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Math & Numbers

Perfect Number Checker

σ(n) = 2n ⟺ perfect. Factorization-based σ(n), proper-divisor sum, deficient/perfect/abundant classification, abundancy index, Euclid–Euler form. n ≤ 10¹².

Math & Numbers

PERT Network Analyzer (Expected Duration & Variance)

Three-point PERT estimates: te and σ² per activity, critical path, expected project duration and variance, and normal completion probability for a target time.

Math & Numbers

pH↔Hydrogen Ion Concentration Converter ([H⁺] = 10^(−pH))

Convert pH ↔ [H⁺] in mol/L, mmol/L, µmol/L or nmol/L with the full unit table — pH 7.40 ↔ 39.8 nmol/L.

Math & Numbers

Magnetic Permeability Converter (H/m ↔ relative μ_r)

Convert magnetic permeability (μ) between absolute permeability in henry per metre (H/m, SI unit; equivalently N/A² or T·m/A) and relative permeability μ_r (dimensionless). Vacuum permeability μ₀ = 4π×10⁻⁷ H/m ≈ 1.25663706×10⁻⁶ H/m (defined pre-2019; since the 2019 SI redefinition it is a measured quantity with relative uncertainty 1.6×10⁻¹⁰, so the 4π×10⁻⁷ form is still exact for all engineering purposes). Relations used: μ = μ_r × μ₀ and μ_r = μ / μ₀ (magnetic susceptibility χ_m = μ_r − 1). Reference: vacuum μ_r = 1, copper 0.999994 (diamagnetic), aluminum 1.000022 (paramagnetic), iron ≈ 5000 (ferromagnetic).

Math & Numbers

Poisson's Ratio Calculator

Calculate Poisson's ratio ν = −ε_transverse / ε_longitudinal and solve any of the three unknowns: ratio, lateral strain, or longitudinal strain. Tensile ε_long > 0 produces lateral contraction ε_lat < 0. Typical values: steel ≈ 0.30, aluminum ≈ 0.33, rubber ≈ 0.49, cork ≈ 0. Theoretical isotropic range 0 ≤ ν ≤ 0.5.

Math & Numbers

Pipe Friction Factor Calculator (Colebrook-White / Haaland)

Compute the Darcy friction factor: laminar closed-form f=64/Re for Re<2000, or iterative Colebrook-White solution for transitional/turbulent flow, with the explicit Haaland approximation always returned as a cross-check. Reports relative roughness ε/D, absolute roughness (m), diameter (m), flow regime (laminar/transitional/turbulent), effective method and iteration count. Roughness ε in m/mm/µm, diameter D in m/cm/mm.

Math & Numbers

Pipe Pressure Drop Calculator (Darcy-Weisbach)

Compute the Darcy-Weisbach major (friction) pressure drop in a straight pipe: ΔP = f·(L/D)·(ρ·v²/2) Pa and head loss h_f = f·(L/D)·v²/(2g) m. The user supplies the Darcy friction factor f (not the Fanning factor). Length in m/km/ft, diameter in m/cm/mm/inch, density in kg/m³/g/cm³/lb/ft³ — all normalised to SI internally. Returns ΔP in Pa, kPa and bar, and head loss in m and ft. Gravity defaults to 9.81 m/s² and may be overridden.