Physics Formulas

Magnetic Flux Density Formula

Reference for magnetic flux density B = Phi/A. Calculate flux density from total flux and cross-sectional area, understand the tesla unit, and see examples.

Projectile Motion Range Formula

Reference for ideal projectile motion. Calculate range, max height, and flight time using R = v squared times sin(2theta)/g with angle and velocity examples.

Kepler's Third Law Formula

Kepler's Third Law relates a planet's orbital period to its distance from the Sun. Includes formula, examples, and applications to exoplanets.

Bose-Einstein Distribution Formula

Reference for the Bose-Einstein distribution giving the average number of bosons in a quantum state. Applies to photons, phonons, and integer-spin particles.

Coefficient of Restitution Formula

Calculate how elastic a collision is using the coefficient of restitution. Ranges from 0 (perfectly inelastic) to 1 (perfectly elastic).

Compton Scattering Formula

Compton scattering: delta-lambda = (h/mec)(1 - cos theta). Calculate the wavelength shift of X-rays scattered by electrons in matter.

Coriolis Force Formula

Calculate the Coriolis force on a moving object in a rotating reference frame. Explains why weather systems spiral and why long-range projectiles drift.

Damped Harmonic Oscillator Formula

The equation of motion and solution for a damped harmonic oscillator. Covers underdamped, critically damped, and overdamped regimes with real-world examples.

Fermi-Dirac Distribution Formula

The Fermi-Dirac distribution gives the probability that a quantum state at energy E is occupied by a fermion at thermal equilibrium.

Hall Effect Formula

Hall effect: V_H = (I * B) / (n * e * t). Calculate the transverse voltage produced when a magnetic field deflects charge carriers in a conductor.

Hawking Radiation Temperature Formula

Calculate the temperature of Hawking radiation emitted by a black hole. Derived by Stephen Hawking in 1974, linking quantum mechanics and general relativity.

Length Contraction Formula

Calculate the relativistic length contraction of an object moving at relativistic speeds. A key result of Einstein's special theory of relativity.

Lorentz Transformation Equations

The Lorentz transformation equations convert spacetime coordinates between two inertial reference frames moving at constant velocity relative to each other.

Maxwell-Boltzmann Speed Distribution

The Maxwell-Boltzmann distribution gives the probability of gas molecule speeds at a given temperature. Derives most probable, mean, and RMS speeds.

Orbital Energy Formula

Calculate the total mechanical energy of an orbiting satellite or planet. Negative orbital energy means the object is gravitationally bound.

Parallel Axis Theorem

Calculate the moment of inertia about any axis using the parallel axis theorem. Adds Md² to the center-of-mass moment of inertia.

Relativistic Momentum Formula

Calculate the momentum of particles moving at relativistic speeds. Shows why classical momentum breaks down near the speed of light.

Rydberg Formula

The Rydberg formula predicts the wavelengths of spectral lines emitted by hydrogen and hydrogen-like atoms. Includes worked examples.

Simple Harmonic Motion Formulas

The complete set of simple harmonic motion equations: position, velocity, acceleration, period, frequency, and energy for springs and pendulums.

Stokes' Law

Stokes' law: F_d = 6*pi*eta*r*v. Calculate the viscous drag force on a small sphere moving slowly through a viscous fluid at low Reynolds number.

Tsiolkovsky Rocket Equation

The Tsiolkovsky Rocket Equation relates a rocket's velocity change to its exhaust speed and mass ratio. The fundamental equation of rocket science.

Venturi Effect Formula

The Venturi effect: fluid speeds up and pressure drops when flowing through a constriction. Based on Bernoulli's equation and the continuity equation.

Vis-Viva Equation

Calculate orbital speed at any point in an elliptical orbit. The vis-viva equation relates orbital speed to position and the semi-major axis.

Wien's Displacement Law

Wien's displacement law: lambda_max = b/T. Find the peak wavelength of thermal radiation emitted by a blackbody at any temperature.

Radioactive Decay Formula (Half-Life)

The radioactive decay formula shows how unstable atoms disintegrate over time. Calculate remaining quantity using half-life or decay constant.

Escape Velocity Formula

Reference for escape velocity formula v = sqrt(2GM/r). Returns escape speed from Earth, Moon, Mars, and Jupiter with worked examples in km/s and mph.

Gravitational Potential Energy Formula

Reference for U = -GMm/r and near-surface U = mgh gravitational potential energy. Covers escape velocity, orbital energy, and worked examples.

Magnetic Flux Formula

Reference for the magnetic flux formula (Phi = B x A x cos theta). Covers Faraday induction, solenoids, and flux density with worked examples.

Angular Momentum

Reference for angular momentum L = Iw or L = mvr. Includes moment of inertia for spheres, disks, rods, and cylinders with worked examples.

Buoyancy Formula (Archimedes Principle)

Reference for Archimedes buoyancy F_b = ρ × V_disp × g. Covers fluid density and displaced volume with examples for ships, submarines, and hot air balloons.

Capacitance Formula

Reference for capacitance: C = Q/V, parallel plate C = e0*A/d, and energy E = 0.5CV2. Covers series, parallel, RC time constants, and dielectrics.

Carnot Efficiency Formula

Reference for Carnot efficiency η = 1-Tc/Th — the maximum possible heat engine efficiency. Enter cold and hot reservoir temperatures to find the Carnot limit.

Centripetal Acceleration Formula

Reference for centripetal acceleration a = v squared over r and a = omega squared times r. Covers the link to centripetal force with orbit and turn examples.

Centripetal Force Formula

The centripetal force formula F = mv²/r calculates the inward force needed for circular motion. Learn with step-by-step examples.

Coulomb's Law Formula

Coulomb's Law calculates the electric force between two charges: F = kq1q2/r². Learn about charge interaction with examples.

Dalton's Law of Partial Pressures

Dalton's Law states total gas pressure equals the sum of partial pressures. Learn the formula P_total = P₁ + P₂ + ... with examples.

de Broglie Wavelength Formula

Reference for the de Broglie wavelength formula lambda = h over p. Calculates the quantum wavelength of electrons and particles from momentum with examples.

De Broglie Wavelength Formula

The de Broglie formula λ = h/mv calculates the wavelength of matter waves. Understand wave-particle duality with worked examples.

Doppler Effect Formula

The Doppler effect formula calculates frequency shifts for moving sound and light sources. Includes formulas for both approaching and receding.

Drag Equation

Reference for the drag equation F = 0.5pv2CdA. Covers drag coefficient, frontal area, and fluid density for aerodynamic resistance on vehicles and projectiles.

Electromagnetic Induction

Reference for Faraday's law and Lenz's law. Calculate induced EMF from changing magnetic flux with worked examples. Covers flux linkage and solenoids.

Entropy Change Formula

The entropy change formula calculates disorder change in thermodynamic processes using the second law. Learn with examples.

Faraday's Law of Induction

Faraday's law EMF = -dPhi/dt calculates induced voltage from changing magnetic flux. Learn electromagnetic induction with examples.

Friction Formula

The friction formula calculates static and kinetic friction forces between surfaces. Essential for mechanics and engineering problems.

Gay-Lussac's Law

Gay-Lussac's Law relates gas pressure and temperature at constant volume. Learn the formula P₁/T₁ = P₂/T₂ with worked examples.

Heisenberg Uncertainty Principle

The Heisenberg uncertainty principle sets fundamental limits on measuring position and momentum simultaneously. Learn with examples.

Hooke's Law (Spring Constant)

Hooke's law F=kx describes a spring's restoring force. Calculate spring constant, force, or displacement. Covers elastic limits and spring energy storage.

Hooke's Law Formula

Hooke's Law calculates the force in a spring using F = -kx. Learn how spring constant and displacement determine restoring force with examples.

Ideal Gas Equation (PV = nRT)

The ideal gas equation PV = nRT relates pressure, volume, moles, and temperature. Covers STP conditions, combined gas law, and worked chemistry examples.

Impulse Formula

Reference for the impulse formula J = F*Δt, which calculates the change in momentum. Covers impulse-momentum theorem, collision analysis, and force-time graphs.

Impulse-Momentum Theorem

Reference for impulse-momentum theorem J = Ft = Δp = mΔv. Covers elastic and inelastic collisions, conservation of momentum, and crash and rocket examples.

Lensmaker's Equation

The lensmaker's equation calculates focal length from lens curvature and refractive index. Essential for optics and lens design.

Lorentz Force Formula

The Lorentz force formula F = qE + qv × B calculates the force on a charged particle in electric and magnetic fields. With worked examples.

Mass-Energy Equivalence (E = mc²)

Einstein's E = mc² shows that mass and energy are interchangeable. Learn the most famous physics formula with worked examples.

Newton's Laws of Motion

Newton's three laws of motion with formulas and real-world examples: inertia, F=ma, and action-reaction. The foundation of classical mechanics and dynamics.

Ohm's Law Formula

Ohm's Law relates voltage, current, and resistance: V = IR. Includes power variations and practical examples for circuit analysis.

Pascal's Law

Pascal's law states that pressure applied to a confined fluid is transmitted equally in all directions. Learn with examples.

Pendulum Period Formula

Calculate the period of a simple pendulum with T = 2pi sqrt(L/g). Learn how length and gravity affect swing time with examples.

Photoelectric Effect Formula

The photoelectric effect formula E = hf - φ calculates the kinetic energy of electrons emitted when light strikes a metal surface.

Planck's Radiation Law

Planck's radiation law describes the spectral distribution of electromagnetic radiation from a black body. Learn with examples.

Snell's Law Formula

Snell's Law calculates refraction of light between media: n1 sin(a1) = n2 sin(a2). Includes total internal reflection and examples.

Sound Intensity Level (Decibels)

Reference for decibel formula L = 10 log₁₀(I/I₀) where I₀ = 10⁻¹² W/m². Covers dB addition, inverse square law, and a reference table from 0 dB to 194 dB.

Sound Intensity Level Formula

Sound intensity level L = 10 × log₁₀(I/I₀) converts watts per m² to decibels. Covers 0 dB threshold, 130 dB pain threshold, and worked examples.

Specific Heat Formula

Calculate heat energy to change an object's temperature using Q=mcΔT. Covers specific heat values for water, metals, and common materials with examples.

Stefan-Boltzmann Law

The Stefan-Boltzmann law calculates total radiant energy emitted by a black body using P = σAT⁴. Learn with worked examples.

Stefan-Boltzmann Law

The Stefan-Boltzmann law P = σAT⁴ calculates the total power radiated by a blackbody. Learn thermal radiation with worked examples.

Thin Lens Equation

The thin lens equation 1/f = 1/do + 1/di relates focal length, object distance, and image distance. Learn optics with worked examples.

Time Dilation Formula

Einstein's time dilation formula calculates how time slows at high speeds. Learn the Lorentz factor formula with worked examples.

Torque Formula

Reference for the torque formula τ = r × F × sin(θ) in N·m. Covers right-hand rule, rotational equilibrium, and moment of inertia.

Torricelli's Theorem

Torricelli's theorem v = sqrt(2gh) calculates the speed of fluid flowing from an opening in a container. Learn with examples.

Universal Gas Constant (R)

The universal gas constant R = 8.314 J/(mol·K) connects pressure, volume, temperature, and moles in ideal gas calculations.

Wave Equation Formula

The wave equation v = fλ relates wave speed, frequency, and wavelength. Learn how to calculate wave properties with worked examples.

Wave Interference Formula

The wave interference formula calculates constructive and destructive interference patterns. Learn path difference with examples.

Wave Speed Formula

Reference for v = f × λ wave speed formula. Covers sound, light, and water waves with worked examples, Hz to kHz conversions, and speed in different media.

Work-Energy Theorem

Reference for the work-energy theorem: net work equals change in kinetic energy. Covers derivation from Newton's second law with force and motion examples.

Coulomb's Law

Calculate the electrostatic force between two charged particles using Coulomb's law F = kq1*q2/r^2. Solve for force, charge, or separation with worked examples.

Electric Field Formula

Reference for the electric field formula E = kQ over r squared. Calculate field strength from a point charge, direction conventions, and worked examples.

Magnetic Force on a Moving Charge

Calculate the force on a charged particle moving through a magnetic field. The basis of electric motors and particle accelerators.

Newton's Law of Universal Gravitation

Reference for Newton gravitational force F = G*m1*m2/r^2. Calculates attraction between any two masses and explains planetary orbits and tidal forces.

Density Formula

The density formula ρ = m/V calculates how much mass is packed into a given volume. Learn to solve density problems with clear examples.

Hooke's Law

Hooke's law F = -kx describes the restoring force of a spring. Learn to calculate spring force with the spring constant and displacement.

Kinematic Equations

The four kinematic equations describe motion with constant acceleration. Master velocity, displacement, and time calculations with step-by-step examples.

Kinetic Energy Formula

The kinetic energy formula KE = ½mv² calculates the energy of a moving object. Learn how mass and velocity affect kinetic energy with examples.

Momentum Formula

The momentum formula p = mv calculates an object's momentum from its mass and velocity. Essential for collision and impulse problems.

Newton's Second Law

Newton's second law F=ma: force equals mass times acceleration. Calculate force, mass, or acceleration with worked examples in SI and imperial units.

Potential Energy Formula

The gravitational potential energy formula PE = mgh calculates stored energy based on height. Essential for energy conservation problems.

Power Formula

The power formula P = W/t calculates the rate at which work is done or energy is transferred. Learn to calculate power in watts with examples.

Pressure Formula

The pressure formula P = F/A calculates the force per unit area. Understand pressure in pascals with practical worked examples.

Wave Speed Formula

The wave speed formula v = fλ relates the speed of a wave to its frequency and wavelength. Essential for sound, light, and wave physics.

Weight Formula

The weight formula W = mg calculates the gravitational force on an object. Learn how weight differs from mass with clear examples.

Work Formula

The work formula W = Fd·cos(θ) calculates the work done by a force over a distance. Includes angle consideration and step-by-step examples.