JEE Main Formula Sheet — Physics Chemistry Maths Quick Reference 2027
Complete JEE Main 2027 formula sheet: Physics (Mechanics, Electrodynamics, Optics, Modern), Chemistry (Physical, Organic, Inorganic), Maths (Algebra, Calculus, Coordinate, Vectors). One-page quick reference for daily revision.
In short: Every high-yield formula you need for JEE Main 2027 — Physics, Chemistry, and Maths — organized by topic in tables. No derivations, no theory. Just the formulas, conditions, and units you need to recall in 30 seconds during the exam. Bookmark this page and revise one subject per day.
Physics — Mechanics
Formula
Expression
Where Used
Equations of motion
v = u + at, s = ut + ½at², v² = u² + 2as
Kinematics
Projectile — Time of flight
T = 2u sinθ / g
Projectile motion
Projectile — Range
R = u² sin2θ / g
Projectile motion
Projectile — Max height
H = u² sin²θ / 2g
Projectile motion
Newton's Second Law
F = ma = dp/dt
Force and acceleration
Friction
f = μN (static: f ≤ μₛN)
Contact force problems
Work done
W = F·s·cosθ
Energy calculations
Kinetic energy
KE = ½mv²
Energy problems
Potential energy (gravity)
PE = mgh
Near Earth's surface
Work-Energy Theorem
W_net = ΔKE
All mechanics problems
Power
P = F·v = dW/dt
Rate of work
Momentum
p = mv
Collision, impulse
Impulse
J = FΔt = Δp
Impact problems
Coefficient of restitution
e = (v₂ - v₁)/(u₁ - u₂)
Collisions
Centre of mass
x_cm = Σmᵢxᵢ / Σmᵢ
System of particles
Physics — Rotational Mechanics
Formula
Expression
Where Used
Torque
τ = r × F = Iα
Rotational dynamics
Moment of inertia (ring)
I = MR²
Axis through centre
Moment of inertia (disc)
I = ½MR²
Axis through centre
Moment of inertia (solid sphere)
I = ⅖MR²
Axis through centre
Moment of inertia (hollow sphere)
I = ⅔MR²
Axis through centre
Moment of inertia (rod, centre)
I = ML²/12
Axis through centre
Moment of inertia (rod, end)
I = ML²/3
Axis through one end
Parallel axis theorem
I = I_cm + Md²
Shifted axis
Angular momentum
L = Iω = r × p
Rotational conservation
Rotational KE
KE = ½Iω²
Rolling, spinning
Rolling (no slip)
v = Rω, KE = ½mv²(1 + k²/R²)
Rolling problems
Physics — Gravitation and SHM
Formula
Expression
Where Used
Gravitational force
F = GMm/r²
Universal gravitation
Gravitational PE
U = -GMm/r
Orbital mechanics
Orbital velocity
v₀ = √(GM/r)
Satellite orbit
Escape velocity
vₑ = √(2GM/R) = √(2gR)
Escape from surface
Time period (satellite)
T = 2π√(r³/GM)
Kepler's third law
g at height h
g' = g(1 + h/R)⁻² ≈ g(1 - 2h/R) for h << R
Variation of g
g at depth d
g' = g(1 - d/R)
Variation of g
SHM displacement
x = A sin(ωt + φ)
Simple harmonic motion
SHM velocity
v = ω√(A² - x²)
SHM kinematics
SHM time period (spring)
T = 2π√(m/k)
Spring-mass system
SHM time period (pendulum)
T = 2π√(l/g)
Simple pendulum
SHM total energy
E = ½kA² = ½mω²A²
Energy in SHM
Physics — Thermodynamics and Waves
Formula
Expression
Where Used
First law
ΔQ = ΔU + ΔW
All thermodynamic processes
Ideal gas
PV = nRT
Gas calculations
Work done (isothermal)
W = nRT ln(V₂/V₁)
Isothermal process
Adiabatic relation
PVᵞ = constant, TVᵞ⁻¹ = constant
Adiabatic process
Efficiency (Carnot)
η = 1 - T₂/T₁
Heat engine
Speed of sound
v = √(γRT/M)
Gas medium
Wave speed
v = fλ = ω/k
All waves
Beat frequency
f_beat =
f₁ - f₂
Doppler effect
f' = f(v ± v₀)/(v ∓ vₛ)
Moving source/observer
Resonance (closed pipe)
f = (2n-1)v/4L, n = 1,2,3...
Organ pipes
Resonance (open pipe)
f = nv/2L, n = 1,2,3...
Organ pipes
Physics — Electrostatics and Current
Formula
Expression
Where Used
Coulomb's law
F = kq₁q₂/r², k = 1/4πε₀
Point charges
Electric field (point)
E = kq/r²
Field calculations
Electric potential
V = kq/r
Potential energy
Gauss's law
∮E·dA = q_enc/ε₀
Symmetric charge distributions
Capacitance (parallel plate)
C = ε₀A/d, with dielectric: C = Kε₀A/d
Capacitors
Energy in capacitor
U = ½CV² = Q²/2C = ½QV
Energy storage
Capacitors in series
1/C = 1/C₁ + 1/C₂ + ...
Series combination
Capacitors in parallel
C = C₁ + C₂ + ...
Parallel combination
Ohm's law
V = IR
DC circuits
Kirchhoff's laws
ΣI = 0 (junction), ΣV = 0 (loop)
Circuit analysis
Power
P = VI = I²R = V²/R
Electric power
Wheatstone bridge
P/Q = R/S (balanced)
Resistance measurement
Meter bridge
R = S·l/(100-l)
Practical experiment
Physics — Magnetism, EMI, and Optics
Formula
Expression
Where Used
Biot-Savart law
dB = (μ₀/4π)(Idl × r̂)/r²
Magnetic field of current
Ampere's law
∮B·dl = μ₀I_enc
Solenoid, toroid
Force on conductor
F = BIL sinθ
Current in magnetic field
Force on charge
F = qv × B
Lorentz force
Solenoid
B = μ₀nI
Inside long solenoid
Faraday's law
ε = -dΦ/dt
Electromagnetic induction
Self-inductance
ε = -LdI/dt
Inductor
Energy in inductor
U = ½LI²
Stored magnetic energy
Impedance (LCR)
Z = √(R² + (ωL - 1/ωC)²)
AC circuits
Resonance frequency
f₀ = 1/(2π√LC)
LCR resonance
Mirror formula
1/f = 1/v + 1/u
Mirrors
Lens formula
1/f = 1/v - 1/u
Lenses
Lens maker's
1/f = (n-1)(1/R₁ - 1/R₂)
Lens properties
YDSE fringe width
β = λD/d
Interference
Single slit central max
Width = 2λD/a
Diffraction
Physics — Modern Physics
Formula
Expression
Where Used
Photoelectric equation
KE_max = hν - φ
Photoelectric effect
de Broglie wavelength
λ = h/mv = h/p
Wave-particle duality
Bohr radius
rₙ = 0.529 × n²/Z Å
Hydrogen-like atoms
Bohr energy
Eₙ = -13.6 × Z²/n² eV
Energy levels
Hydrogen spectrum
1/λ = RZ²(1/n₁² - 1/n₂²)
Spectral lines
Binding energy
BE = [Zm_p + (A-Z)m_n - M] × 931.5 MeV
Nuclear stability
Radioactive decay
N = N₀e^(-λt), T₁/₂ = 0.693/λ
Half-life problems
Mass-energy
E = mc²
Nuclear reactions
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x² + y² + 2gx + 2fy + c = 0, centre (-g,-f), r = √(g²+f²-c)
Circle equation
Parabola
y² = 4ax → Focus (a,0), Directrix x = -a
Conic section
Ellipse
x²/a² + y²/b² = 1, e = √(1-b²/a²)
Conic section
Hyperbola
x²/a² - y²/b² = 1, e = √(1+b²/a²)
Conic section
Maths — Vectors and 3D
Formula
Expression
Where Used
Dot product
a·b =
a
Cross product magnitude
a×b
Scalar triple product
[a b c] = a·(b×c)
Volume of parallelepiped
Direction cosines
l² + m² + n² = 1
Line in 3D
Distance between point and plane
d =
ax₁+by₁+cz₁+d
Angle between planes
cosθ =
a₁a₂+b₁b₂+c₁c₂
Maths — Probability and Statistics
Formula
Expression
Where Used
Probability
P(E) = favourable outcomes / total outcomes
Basic probability
Addition rule
P(A∪B) = P(A) + P(B) - P(A∩B)
Union of events
Conditional probability
P(A
B) = P(A∩B)/P(B)
Bayes' theorem
P(A
B) = P(B
Binomial distribution
P(X=r) = ⁿCᵣ pʳ qⁿ⁻ʳ
n trials, p = success
Mean (Binomial)
μ = np
Expected value
Variance (Binomial)
σ² = npq
Spread
Mean
x̄ = Σxᵢ/n
Central tendency
Variance
σ² = Σ(xᵢ-x̄)²/n
Dispersion
Important Constants for JEE
Constant
Value
Speed of light (c)
3 × 10⁸ m/s
Planck's constant (h)
6.63 × 10⁻³⁴ J·s
Electron charge (e)
1.6 × 10⁻¹⁹ C
Avogadro's number (Nₐ)
6.022 × 10²³ mol⁻¹
Gas constant (R)
8.314 J/mol·K = 0.0821 L·atm/mol·K
Faraday constant (F)
96500 C/mol
Boltzmann constant (k)
1.38 × 10⁻²³ J/K
Permittivity (ε₀)
8.854 × 10⁻¹² C²/N·m²
Permeability (μ₀)
4π × 10⁻⁷ T·m/A
Rydberg constant (R)
1.097 × 10⁷ m⁻¹
g (acceleration)
9.8 m/s²
1 eV
1.6 × 10⁻¹⁹ J
1 AMU
931.5 MeV/c²
π
3.14159
e (Euler's)
2.71828
Frequently Asked Questions
Q1. How many formula-based questions come in JEE Main?
Roughly 40-50 percent of JEE Main questions can be solved directly by applying the right formula and plugging in values. The remaining need conceptual understanding or multi-step problem solving — but knowing formulas is the first step for all of them.
Q2. Should I memorize all these formulas?
Yes, but do it in stages. Start with the formulas you use most often (Mechanics, Calculus, Physical Chemistry). Then add topic by topic. Write each formula 3 times daily from memory. Within 2-3 weeks, you will recall most of them automatically.
Q3. Is this formula sheet enough for JEE Main?
This sheet covers the core formulas for all major topics. For JEE Advanced, you will need additional depth in certain areas (complex integration techniques, advanced organic mechanisms). For JEE Main, this list covers 90 percent of what you need.
Q4. Which subject has the most formulas to remember?
Physics has the most individual formulas (150+), but many are variations of the same concept. Maths has fewer formulas but requires deeper understanding of when to apply them. Chemistry requires remembering both formulas and facts (reactions, properties, exceptions).
Q5. How should I revise this before the exam?
In the last week, revise one subject per day. Day 1: Physics Mechanics + Electrodynamics. Day 2: Physics Optics + Modern. Day 3: Chemistry Physical. Day 4: Chemistry Organic + Inorganic. Day 5: Maths Algebra + Trig. Day 6: Maths Calculus + Coordinate. Day 7: Full review of weak areas.
Q6. Are formulas the same for JEE Main January and April sessions?
Yes. The syllabus and therefore the required formulas are identical for both sessions. Only the question paper changes.
