neutral (black)the Indian household supply; the earth wire is green204
15 A and 5 A circuits15 A for high-power appliances such as geysers and air coolers, 5 A for bulbs and fans204
AC at 50 Hzthe frequency of the household supply in India206

To find which circuit an appliance needs, use I = P/V from Chapter 11. Revise: Magnetic effects notes.

Chemistry, Chapter 1: Reaction types, with one equation each

TypeWhat happensAn equation from the chapterPage
Combinationtwo or more reactants give a single productCaO + H₂O → Ca(OH)₂ + heat6
Exothermicheat is given outCH₄ + 2O₂ → CO₂ + 2H₂O7
Respiration (exothermic)glucose is burnt in cellsC₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy7
Thermal decompositionone reactant breaks down on heatingCaCO₃ → CaO + CO₂ (heat); 2FeSO₄ → Fe₂O₃ + SO₂ + SO₃ (heat)8
Decomposition by heat, giving a brown gaslead nitrate breaks down2Pb(NO₃)₂ → 2PbO + 4NO₂ + O₂9
Decomposition by lightsilver chloride turns grey in sunlight; black and white photography relies on this (page 10)2AgCl → 2Ag + Cl₂ (sunlight)9
Endothermicenergy is taken indecomposition reactions need energy as heat, light or electricity10
Displacementa more reactive metal pushes out a less reactive oneFe + CuSO₄ → FeSO₄ + Cu11
Double displacement (precipitation)ions are exchanged; an insoluble solid formsNa₂SO₄ + BaCl₂ → BaSO₄ + 2NaCl11
Redoxone substance gains oxygen (oxidised), the other loses it (reduced)CuO + H₂ → Cu + H₂O (heat)12

Oxidation is gaining oxygen or losing hydrogen; reduction is losing oxygen or gaining hydrogen (page 14). Corrosion (rust on iron, black on silver, green on copper) and rancidity (oxidised fats and oils) are both oxidation in daily life (page 13). Revise: Chemical reactions notes.

Chemistry, Chapter 2: Acids, bases and salts

General word equationExample from the chapterPage
Acid + metal → salt + hydrogen gasalso, with a base: 2NaOH + Zn → Na₂ZnO₂ + H₂ (sodium zincate)20
Metal carbonate or hydrogencarbonate + acid → salt + carbon dioxide + waterNa₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂20-21
Test for CO₂: lime water turns milkyCa(OH)₂ + CO₂ → CaCO₃ + H₂O20
Base + acid → salt + water (neutralisation)NaOH + HCl → NaCl + H₂O21
Metal oxide + acid → salt + watercopper oxide in dilute HCl gives blue-green copper(II) chloride21

The pH scale (page 25). It runs from 0, the most acidic, to 14, the most alkaline. 7 is neutral, below 7 is acidic, above 7 is basic. A higher hydrogen ion concentration means a lower pH. Numbers to know: the body works between pH 7.0 and 7.8, rain below 5.6 is acid rain (page 26), and tooth decay starts below 5.5 in the mouth (page 27).

Chemical from common saltEquation or formulaPage
Chlor-alkali process2NaCl + 2H₂O → 2NaOH + Cl₂ + H₂ (chlorine at the anode, hydrogen at the cathode)30
Bleaching powder2Ca(OH)₂ + 2Cl₂ → Ca(ClO)₂ + CaCl₂ + 2H₂O; the book writes bleaching powder as Ca(ClO)₂30
Baking soda, madeNaCl + NH₃ + CO₂ + H₂O → NaHCO₃ + NH₄Cl31
Baking soda, heated2NaHCO₃ → Na₂CO₃ + H₂O + CO₂31
Washing sodaNa₂CO₃ + 10H₂O → Na₂CO₃·10H₂O31
Water of crystallisationcopper sulphate CuSO₄·5H₂O; gypsum CaSO₄·2H₂O32
Plaster of Parisgypsum heated at 373 K gives CaSO₄·½H₂O; with water it sets back into gypsum: CaSO₄·½H₂O + 1½H₂O → CaSO₄·2H₂O32-33

Revise: Acids, bases and salts notes.

Chemistry, Chapter 3: Metals and non-metals

Reaction patternEquations from the chapterPage
Metal + oxygen → metal oxide2Cu + O₂ → 2CuO; 4Al + 3O₂ → 2Al₂O₃41
Amphoteric oxide (reacts with acid and with base)Al₂O₃ + 6HCl → 2AlCl₃ + 3H₂O; Al₂O₃ + 2NaOH → 2NaAlO₂ + H₂O41
Soluble metal oxide + water → alkaliNa₂O + H₂O → 2NaOH41
Metal + water → metal oxide or hydroxide + hydrogen2Na + 2H₂O → 2NaOH + H₂ + heat; Ca + 2H₂O → Ca(OH)₂ + H₂; with steam, 3Fe + 4H₂O → Fe₃O₄ + 4H₂43
Metal + dilute acid → salt + hydrogennot with nitric acid, which is an oxidising agent (except Mg and Mn with very dilute HNO₃)43-44
Roasting (sulphide ore, excess air)2ZnS + 3O₂ → 2ZnO + 2SO₂51
Calcination (carbonate ore, limited air)ZnCO₃ → ZnO + CO₂51
Reduction with carbonZnO + C → Zn + CO51
Thermit reactionFe₂O₃ + 2Al → 2Fe + Al₂O₃ + heat52
Electrolytic reduction (very reactive metals)at the cathode Na⁺ + e⁻ → Na; at the anode 2Cl⁻ → Cl₂ + 2e⁻52

Activity series (Table 3.2, page 45), most to least reactive: potassium (K), sodium (Na), calcium (Ca), magnesium (Mg), aluminium (Al), zinc (Zn), iron (Fe), lead (Pb), [hydrogen (H)], copper (Cu), mercury (Hg), silver (Ag), gold (Au). A metal above another displaces it from its salt solution; metals above hydrogen give hydrogen with dilute acids. Revise: Metals and non-metals notes.

Chemistry, Chapter 4: Carbon and its compounds

Rule or reactionFormula or equationPage
Homologous seriesnext members differ by one −CH₂− unit, that is 12 + 2 = 14 u in molecular mass66
General formulasalkenes CₙH₂ₙ (given in the book); by the same count, alkanes CₙH₂ₙ₊₂ and alkynes CₙH₂ₙ₋₂67
CombustionC + O₂ → CO₂ + heat and light69
Oxidation of ethanolCH₃CH₂OH → CH₃COOH, with alkaline KMnO₄ or acidified K₂Cr₂O₇ and heat71
Addition (hydrogenation)unsaturated + H₂ → saturated, with a nickel or palladium catalyst; used to harden vegetable oils71
SubstitutionCH₄ + Cl₂ → CH₃Cl + HCl, in sunlight71
Ethanol + sodium2Na + 2CH₃CH₂OH → 2CH₃CH₂O⁻Na⁺ + H₂72
Dehydration of ethanolCH₃CH₂OH → CH₂=CH₂ + H₂O, with hot concentrated H₂SO₄ at 443 K72
EsterificationCH₃COOH + CH₃CH₂OH → CH₃COOCH₂CH₃ + H₂O, with an acid catalyst; the ester smells sweet73
Saponificationester + NaOH → alcohol + sodium salt of the acid; the basis of soap73
Ethanoic acid with a base and with carbonatesNaOH + CH₃COOH → CH₃COONa + H₂O; 2CH₃COOH + Na₂CO₃ → 2CH₃COONa + H₂O + CO₂; CH₃COOH + NaHCO₃ → CH₃COONa + H₂O + CO₂74

Revise: Carbon and its compounds notes.

Biology: the key relations and numbers

Relation or numberDetailPage
Photosynthesis6CO₂ + 12H₂O → C₆H₁₂O₆ + 6O₂ + 6H₂O, with chlorophyll and sunlight82
First step of respirationglucose (6 carbons) → pyruvate (3 carbons), in the cytoplasm87
Without oxygen, in yeastpyruvate → ethanol + carbon dioxide (fermentation, anaerobic)87
With oxygen, in mitochondriapyruvate → carbon dioxide + water; far more energy than the anaerobic route87-88
Lack of oxygen in musclepyruvate → lactic acid, which causes cramps88
ATPthe energy currency of the cell88
Blood pressure about 120/80 mm of Hgsystolic 120, diastolic 80 (in a "More to Know!" box, which CBSE does not assess)93
Kidney filtrate about 180 L a dayonly a litre or two a day leaves as urine97
Mendel, one traitF1 all tall; in F2 one quarter are short; TT : Tt : tt = 1 : 2 : 1130
Sex determinationwomen XX, men XY; the father's X gives a girl, his Y a boy, so half the children are boys132
1 per cent and 10 per centgreen plants capture about 1% of the sunlight on their leaves; about 10% of the energy at one level reaches the next210
OzoneUV splits O₂ into two O atoms; O + O₂ → O₃. Ozone high up shields us from UV212-213

Revise: Life processes notes, Heredity notes and Our environment notes.

What CBSE 2026-27 does not test in the board paper

The Science curriculum for 2026-27 lists some topics as taught but assessed only in school: periodic classification of elements, evolution, and the electric motor, electromagnetic induction and the electric generator (pages 4 to 6). The colour of the Sun at sunrise and sunset is left out of the light unit, and information printed in boxes in the textbook is not assessed in the year-end exam (page 6). The curriculum's "Note for Teachers" (page 6) also lists heredity and the effects of electric current as not assessed in the year-end exam, while the unit lists on pages 5 and 6 include them; check with your teacher which reading your school follows. The heredity and Chapter 12 lines above are kept for that reason.

8 worked questions (our own)

Question 1 (concave mirror). A concave shaving mirror has a radius of curvature of 40 cm. A man's face is 12 cm in front of it. Find the image distance and the magnification, and describe the image.

Answer. f = R/2 = −20 cm (concave, in front of the mirror) and u = −12 cm. 1/v = 1/f − 1/u = −1/20 + 1/12 = (−3 + 5)/60 = 1/30, so v = +30 cm, behind the mirror. m = −v/u = −(30)/(−12) = +2.5. The image is virtual, erect and 2.5 times the size of the face, which is why the mirror works for shaving.

Question 2 (speed of light in a medium). A clear plastic block is 3.0 cm thick and has a refractive index of 1.6. Take c = 3.0 × 10⁸ m s⁻¹. (a) How fast does light travel in the plastic? (b) How long does light take to cross the block? (c) How far would light travel in air in that same time?

Answer. (a) n = c/v, so v = c/n = 3.0 × 10⁸ / 1.6 = 1.875 × 10⁸ m s⁻¹. (b) t = distance/speed = 0.030 m / (1.875 × 10⁸ m s⁻¹) = 1.6 × 10⁻¹⁰ s. (c) In air, 3.0 × 10⁸ × 1.6 × 10⁻¹⁰ = 0.048 m = 4.8 cm, which is n times the thickness (1.6 × 3.0 cm): light is slowed in the plastic by the factor n.

Question 3 (lens and power). A reading magnifier is a convex lens of power +12.5 D. A postage stamp 2.5 cm wide is held 6 cm from it. (a) Where is the image, and what is the magnification? (b) How wide does the stamp look in the image?

Answer. (a) f = 1/P = 1/12.5 m = 0.08 m = +8 cm, and u = −6 cm. 1/v = 1/f + 1/u = 1/8 − 1/6 = (3 − 4)/24 = −1/24, so v = −24 cm: the image is on the same side as the stamp. m = v/u = (−24)/(−6) = +4: virtual, erect and 4 times bigger. (b) h′ = m × h = 4 × 2.5 cm = 10 cm wide.

Question 4 (resistivity). A copper wire is 100 m long with a cross-section of 1.0 mm². Use ρ = 1.62 × 10⁻⁸ Ω m for copper and 2.63 × 10⁻⁸ Ω m for aluminium (Table 11.2). (a) Find the resistance of the copper wire. (b) What length of aluminium wire, with the same cross-section, has the same resistance?

Answer. (a) A = 1.0 mm² = 1.0 × 10⁻⁶ m². R = ρl/A = (1.62 × 10⁻⁸ × 100)/(1.0 × 10⁻⁶) = 1.62 Ω. (b) l = RA/ρ = (1.62 × 1.0 × 10⁻⁶)/(2.63 × 10⁻⁸) ≈ 61.6 m. Aluminium resists more per metre, so the same resistance needs a shorter wire.

Question 5 (find the missing resistor). A 2 Ω resistor is joined in series with a parallel pair made of a 10 Ω resistor and an unknown resistor R. Across a 24 V battery the battery current is 3 A. Find (a) R, (b) the current in each resistor of the pair, (c) the heat produced in the 2 Ω resistor in 2 minutes.

Answer. (a) Total resistance = V/I = 24/3 = 8 Ω, so the pair is 8 − 2 = 6 Ω. 1/R = 1/6 − 1/10 = (5 − 3)/30 = 1/15, so R = 15 Ω. (b) The pair has V = 3 × 6 = 18 V across it: 18/10 = 1.8 A in the 10 Ω and 18/15 = 1.2 A in R (1.8 + 1.2 = 3 A). (c) H = I²Rt = 3² × 2 × 120 = 2,160 J.

Question 6 (power and the house circuit). A room heater is rated 1,760 W at 220 V. Find (a) the current it draws, (b) its resistance when working. (c) Should it go on the 5 A circuit or the 15 A circuit? (d) One evening the supply falls to 198 V. If its resistance stays the same, what power does the heater give, and by what percentage has its power fallen?

Answer. (a) I = P/V = 1,760/220 = 8 A. (b) R = V²/P = 220 × 220/1,760 = 27.5 Ω (check: V/I = 220/8 = 27.5 Ω). (c) The 15 A circuit: 8 A is more than a 5 A circuit is meant to carry. (d) P = V²/R = 198 × 198/27.5 = 1,425.6 W. The voltage fell by 10%, but the power fell by (1,760 − 1,425.6)/1,760 = 19%, because power goes with the square of the voltage (0.9 × 0.9 = 0.81).

Question 7 (balance and name the reaction). Fill in the missing numbers so that each equation is balanced, and name the type of reaction. (a) Mg + __HCl → MgCl₂ + H₂ (b) CuCO₃ → CuO + CO₂, on heating (c) BaCl₂ + H₂SO₄ → BaSO₄ + __HCl (d) 2Al + __CuO → Al₂O₃ + __Cu. In (d), which substance is oxidised and which is reduced?

Answer. (a) 2HCl: 1 Mg, 2 H and 2 Cl on each side. A metal with an acid gives a salt and hydrogen; Mg pushes hydrogen out of the acid, so it is a displacement reaction. (b) Already balanced (1 Cu, 1 C, 3 O on each side): thermal decomposition. (c) 2HCl: white insoluble BaSO₄ forms, so it is double displacement (precipitation). (d) 3CuO and 3Cu: 2 Al, 3 Cu and 3 O on each side. Aluminium is oxidised (it gains oxygen) and copper(II) oxide is reduced (it loses oxygen), so it is a redox reaction, and also a displacement, like the thermit reaction.

Question 8 (biology). (a) Count the carbon, hydrogen and oxygen atoms on each side of the photosynthesis equation in the biology table. Why does water appear on both sides? (b) A tall pea plant Tt is crossed with a short plant tt and 360 seeds grow. About how many plants are tall?

Answer. (a) Left: 6 C; 12 × 2 = 24 H; 6 × 2 + 12 = 24 O. Right: 6 C; 12 + 6 × 2 = 24 H; 6 + 6 × 2 + 6 = 24 O. So it is balanced. Water is split during photosynthesis (page 82), and some water is made again, so the book writes 12H₂O taken in and 6H₂O given out; cancelling 6H₂O from each side leaves 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂, still balanced. (b) Tt makes T and t gametes in equal numbers and tt makes only t, so half the seeds are Tt (tall) and half tt (short): about 180 tall plants, a 1 : 1 ratio.

Three mistakes that cost marks

  1. Using the mirror sign in a lens problem. The mirror formula adds (1/v + 1/u) and m = −v/u; the lens formula subtracts (1/v − 1/u) and m = v/u. Write the formula at the top of the answer before you put numbers in.
  2. Forgetting to convert units before using R = ρl/A or P = 1/f. Area must be in m² and focal length in metres. 1 mm² is 10⁻⁶ m², not 10⁻³ m².
  3. Writing an unbalanced equation. Count every atom on both sides after you write it; in Question 7 three of the four equations need a number.

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Sources

All opened and read on 5 November 2026. NCERT page numbers are printed page numbers; CBSE page numbers are PDF pages.

The formulas, equations and numbers are the textbook's; the layout, the notes and the 8 questions are our own, and every answer was re-computed by script. This page is general information; follow your teacher, the textbook and CBSE's own notices.

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