Physics formulas are the mathematical expressions that describe the fundamental laws and relationships governing the physical world. This comprehensive reference guide provides essential equations across all major areas of physics, complete with explanations and variable definitions.
Classical Mechanics
Newton's Second Law
$$F = ma$$
The net force on an object equals mass times acceleration
F = Force (N), m = Mass (kg), a = Acceleration (m/s²)
Kinematic Equations
$$v = v_0 + at$$
$$s = v_0t + \frac{1}{2}at^2$$
$$v^2 = v_0^2 + 2as$$
Motion equations for constant acceleration
v = Final velocity, v₀ = Initial velocity, a = Acceleration, t = Time, s = Displacement
Work and Energy
$$W = F \cdot d \cos\theta$$
$$KE = \frac{1}{2}mv^2$$
$$PE = mgh$$
Work done by force and kinetic/potential energy
W = Work (J), F = Force (N), d = Distance (m), θ = Angle, KE = Kinetic Energy, PE = Potential Energy, g = Gravitational acceleration, h = Height
Momentum and Impulse
$$p = mv$$
$$J = F \Delta t = \Delta p$$
Linear momentum and impulse-momentum theorem
p = Momentum (kg⋅m/s), J = Impulse (N⋅s), Δt = Time interval, Δp = Change in momentum
Rotational Motion
$$\tau = I\alpha$$
$$L = I\omega$$
$$KE_{rot} = \frac{1}{2}I\omega^2$$
Rotational dynamics and angular momentum
τ = Torque (N⋅m), I = Moment of inertia (kg⋅m²), α = Angular acceleration (rad/s²), L = Angular momentum, ω = Angular velocity (rad/s)
Universal Gravitation
$$F = G\frac{m_1m_2}{r^2}$$
Gravitational force between two masses
G = Gravitational constant (6.67×10⁻¹¹ N⋅m²/kg²), m₁, m₂ = Masses, r = Distance between centers
Thermodynamics
Ideal Gas Law
$$PV = nRT$$
Relationship between pressure, volume, and temperature for ideal gases
P = Pressure (Pa), V = Volume (m³), n = Number of moles, R = Gas constant (8.314 J/mol⋅K), T = Temperature (K)
First Law of Thermodynamics
$$\Delta U = Q - W$$
Conservation of energy in thermodynamic processes
ΔU = Change in internal energy (J), Q = Heat added to system (J), W = Work done by system (J)
Heat Transfer
$$Q = mc\Delta T$$
$$Q = mL$$
Heat required for temperature change and phase transitions
Q = Heat (J), m = Mass (kg), c = Specific heat capacity (J/kg⋅K), ΔT = Temperature change, L = Latent heat (J/kg)
Carnot Efficiency
$$\eta = 1 - \frac{T_c}{T_h}$$
Maximum theoretical efficiency of heat engine
η = Efficiency, Tc = Cold reservoir temperature (K), Th = Hot reservoir temperature (K)
Entropy
$$\Delta S = \frac{Q}{T}$$
Change in entropy for reversible processes
ΔS = Change in entropy (J/K), Q = Heat transfer (J), T = Temperature (K)
Electromagnetism
Coulomb's Law
$$F = k\frac{q_1q_2}{r^2}$$
Electrostatic force between point charges
k = Coulomb constant (8.99×10⁹ N⋅m²/C²), q₁, q₂ = Charges (C), r = Distance (m)
Electric Field and Potential
$$E = \frac{F}{q} = k\frac{Q}{r^2}$$
$$V = k\frac{Q}{r}$$
Electric field strength and electric potential
E = Electric field (N/C), V = Electric potential (V), Q = Source charge, q = Test charge
Ohm's Law
$$V = IR$$
$$P = VI = I^2R = \frac{V^2}{R}$$
Relationship between voltage, current, and resistance
V = Voltage (V), I = Current (A), R = Resistance (Ω), P = Power (W)
Magnetic Force
$$F = qvB\sin\theta$$
$$F = BIL\sin\theta$$
Force on moving charge and current-carrying conductor in magnetic field
q = Charge (C), v = Velocity (m/s), B = Magnetic field (T), I = Current (A), L = Length (m), θ = Angle
Faraday's Law
$$\varepsilon = -\frac{d\Phi_B}{dt}$$
Induced EMF due to changing magnetic flux
ε = Induced EMF (V), ΦB = Magnetic flux (Wb), t = Time (s)
Maxwell's Equations (Simplified)
$$\nabla \cdot E = \frac{\rho}{\varepsilon_0}$$
$$\nabla \cdot B = 0$$
$$\nabla \times E = -\frac{\partial B}{\partial t}$$
$$\nabla \times B = \mu_0 J + \mu_0\varepsilon_0\frac{\partial E}{\partial t}$$
Fundamental equations of electromagnetism
ρ = Charge density, J = Current density, ε₀ = Permittivity of free space,
μ₀ = Permeability of free space
Waves and Optics
Wave Equation
$$v = f\lambda$$
$$c = 3.00 \times 10^8 \text{ m/s}$$
Relationship between wave speed, frequency, and wavelength
v = Wave speed (m/s), f = Frequency (Hz), λ = Wavelength (m), c = Speed of light
Snell's Law
$$n_1\sin\theta_1 = n_2\sin\theta_2$$
Refraction of light at interface between media
n₁, n₂ = Refractive indices, θ₁, θ₂ = Angles of incidence and refraction
Lens Equation
$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$
Thin lens formula relating focal length and object/image distances
f = Focal length (m), do = Object distance (m), di = Image distance (m)
Doppler Effect
$$f' = f\frac{v \pm v_r}{v \pm v_s}$$
Frequency shift due to relative motion between source and observer
f' = Observed frequency, f = Source frequency, v = Wave speed, vr = Receiver velocity, vs = Source velocity
Interference and Diffraction
$$d\sin\theta = m\lambda$$ (constructive)
$$d\sin\theta = (m + \frac{1}{2})\lambda$$ (destructive)
Conditions for constructive and destructive interference
d = Slit separation, θ = Angle, m = Order (integer), λ = Wavelength
Modern Physics
Einstein's Mass-Energy Equivalence
$$E = mc^2$$
Equivalence of mass and energy
E = Energy (J), m = Mass (kg), c = Speed of light (3×10⁸ m/s)
Planck's Equation
$$E = hf = \frac{hc}{\lambda}$$
Energy of electromagnetic radiation quantum
h = Planck constant (6.626×10⁻³⁴ J⋅s), f = Frequency, λ = Wavelength
De Broglie Wavelength
$$\lambda = \frac{h}{p} = \frac{h}{mv}$$
Matter wave wavelength
λ = De Broglie wavelength, p = Momentum, m = Mass, v = Velocity
Heisenberg Uncertainty Principle
$$\Delta x \Delta p \geq \frac{\hbar}{2}$$
Fundamental limit on simultaneous measurement precision
Δx = Position uncertainty, Δp = Momentum uncertainty, ℏ = Reduced Planck constant (h/2π)
Lorentz Factor
$$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$
Relativistic correction factor
γ = Lorentz factor, v = Velocity, c = Speed of light
Radioactive Decay
$$N(t) = N_0 e^{-\lambda t}$$
Exponential decay of radioactive nuclei
N(t) = Number at time t, N₀ = Initial number, λ = Decay constant, t = Time
Fundamental Physical Constants
| Constant | Symbol | Value | Units |
|---|---|---|---|
| Speed of light in vacuum | c | 2.998 × 10⁸ | m/s |
| Planck constant | h | 6.626 × 10⁻³⁴ | J⋅s |
| Reduced Planck constant | ℏ | 1.055 × 10⁻³⁴ | J⋅s |
| Elementary charge | e | 1.602 × 10⁻¹⁹ | C |
| Electron mass | mₑ | 9.109 × 10⁻³¹ | kg |
| Proton mass | mₚ | 1.673 × 10⁻²⁷ | kg |
| Neutron mass | mₙ | 1.675 × 10⁻²⁷ | kg |
| Avogadro constant | Nₐ | 6.022 × 10²³ | mol⁻¹ |
| Boltzmann constant | k | 1.381 × 10⁻²³ | J/K |
| Gas constant | R | 8.314 | J/(mol⋅K) |
| Gravitational constant | G | 6.674 × 10⁻¹¹ | N⋅m²/kg² |
| Permittivity of free space | ε₀ | 8.854 × 10⁻¹² | F/m |
| Permeability of free space | μ₀ | 4π × 10⁻⁷ | H/m |
📏 SI Base Units
- Length: meter (m)
- Mass: kilogram (kg)
- Time: second (s)
- Electric Current: ampere (A)
- Temperature: kelvin (K)
- Amount of Substance: mole (mol)
- Luminous Intensity: candela (cd)
🔬 Example Derivation: Kinetic Energy
Starting from Newton's second law and the work-energy theorem:
$$W = \int F \, dx = \int ma \, dx = \int m\frac{dv}{dt} \, dx$$
$$= \int mv \, dv = \frac{1}{2}mv^2 - \frac{1}{2}mv_0^2$$
For motion from rest (v₀ = 0), the kinetic energy is KE = ½mv²
Frequently Asked Questions
What are the most important physics formulas?
Key physics formulas include Newton's laws (F=ma), energy equations (E=mc²), electromagnetic laws (F=qE), thermodynamic relations (PV=nRT), and wave equations (v=fλ). These fundamental equations form the basis of classical and modern physics and appear frequently in problem-solving.
How do I remember physics formulas?
Remember physics formulas by understanding their physical meaning, practicing derivations, using dimensional analysis, creating formula sheets, and applying them to solve problems regularly. Focus on understanding the underlying concepts rather than pure memorization, as this helps with retention and application.
What units are used in physics formulas?
Physics formulas primarily use SI units: meters (m) for length, kilograms (kg) for mass, seconds (s) for time, amperes (A) for current, kelvin (K) for temperature, moles (mol) for amount of substance, and candela (cd) for luminous intensity. Derived units combine these base units.