Science & Education
θ_c = arcsin(n₂/n₁) with the Brewster angle — glass 41.81°, diamond 24.44°, the physics of fibers and sparkle.
critical-angle-total-reflectionScience & Education
r_s, r_p, R_s, R_p, T = 1−R, and the Brewster angle for any dielectric interface, with the 4% normal-incidence anchor.
fresnel-equationsScience & Education
dτ = dt·√(1 − 2GM/(rc²)) for Earth, Sun, or custom mass: Schwarzschild radius, dilation factor, and daily/yearly clock lag outside the horizon.
gravitational-time-dilationScience & Education
E₀ = mc² for electron, proton, neutron, or custom mass: energy in J and eV-scale units, mass in kg and u — the collider mass table.
rest-mass-energyScience & Education
1/λ = R·Z²(1/n₁² − 1/n₂²) for hydrogen-like ions with reduced-mass correction: wavelength, photon energy, frequency, band, Pickering and Balmer notes.
rydberg-formula-calculatorScience & Education
a·sinθ = mλ minima with the double-wide central maximum and optional screen positions.
single-slit-diffractionScience & Education
n₁·sinθ₁ = n₂·sinθ₂ for either angle, with the total-internal-reflection regime and critical angle when sinθ exceeds 1.
snell-law-calculatorScience & Education
|S| = √(s(s+1))ℏ for integer or half-integer s: multiplicity 2s+1, the mₛ ladder, S_z and polar angle for a chosen projection, and why |S| > s always holds.
spin-angular-momentumScience & Education
Hydrogen level n: r_n = n²a₀, E_n = −13.605693/n² eV, v_n = αc/n, orbital period, plus optional transition energies with named series lines.
bohr-model-calculatorScience & Education
Rydberg lines for Lyman/Balmer/Paschen/Brackett/Pfund: vacuum wavelengths, photon energies, named lines with Balmer colors, series limit.
hydrogen-spectrum-seriesDate & Time
Parse ISO 8601 durations, validate ISO 8601-2 extensions, run calendar-true arithmetic, sort by real length at an anchor, and diff datetimes.
iso-8601-duration-parser-arithmetic-workbenchMedia
Analyze an audio file, rank the most seamless loop points by cross-correlation, and export the best trimmed loop with a wrap-around crossfade.
audio-loop-seam-finder