266 interactive formulas · 9 domains

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Every one of the 266 formulas comes alive as an accurate, hands-on simulation — with derivations, worked examples, and the stories of the people who discovered them.

266
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9
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450+
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Hand-built, physically exact — fire electrons one at a time at a double slit, build atoms from quarks, bend starlight around a black hole, set off a chain reaction. Every pixel computed from the real equation.

Relativity◆ Premium sim
θ=4GMc2b\theta = \frac{4GM}{c^{2}b}

General Relativity: Light Bending & Curved Spacetime

Mass curves spacetime, and light follows the straightest possible path through that curved geometry — so starlight grazing the Sun bends by 1.75 arcseconds, exactly twice what Newton's gravity-on-light would give. The same curvature, turned up, gives gravitational lensing, Einstein rings, ripples in spacetime itself (gravitational waves), and at the extreme, black holes from which no path leads out.

Quantum◆ Premium sim
λ=hp\lambda = \frac{h}{p}

de Broglie Wavelength

Momentum and wavelength are inversely related through Planck's constant — big things have unmeasurably tiny wavelengths.

Nuclear & Particle◆ Premium sim
p=uud,n=udd,ZAX:  A=Z+Np = uud, \quad n = udd, \quad {}^{A}_{Z}X: \; A = Z + N

Building Atoms from the Standard Model

Everything you've ever touched is three particles: up quarks, down quarks, and electrons. Two ups and a down make a proton (+1); one up and two downs make a neutron (0). The proton count Z picks the element, the neutron count N picks the isotope, and the electron count sets the charge. Stray too far from the stable Z–N balance and the weak force flips a quark — beta decay — to restore it.

Quantum◆ Premium sim
Lint=eψˉγμψAμ\mathcal{L}_{\text{int}} = -e\,\bar{\psi}\gamma^{\mu}\psi A_{\mu}

Standard Model Interactions

Every particle reaction in nature is built from a handful of vertices — an electron emitting a photon, a quark emitting a W boson, a gluon splitting. Glue these elementary moves together and you get beta decay, annihilation, Compton scattering, pair production. The bookkeeping rules are absolute: electric charge, lepton number, and baryon number in must equal out. If a reaction conserves them all, somewhere in the universe it happens.

Mechanics◆ Premium sim
T2=4π2GMa3T^2 = \frac{4\pi^2}{GM} a^3

Kepler's Third Law

Farther orbits take longer — and not linearly: the period grows as the 3/2 power of the orbital radius.

Nuclear & Particle◆ Premium sim
Nn=N0kn,k=νpN_{n} = N_{0}\,k^{n}, \qquad k = \nu \, p

Nuclear Chain Reaction

One neutron splits a uranium-235 nucleus, releasing ~200 MeV and ν ≈ 2.4 fresh neutrons. If, on average, more than one of those goes on to cause another fission (k > 1), the population explodes geometrically — 2, 4, 8, … 2⁸⁰ in microseconds. A reactor is the art of pinning k at exactly 1.000; a bomb is k ≈ 2 with nothing in the way.

Electromagnetism◆ Premium sim
F=q(E+v×B)\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})

Lorentz Force Law

Electric fields push charges; magnetic fields deflect moving charges sideways.

Mechanics◆ Premium sim
Ftidal2GMmRd3F_{\text{tidal}} \approx \frac{2GMmR}{d^{3}}

Tidal Force

Gravity weakens with distance, so the Moon pulls Earth's near side harder than its center, and the center harder than the far side. In Earth's frame that difference stretches the planet along the Moon line and squeezes it sideways — two ocean bulges, two high tides a day. Because the effect goes as 1/d³ (not 1/d²), the nearby Moon out-tides the enormous Sun.

Thermodynamics◆ Premium sim
S=kBlnWS = k_B \ln W

Boltzmann Entropy

Entropy counts the number of microscopic ways a macroscopic state can be realized — more ways means higher entropy.

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θ=4GMc2b\theta = \frac{4GM}{c^{2}b}
General Relativity: Light Bending & Curved Spacetime
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