Physics
Kinematics, circuits, optics, radioactive decay, spectroscopy, and simulators for wave interference, the double pendulum, and the kinetic theory of gases.
Physics problems usually reduce to one clean relationship applied without slips: the SUVAT equations for motion, momentum conservation in a collision, Hooke’s law for a spring, the thin-lens equation for optics, Ohm’s law for a circuit, exponential decay for a radioactive sample. Mechanics runs deepest here, through projectile flight, work and energy, and buoyancy in a fluid. Each instrument keeps its governing relationship one click away and states the assumptions behind it, so you spend your attention on the setup rather than the algebra.
The optical instruments run from the relation that links a wavelength to its frequency, through lens and mirror imaging, to wave interference and the absorbance of a sample. The double-slit page computes exact fringe positions and the full intensity profile for one slit, two slits, N slits, or a diffraction grating, with the single-slit envelope drawn separately from the interference term. Two further simulators run a system forward in time: the double pendulum integrates a chaotic system four ways and reports the energy error each integrator commits, and the kinetic theory page builds a speed histogram from event-driven hard-disk collisions and shows it converging onto the Maxwell-Boltzmann curve.
Mechanics and Motion
Solve constant-acceleration motion, spring and buoyant forces, projectiles, and the energy and momentum that carry through a system.
Kinematics Calculator
Solve one-dimensional constant-acceleration motion from displacement, velocity, acceleration, and time with the equation used shown.
Projectile Motion Calculator: Range, Height, and Trajectory Plot
Range, maximum height, and time of flight for 2D projectile motion, plotted.
Buoyancy Calculator: Buoyant Force, Float or Sink, and Fraction Submerged
Solve buoyant force from Archimedes' principle F = ρ·V·g, get a float or sink verdict from densities, and find the fraction submerged, with a sourced fluid density table.
Hooke's Law Calculator: Spring Constant and Elastic Energy
Solve Hooke's law F = -kx for force, spring constant, or displacement, plus elastic energy U = (1/2)kx^2. SI and imperial units, signed restoring force, and the sign convention named.
Momentum Calculator
Calculate momentum p = mv, impulse J = FΔt, and the final velocities of a 1D collision from a coefficient of restitution. Signed convention and kinetic energy lost shown.
Work Calculator (Physics): Work, Energy, and Power
Work, energy, and power in one calculator: work (W = F d cos θ), power, kinetic energy, gravitational PE, and the work-energy theorem, each with its formula and convention shown.
Double Pendulum Simulator: Equations of Motion, Energy, and Chaos
Four integrators on one double pendulum, each with its own energy error.
Waves, Light, and Optics
Relate a wave to its frequency, image a source through a lens or mirror, and read how interference and absorption shape the light that comes out.
Frequency to Wavelength Calculator: Exact Speed of Light
Frequency to wavelength with the exact speed of light, plus photon energy.
Lens and Mirror Equation Calculator
Solve thin-lens and spherical-mirror image distances with the real-is-positive Gaussian sign convention stated.
Double Slit Experiment and Wave Interference Simulator
Exact fringe positions and an intensity profile with its diffraction envelope shown separately.
Beer-Lambert Law Calculator
Solve decadic absorbance, molar absorptivity, path length, concentration, and transmittance for a one-species optical sample.
Circuits, Heat, and Radioactive Decay
Solve a resistive circuit, follow a first-order decay through its half-lives, and watch a gas build its own speed distribution from collisions.
Ohm's Law Calculator
Solve voltage, current, resistance, and power for resistive circuit magnitudes, with formulas and consistency checks.
Half-Life Decay Calculator
Solve first-order exponential decay from initial amount, remaining amount, half-life, or elapsed time with a step schedule.
Kinetic Theory of Gases Simulator: Maxwell-Boltzmann Distribution
A two-dimensional hard-disk gas that derives its speed distribution from collisions.