Math & Numbers
Newton-Raphson iteration for f(x) = 0 with analytic or numeric derivative, full iteration table, and explicit convergence/divergence reporting.
newton-raphson-root-finderMath & Numbers
Decompose N(x)/D(x) into A/(x−r)^j + (Bx + C)/((x−α)² + β²) with long division for improper fractions and numeric residual verification.
partial-fraction-decomposerMath & Numbers
Rescale any recipe's ingredient list to a new serving count, converting cups/tbsp/tsp ⇄ grams/ml with per-ingredient densities and kitchen-friendly fraction output.
recipe-ingredient-scalerMath & Numbers
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).
permeability-converterMath & Numbers
Convert radioactivity (radionuclide activity) between becquerel (Bq, SI base = 1 decay/s), kilo/mega/gigabecquerel, curie (Ci = 3.7×10^10 Bq, exact 1950 ICRU definition, originally the activity of 1 g of radium-226), milli/microcurie, and disintegrations per minute (dpm = 1/60 Bq, exact). Converts via becquerel to the target unit and lists the equivalent value in all eight units. Reference: banana (K-40) ≈ 15 Bq, smoke detector (Am-241) ≈ 37 kBq = 1 µCi.
radioactivity-converterMath & Numbers
Convert radiation absorbed dose between Gy (gray = J/kg, SI base), kGy (1 = 1000 Gy), cGy (1 = 0.01 Gy), mGy (1 = 0.001 Gy), and rad (1 = 0.01 Gy). Converts via Gy to the target unit and lists the equivalent value in all five units. ⚠️ Absorbed dose is NOT equivalent dose: converting Gy → Sv requires multiplying by the radiation weighting factor w_R (X/γ/β = 1, neutrons 5–20, alpha 20) — use the dose-equivalent converter for that side. Reference values: chest X-ray ≈ 1e-4, CT scan ≈ 1e-2, radiotherapy fraction ≈ 2, whole-body LD50/60 ≈ 4–6 Gy.
radiation-absorbed-dose-converterMath & Numbers
Convert radiation equivalent dose between Sv (sievert, SI base), mSv (1 = 0.001 Sv), µSv (1 = 1e-6 Sv), rem (1 = 0.01 Sv), and mrem (1 = 1e-5 Sv). Converts via Sv to the target unit and lists the equivalent value in all five units. ⚠️ Equivalent dose is NOT absorbed dose: equivalent dose = absorbed dose (Gy) × radiation weighting factor w_R (X/γ/β = 1, neutrons 5–20, alpha 20). Converting Sv → Gy requires dividing by w_R — use the absorbed-dose converter for that side. Reference values: natural background ≈ 3 mSv/yr, chest CT ≈ 7 mSv, annual occupational limit ≈ 50 mSv/yr, ARS threshold ≈ 1 Sv.
radiation-dose-equivalent-converterMath & Numbers
Saturated pressure ↔ temperature lookup for common HVAC refrigerants via the Antoine fit ln(P) = A − B/(T_C + C): R-22 (HCFC-22), R-134a (HFC-134a), and R-410A (R-32/R-125 near-azeotropic blend). Coefficients fitted against the ASHRAE Handbook / NIST REFPROP saturation tables. Two modes: solve saturation pressure from temperature, or solve saturation temperature from pressure. Pressure may be absolute or gauge (atmospheric default 1.01325 bar) in bar/MPa/kPa/PSI; temperature in °C/K/°F. Engineering estimate only — does not replace the manufacturer's P-T chart.
refrigerant-pressure-temperatureMath & Numbers
Compute the operating time of an inverse-time overcurrent relay per IEC 60255-151: t = TMS·(k/((I/I_s)^α − 1)). Supports Standard Inverse (SI), Very Inverse (VI), Extremely Inverse (EI) and Long-Time Inverse (LTI) curves, and samples a T-I characteristic.
relay-setting-calculatorMath & Numbers
Calculate the total cross-sectional area of reinforcing steel: A = n·π·D²/4. Choose a standard metric diameter (6–40 mm) or a custom diameter and the number of bars. Also returns the single-bar area, perimeter, theoretical unit weight (ρ=7850 kg/m³), and total weight.
rebar-area-calculatorMath & Numbers
Calculate rebar spacing and bar count over a width b perpendicular to the bars. From spacing: n = floor(b/s)+1, bars per meter = 1000/s. From count: spacing s = b/(n−1). All lengths in mm.
rebar-spacing-calculatorMath & Numbers
Convert between pH, [H+], pOH and [OH-], or compute pH from a strong acid/base concentration, including dilution.
ph-calculator