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Physics Calculator: Formulas, Calculators and Solved Examples for Class 9–12 and JEE/NEET
- Physics calculators cover the five core domains tested in Indian board exams and JEE/NEET: Mechanics, Thermodynamics, Waves & Optics, Electricity & Magnetism, and Modern Physics.
- The most-used physics formulas in one place: v = u + at, F = ma, KE = ½mv², E = mc², P = IV, λ = h/p — each with worked examples and unit awareness.
- Unit awareness prevents the single most common physics exam error: mixing SI and CGS units in the same equation. Always convert to SI (kg, m, s, A, K) before calculating.
- For JEE Main/Advanced: Mechanics (20–25% of paper), Electricity (18–22%), Optics (10–15%), Modern Physics (10–15%). Allocate study time accordingly.
Use our free Physics Calculator to solve any physics equation — input the known variables, select the formula, and get the unknown with full working shown.
MODULE 1: MECHANICS
Kinematics — Equations of Motion
For uniform acceleration (constant a):
| Equation | Formula | Variables |
|---|---|---|
| Velocity | v = u + at | v = final velocity, u = initial, a = acceleration, t = time |
| Displacement | s = ut + ½at² | s = displacement |
| Velocity-displacement | v² = u² + 2as | Eliminates t |
| Average velocity | s = ½(u + v)t | Eliminates a |
Worked Example: A car starts from rest (u = 0) and accelerates at 4 m/s² for 10 seconds. Find final velocity and distance covered.
v = 0 + (4)(10) = 40 m/s s = 0(10) + ½(4)(10²) = 0 + 200 = 200 m
Newton's Laws and Forces
| Quantity | Formula | Unit |
|---|---|---|
| Force | F = ma | Newton (N) = kg·m/s² |
| Weight | W = mg | N (g = 9.8 m/s²) |
| Momentum | p = mv | kg·m/s |
| Impulse | J = FΔt = Δp | N·s |
| Friction (kinetic) | f = μₖN | N |
| Friction (static max) | f_s = μₛN | N |
g values for India: Use g = 9.8 m/s² (standard); JEE often uses g = 10 m/s² for simpler calculation — check the problem.
Work, Energy, and Power
| Quantity | Formula | Unit |
|---|---|---|
| Work | W = Fs cos θ | Joule (J) |
| Kinetic energy | KE = ½mv² | J |
| Potential energy (gravity) | PE = mgh | J |
| Conservation of energy | KE₁ + PE₁ = KE₂ + PE₂ | J |
| Power | P = W/t = Fv | Watt (W) = J/s |
| Efficiency | η = (Output/Input) × 100% | % |
Worked Example — JEE style: A 2 kg block slides down a frictionless incline of height 5 m. Find its velocity at the bottom. Using conservation of energy: mgh = ½mv² (2)(10)(5) = ½(2)v² 100 = v² v = 10 m/s
Circular Motion and Gravitation
| Quantity | Formula | Unit |
|---|---|---|
| Centripetal acceleration | a_c = v²/r = ω²r | m/s² |
| Centripetal force | F_c = mv²/r | N |
| Angular velocity | ω = 2π/T = 2πf | rad/s |
| Gravitational force | F = Gm₁m₂/r² | N |
| Orbital velocity | v = √(GM/r) | m/s |
| Escape velocity | v_e = √(2GM/R) = √(2gR) | m/s |
Earth escape velocity: v_e = √(2 × 9.8 × 6.4 × 10⁶) ≈ 11.2 km/s
Simple Harmonic Motion (SHM)
| Quantity | Formula |
|---|---|
| Time period (spring) | T = 2π√(m/k) |
| Time period (pendulum) | T = 2π√(L/g) |
| Angular frequency | ω = √(k/m) |
| Displacement | x = A sin(ωt + φ) |
| Max velocity | v_max = Aω |
| Max acceleration | a_max = Aω² |
MODULE 2: THERMODYNAMICS
Temperature and Heat
Quantity Formula Unit Heat capacity Q = mcΔT J (c in J/kg·K) Latent heat Q = mL J Thermal expansion (linear) ΔL = LαΔT m Thermal expansion (volume) ΔV = VγΔT m³ Heat conduction Q/t = kA(ΔT/d) W
| Quantity | Formula | Unit |
|---|---|---|
| Heat capacity | Q = mcΔT | J (c in J/kg·K) |
| Latent heat | Q = mL | J |
| Thermal expansion (linear) | ΔL = LαΔT | m |
| Thermal expansion (volume) | ΔV = VγΔT | m³ |
| Heat conduction | Q/t = kA(ΔT/d) | W |
Specific heat capacities (common values):
- Water: 4,186 J/kg·K
- Ice: 2,090 J/kg·K
- Copper: 385 J/kg·K
- Aluminium: 900 J/kg·K
Ideal Gas Laws
| Law | Formula | Condition |
|---|---|---|
| Boyle's | P₁V₁ = P₂V₂ | Constant T |
| Charles' | V₁/T₁ = V₂/T₂ | Constant P |
| Gay-Lussac's | P₁/T₁ = P₂/T₂ | Constant V |
| Ideal Gas | PV = nRT | All conditions |
| Combined | P₁V₁/T₁ = P₂V₂/T₂ | General |
R = 8.314 J/mol·K | 1 atm = 101,325 Pa | 0°C = 273.15 K
Laws of Thermodynamics
| Law | Statement | Formula |
|---|---|---|
| 0th | Thermal equilibrium is transitive | — |
| 1st | Energy conservation | ΔU = Q − W |
| 2nd | Entropy increases | dS ≥ dQ/T |
| Efficiency (Carnot) | η = 1 − T_cold/T_hot | Always < 100% |
MODULE 3: WAVES AND OPTICS
Wave Properties
Quantity Formula Unit Wave speed v = fλ m/s Time period T = 1/f s Frequency f = v/λ Hz Speed of sound (air, 0°C) 332 m/s — Speed of light (vacuum) 3 × 10⁸ m/s —
Optics — Mirrors and Lenses
Formula Name Notes 1/f = 1/v + 1/u Mirror/lens formula Sign convention critical m = v/u = h_i/h_o Magnification Negative = inverted n = c/v Refractive index n > 1 for denser media n₁ sin θ₁ = n₂ sin θ₂ Snell's Law Refraction sin C = n₂/n₁ Critical angle For TIR (n₁ > n₂) P = 1/f Lens power Dioptre (f in metres)
| Quantity | Formula | Unit |
|---|---|---|
| Wave speed | v = fλ | m/s |
| Time period | T = 1/f | s |
| Frequency | f = v/λ | Hz |
| Speed of sound (air, 0°C) | 332 m/s | — |
| Speed of light (vacuum) | 3 × 10⁸ m/s | — |
| Formula | Name | Notes |
|---|---|---|
| 1/f = 1/v + 1/u | Mirror/lens formula | Sign convention critical |
| m = v/u = h_i/h_o | Magnification | Negative = inverted |
| n = c/v | Refractive index | n > 1 for denser media |
| n₁ sin θ₁ = n₂ sin θ₂ | Snell's Law | Refraction |
| sin C = n₂/n₁ | Critical angle | For TIR (n₁ > n₂) |
| P = 1/f | Lens power | Dioptre (f in metres) |
Sign Convention (New Cartesian): Distances measured from pole/optical centre; distances along incident ray direction = positive; opposite = negative.
Young's Double Slit Experiment (YDSE)
| Quantity | Formula |
|---|---|
| Fringe width | β = λD/d |
| Path difference (bright) | Δ = nλ (n = 0, ±1, ±2...) |
| Path difference (dark) | Δ = (2n-1)λ/2 |
| Position of nth bright fringe | y_n = nλD/d |
MODULE 4: MODERN PHYSICS
Photoelectric Effect and Photons
Quantity Formula Value/Unit Photon energy E = hf = hc/λ J Einstein equation hf = φ + KE_max J Work function φ = hf₀ J de Broglie wavelength λ = h/p = h/mv m Planck's constant h = 6.626 × 10⁻³⁴ J·s —
Nuclear Physics
Quantity Formula Mass-energy equivalence E = mc² (c = 3 × 10⁸ m/s) Radioactive decay N = N₀ e^(−λt) Half-life T½ = ln2/λ = 0.693/λ Activity A = λN Becquerel (Bq)
| Quantity | Formula | Value/Unit |
|---|---|---|
| Photon energy | E = hf = hc/λ | J |
| Einstein equation | hf = φ + KE_max | J |
| Work function | φ = hf₀ | J |
| de Broglie wavelength | λ = h/p = h/mv | m |
| Planck's constant | h = 6.626 × 10⁻³⁴ J·s | — |
| Quantity | Formula | |
|---|---|---|
| Mass-energy equivalence | E = mc² (c = 3 × 10⁸ m/s) | |
| Radioactive decay | N = N₀ e^(−λt) | |
| Half-life | T½ = ln2/λ = 0.693/λ | |
| Activity | A = λN | Becquerel (Bq) |
1 amu = 931.5 MeV/c² | 1 eV = 1.6 × 10⁻¹⁹ J
Quick Reference: Important Constants
Constant Symbol Value Speed of light c 3 × 10⁸ m/s Planck's constant h 6.626 × 10⁻³⁴ J·s Elementary charge e 1.6 × 10⁻¹⁹ C Electron mass mₑ 9.11 × 10⁻³¹ kg Proton mass mₚ 1.67 × 10⁻²⁷ kg Avogadro's number Nₐ 6.022 × 10²³ mol⁻¹ Gas constant R 8.314 J/mol·K Gravitational constant G 6.674 × 10⁻¹¹ N·m²/kg² Boltzmann constant k_B 1.38 × 10⁻²³ J/K Permittivity of free space ε₀ 8.85 × 10⁻¹² F/m Permeability of free space μ₀ 4π × 10⁻⁷ T·m/A
FAQ
What is the most important physics formula for JEE?No single formula dominates — but Newton's second law (F = ma), conservation of energy (KE + PE = constant), and the mirror/lens formula (1/f = 1/v + 1/u) appear across the widest range of problems. Ohm's law (V = IR) and Coulomb's law (F = kq₁q₂/r²) are similarly foundational for electricity chapters.
How do I avoid sign errors in optics problems?Always draw a diagram first and establish your coordinate system before writing the mirror/lens formula. Incident light travels left to right by convention. All distances from the pole: positive if in the direction of incident light, negative if against. Apply sign convention to u (object), v (image), and f (focal length) before substituting.
What is the difference between mass and weight in physics?Mass (m) is the amount of matter in an object — measured in kg, constant everywhere. Weight (W = mg) is the gravitational force on that mass — measured in Newtons, varies with g. On the Moon (g = 1.63 m/s²), your mass is unchanged but your weight is 1/6th of Earth's. In Indian board exams and JEE, "find the weight" means find W = mg in Newtons.
How do I convert between SI and CGS units?Key conversions: 1 N = 10⁵ dyne | 1 J = 10⁷ erg | 1 Pa = 10 dyne/cm² | 1 kg = 1,000 g | 1 m = 100 cm. For calculations, always convert to SI first — CGS is rarely required in modern Indian board exams or JEE, but recognising it in older textbooks is useful.
| Constant | Symbol | Value |
|---|---|---|
| Speed of light | c | 3 × 10⁸ m/s |
| Planck's constant | h | 6.626 × 10⁻³⁴ J·s |
| Elementary charge | e | 1.6 × 10⁻¹⁹ C |
| Electron mass | mₑ | 9.11 × 10⁻³¹ kg |
| Proton mass | mₚ | 1.67 × 10⁻²⁷ kg |
| Avogadro's number | Nₐ | 6.022 × 10²³ mol⁻¹ |
| Gas constant | R | 8.314 J/mol·K |
| Gravitational constant | G | 6.674 × 10⁻¹¹ N·m²/kg² |
| Boltzmann constant | k_B | 1.38 × 10⁻²³ J/K |
| Permittivity of free space | ε₀ | 8.85 × 10⁻¹² F/m |
| Permeability of free space | μ₀ | 4π × 10⁻⁷ T·m/A |
FAQ
What is the most important physics formula for JEE?
No single formula dominates — but Newton's second law (F = ma), conservation of energy (KE + PE = constant), and the mirror/lens formula (1/f = 1/v + 1/u) appear across the widest range of problems. Ohm's law (V = IR) and Coulomb's law (F = kq₁q₂/r²) are similarly foundational for electricity chapters.
How do I avoid sign errors in optics problems?
Always draw a diagram first and establish your coordinate system before writing the mirror/lens formula. Incident light travels left to right by convention. All distances from the pole: positive if in the direction of incident light, negative if against. Apply sign convention to u (object), v (image), and f (focal length) before substituting.
What is the difference between mass and weight in physics?
Mass (m) is the amount of matter in an object — measured in kg, constant everywhere. Weight (W = mg) is the gravitational force on that mass — measured in Newtons, varies with g. On the Moon (g = 1.63 m/s²), your mass is unchanged but your weight is 1/6th of Earth's. In Indian board exams and JEE, "find the weight" means find W = mg in Newtons.
How do I convert between SI and CGS units?
Key conversions: 1 N = 10⁵ dyne | 1 J = 10⁷ erg | 1 Pa = 10 dyne/cm² | 1 kg = 1,000 g | 1 m = 100 cm. For calculations, always convert to SI first — CGS is rarely required in modern Indian board exams or JEE, but recognising it in older textbooks is useful.
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