Health

Compute Verhulst logistic growth toward carrying capacity K, with instantaneous dN/dt and capacity percentage.

Education

Two-point linkage LOD scores from recombinant/non-recombinant meioses: θ̂ = r/N, Zmax, LOD at fixed θ, LOD curve table, Morton thresholds (Z≥3 linkage, Z≤−2 excluded). Derived from Morton 1955, Ott 1999, Griffiths, StatPearls. Educational use only.

Text Processing

Audit manuscript for number/date/unit/quote/dash/heading/noun consistency and emit a style sheet; optional AI drift detection

Health

Calculate the loading dose required to rapidly reach a target plasma concentration: LD = Css · Vd / F, where Css is the target concentration, Vd is the volume of distribution, and F is bioavailability (1 for IV, <1 for oral). A loading dose achieves Css essentially immediately (one-compartment IV bolus) instead of waiting 4–5 half-lives for accumulation. For oral loading, divide by F. Maintenance dosing (MD = Css·CL·τ/F) must follow to sustain the concentration. Loading doses are hazardous for narrow-therapeutic-index drugs (digoxin, theophylline, antiarrhythmics) — clinical judgement required. Optional body-weight input converts the result to mg/kg. Not medical advice.

Development

Run a safe, curated set of Lodash helpers on JSON input.

Health

Calculate the maintenance dose that holds the average steady-state concentration at a target value: MD = Css,avg · CL · τ / F, where Css,avg is the target average concentration, CL is clearance, τ is the dosing interval, and F is bioavailability (1 for IV, <1 for oral). Derived from steady-state mass balance (rate in = rate out): the dose per interval equals the amount cleared over one interval, corrected for bioavailability. Targets the AVERAGE Css,avg — the peak Cmax,ss and trough Cmin,ss fluctuate around it depending on t½ and τ. Valid only for linear pharmacokinetics with fixed dose and interval — NOT for Michaelis-Menten drugs (phenytoin). Optional body-weight input converts the result to mg/kg. Not medical advice.

Math & Numbers

Convert luminance between cd/m² (nit, SI base), stilb (1 = 10000 cd/m²), cd/ft² (1 = 10.76391 cd/m²), foot-lambert (1 = 3.426263 cd/m²), apostilb (1 = 0.31831 cd/m²), lambert (1 = 3183.099 cd/m²), and millilambert (1 = 3.183099 cd/m²). All non-SI units except stilb carry a 1/π factor from Lambertian diffuse-emission assumptions. Reference values: LCD display ≈ 200–300, comfortable eye level ≈ 1000, sun surface ≈ 1.6×10⁹ cd/m².

Math & Numbers

Convert luminous intensity between candela (cd, SI base, = 1/683 W/sr at 540 THz), millicandela (1 = 0.001 cd), and candlepower (1 = 0.981 cd, obsolete standard candle). Converts via candela to the target unit and lists the equivalent value in all three units for reference. Reference values: indicator LED ≈ 5–20 mcd, flashlight ≈ 100–1000 cd, car headlight high beam ≈ 75000 cd.

Health

Convert a daily calorie target into grams of carbohydrate, protein and fat. Pick a preset split — balanced (50/30/20), low-carb (35/40/25), keto (10/20/70) or high-protein (40/35/25) — or define your own percentages.

Games

The classic Magic 8 Ball. Ask any yes-or-no question, shake, and get one of 20 traditional answers (yes / no / uncertain). Classic English phrases or localized translations.

Validation

Validate or generate numbers using the Luhn algorithm (mod-10). Works for credit cards, IMEI, IMEISV, SIN, NPI and any custom Luhn-based identifier.

Development

Statically check Markdown links for format errors, broken anchors, and undefined references (no network requests)