Finance

Side-by-side monthly rent-vs-buy simulation: mortgage amortization, property tax, insurance, HOA and maintenance against rent plus renter insurance; the renter invests the down payment and monthly savings at an opportunity-cost rate. Outputs break-even year on net sale proceeds, per-year differential NPV, SALT-cap-aware after-tax cash flows, a differential IRR, and a ±20% tornado sensitivity chart.

Date & Time

Parse ISO 8601 durations, validate ISO 8601-2 extensions, run calendar-true arithmetic, sort by real length at an anchor, and diff datetimes.

Math & Numbers

Smallest primitive root mod n with certificate g^(φ/q) ≠ 1, root count φ(φ(n)), up to 50 listed roots, and candidate verification. n ≤ 10¹².

Math & Numbers

Exact π(n) via a single-pass Sieve of Eratosthenes (n ≤ 10⁷) with n/ln n comparison, density, average gap, and the largest prime ≤ n.

Math & Numbers

Two-person zero-sum games: saddle-point test first, then mixed strategies from a single-phase simplex LP with dual shadow prices, verified by security-level checks.

Math & Numbers

Dijkstra with a full per-iteration trace: settled nodes, relaxations, distance table, and the final path; undirected or directed, negative weights rejected, unreachable targets reported.

Math & Numbers

Compute remaining radionuclide activity A(t) = A₀·2^(−t/T½) with λ = ln2/T½ in Bq/Ci/dpm units, for Tc-99m, F-18 and other isotopes.

Math & Numbers

Convert illuminance between lux (lx = lm/m², SI base), kilolux (1 = 1000 lx), footcandle (1 = 10.7639104 lx), phot (1 = 10000 lx), and nox (1 = 0.001 lx). Converts via lux to the target unit and lists the equivalent value in all five units for reference. Reference values: full moon ≈ 0.25, office lighting ≈ 300–500, overcast day ≈ 1000, direct sunlight ≈ 100000 lux.

Math & Numbers

Convert thermal resistance between K/W (kelvin per watt, SI base), °C/W (1 = 1 K/W, since Δ1 K = Δ1 °C exactly), and °F·h/BTU International Table (1 = 1.8956342 K/W). Converts via K/W to the target unit and lists the equivalent value in all three units for reference. Reference values: CPU heatsink ≈ 0.1–0.3, LED thermal path ≈ 5–20, natural convection ≈ 1 K/W.

Math & Numbers

Convert thermal conductivity between W/(m·K) (watt per metre-kelvin, SI base, = W/(m·°C)), kcal/(m·h·°C) (1 = 1.1627778 W/(m·K)), and BTU/(hr·ft·°F) (1 = 1.7307347 W/(m·K)). Converts via W/(m·K) to the target unit and also lists the equivalent value in all three units for reference. Reference values: copper ≈ 401, aluminum ≈ 237, steel ≈ 50, water ≈ 0.6, air ≈ 0.026, insulation foam ≈ 0.03 W/(m·K).

Math & Numbers

Convert between Brinell (HB), Vickers (HV), and Rockwell (HRC / HRB) hardness via ASTM E140 tabulated data with linear interpolation. Three material classes: carbon/alloy steel (HV 100–960), austenitic stainless (HV 100–600), and cartridge brass (HV 40–200). Any input scale produces all the others; a scale that does not apply in the current hardness band returns 'out of range'. Indicative only — not for acceptance testing per ASTM E140.

Math & Numbers

Linear and volumetric thermal expansion of an isotropic material. Linear: ΔL = α·L₀·ΔT, L₁ = L₀·(1+α·ΔT). Volumetric: ΔV = 3α·V₀·ΔT (β = 3α for isotropic solids). Built-in typical α for carbon/alloy steel, aluminum, copper, austenitic stainless, titanium and glass, plus custom. ΔT in K or °C, length in mm, volume in mm³.