Education

Compute allele and expected genotype frequencies under Hardy-Weinberg equilibrium. Two modes: allele frequency or genotype counts with chi-square test. Derived from Hardy 1908, Weinberg 1908, Wigginton 2005, StatPearls. Educational use only.

Health

Convert hemoglobin between g/dL, g/L, and mmol/L. Factor 0.6206 (g/dL→mmol/L, IFCC/IUPAC monomer, 16.1145 g/mmol); × 10 for g/L. Derived from WHO 2011, IFCC/IUPAC, Young 1987, StatPearls. Not medical advice.

Health

Calculate the HAS-BLED score to estimate major bleeding risk in patients on oral anticoagulation (most commonly combined with CHA₂DS₂-VASc in atrial fibrillation). Each component scores 1 point: Hypertension (uncontrolled, systolic BP >160), Abnormal renal function (dialysis/transplant/Cr >2.26 mg/dL), Abnormal liver function, prior Stroke, prior major Bleeding/predisposition, Labile INR (TTR <60% on warfarin), Elderly (age >65), Drugs (antiplatelet/NSAID), Alcohol (≥8 drinks/week). Range 0–9 (renal/liver and drugs/alcohol can each contribute up to 2). Interpretation: 0 low, 1–2 moderate, ≥3 high risk — regular review and correct reversible factors; a high score alone does NOT justify withholding anticoagulation. Derived from Pisters 2010 (Chest) and the 2023 ACC/AHA/ACCP/HRS AF guideline. The 'labile INR' criterion mainly applies to warfarin users; predictive value is lower for DOACs. Not medical advice.

Math & Numbers

Convert convective heat transfer coefficient (film coefficient h) between W/(m²·K) (watt per square metre-kelvin, SI base, = W/(m²·°C)) and kcal/(m²·h·°C) (1 = 1.1627778 W/(m²·K)). Converts via W/(m²·K) and lists both equivalents. h depends on flow regime and surface, not material. Typical ranges: natural-convection air ≈ 5–25, forced air ≈ 25–250, still water ≈ 100–1000, boiling/condensing water ≈ 2500–50000+ W/(m²·K).

Math & Numbers

Compute the effectiveness (ε) of a heat exchanger by the ε-NTU method. C*=C_min/C_max (0..1), NTU=U·A/C_min, q_max=C_min·(T_h,in-T_c,in), and ε=q_actual/q_max. Supports four arrangements: Parallel flow ε=[1-exp(-NTU(1+C*))]/(1+C*); Counter flow ε=[1-exp(-NTU(1-C*))]/[1-C*·exp(-NTU(1-C*))], or NTU/(1+NTU) when C*=1; Shell-and-tube 1-2 ε=2/[1+C*+√(1+C*²)·(1+exp(-NTU√(1+C*²)))/(1-exp(-NTU√(1+C*²)))]; Crossflow (both unmixed) ε=1-exp{(NTU^0.22/C*)·[exp(-C*·NTU^0.78)-1]}. When C*=0 (phase change on one side, boiler/condenser) every arrangement gives ε=1-exp(-NTU). Optionally supply T_h,in and T_c,in to recover the actual heat-transfer rate q=ε·q_max and both outlet temperatures. Temperatures are used only as differences: Δ°C=ΔK and Δ°F×5/9=ΔK.

Math & Numbers

Estimate the heating (heat-loss) load of a room by the simplified steady-state method. Envelope transmission loss Q_trans = Σ(A_i·U_i·ΔT) over surfaces entered one per line as 'area,U' (U in W/(m²·K)). Cold-air infiltration loss Q_inf = 0.018·ACH·V·ΔT (W), where 0.018 W·h/(m³·K) ≈ ρ·c_p/3600. Total load = Q_trans + Q_inf, optionally multiplied by a safety factor (default 1.0). ΔT = indoor - outdoor (heating, >0). Temperature in °C/K/°F (only differences matter), area in m²/ft².

Math & Numbers

Compute 1-D steady-state heat conduction through a flat slab (Fourier's law): heat flux q = k·ΔT/d (W/m²), heat flow rate Q = k·A·ΔT/d (W), and thermal resistance R = d/(k·A) (K/W). k is the thermal conductivity (W/(m·K)); ΔT is the temperature difference (K; a °C difference equals a K difference, a °F difference is converted by ×5/9); d the slab thickness; A the cross-section area. ΔT may be negative (indicating reverse heat flow), but k, d and A must be positive. Thickness in m/cm/mm, area in m²/cm².

Math & Numbers

Compute convective heat transfer (Newton's law of cooling): heat flux q = h·ΔT (W/m²), heat flow rate Q = h·A·ΔT (W), and convective thermal resistance R_conv = 1/(h·A) (K/W). h is the convective heat-transfer coefficient (W/(m²·K)); ΔT is the temperature difference between the surface and the fluid (K; a °C difference equals a K difference, a °F difference is converted by ×5/9); A the heat-transfer area. ΔT may be negative (indicating reverse heat flow), but h and A must be positive. Area in m²/cm².

Math & Numbers

Compute the Log Mean Temperature Difference (LMTD) of a heat exchanger for parallel or counter flow. Parallel flow: ΔT₁ = T_h,in - T_c,in and ΔT₂ = T_h,out - T_c,out; counter flow: ΔT₁ = T_h,in - T_c,out and ΔT₂ = T_h,out - T_c,in. LMTD = (ΔT₁ - ΔT₂)/ln(ΔT₁/ΔT₂), or ΔT₁ when ΔT₁ = ΔT₂. A non-positive terminal difference (temperature cross) is physically impossible and is rejected. Optionally, with the overall heat transfer coefficient U (W/(m²·K)) and the heat transfer area A (m²), the heat transfer rate Q = U·A·LMTD (W) is returned. Temperatures are used only as differences: Δ°C = ΔK and Δ°F ×5/9 = ΔK; the LMTD is reported in K.

Math & Numbers

Compute thermal radiation from a blackbody/grey body (Stefan-Boltzmann law): blackbody emissive power E_b = σ·T⁴ (W/m²), total radiated power Q_rad = ε·σ·A·T⁴ (W); with an optional surrounding temperature T₀ it also computes the net radiative exchange Q_net = ε·σ·A·(T⁴-T₀⁴) (W). σ = 5.670374419e-8 W/(m²·K⁴); ε is the emissivity (0 < ε ≤ 1, blackbody ε=1); T is the ABSOLUTE temperature (K) — °C and °F are first converted to K (this is an absolute temperature, not a difference); A is the radiating area. Area in m²/cm².

Media

Decode PQ or HLG AVIF, convert BT.2020 to sRGB, and tone map highlights into a viewable SDR PNG.

Media

Decode HEIC photos to compatible JPEG with quality, chroma subsampling, and background controls.