Science & Education

Run the three workhorse normality tests (Shapiro-Wilk AS R94, Anderson-Darling, Lilliefors) with a Q-Q plot and a Monte-Carlo power comparison.

Science & Education

Ksp ↔ molar solubility in either direction for 1:1, 1:2, 1:3 and 2:3 salts, with optional g/L output.

Science & Education

Solve control-system signal flow graphs with Mason's gain formula: forward paths, loops, non-touching combinations, Δ/Δk determinants and the exact transfer function.

Science & Education

a·sinθ = mλ minima with the double-wide central maximum and optional screen positions.

Science & Education

n₁·sinθ₁ = n₂·sinθ₂ for either angle, with the total-internal-reflection regime and critical angle when sinθ exceeds 1.

Science & 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.

Science & Education

a = μ_z·G/m, deflection z = a·[(L/v)²/2 + L·D/v²], and 2z screen separation for spin-1/2 atoms in a field gradient.

Math & Numbers

Carrier-free specific activity from the half-life: A = ln2·N_A/T½ in Bq/mol and Ci/mmol, with optional Bq/g and Ci/g from molar mass.

Design

One master image in, a full multi-platform asset kit out — every crop previewed with verified safe-zone overlays and shipped as a ZIP.

Health

Richness S with Margalef/Menhinick indices, Shannon H′, Pielou evenness J, and Berger–Parker dominance from a named or plain species list.

Health

Compute Gini–Simpson D, dominance λ, reciprocal 1/λ, and Simpson evenness from species counts.

Education

Specific activity = U ÷ mg protein (or U/mL ÷ mg/mL): the purity metric of every purification table, with nkat/mg conversion and the kcat/MW purity ceiling. Educational use only.