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Hargreaves-Samani Reference Evapotranspiration and Crop ET in Excel
Estimate reference ET0 from daily temperatures and extraterrestrial radiation, apply a crop coefficient, and distinguish crop evapotranspiration from irrigation water to apply.
Read the guide →Healthcare & ClinicalHarmless Acute Pancreatitis Score (HAPS) Admission Triage Calculator
Evaluate Lankisch’s 30-minute Harmless Acute Pancreatitis Score (HAPS: no rebound/guarding, normal sex-specific hematocrit, creatinine <= 2.0 mg/dL) to predict a benign non-necrotizing ward course with 98% specificity.
Read the guide →Electrical Power Quality & Data-Center DistributionHarmonic THD, True Power Factor & K-Factor Formula
Calculate IEEE 519 Current Total Harmonic Distortion (THD_I), Total RMS Current, True Total Power Factor PF_disp / SQRT(1 + THD_I^2), and UL 1561 Transformer Eddy-Current K-Factor.
Read the guide →Statistical & Clinical AnalysisHarrell’s C-Index & Somers’ D_xy: Survival Model Concordance for Censored Data
Calculate Frank Harrell’s Cox survival discrimination index C = (N_concordant + 0.5*N_tied) / N_permissible and Somers’ rank correlation D_xy = 2*C - 1.
Read the guide →Clinical Medicine & PhysiologyHarris-Benedict BMR Formula: Classic 1918 vs Revised Roza-Shizgal (1984) Equations
Calculate Basal Metabolic Rate (kcal/day) and Total Energy Expenditure using both the original J. Arthur Harris & Francis G. Benedict (1918) equations and Allan M. Roza & Harry M. Shizgal’s (1984) recalibrated equations.
Read the guide →Development & Labor EconomicsHarris-Todaro Rural-Urban Migration & Unemployment Formula
Solve John Harris & Michael Todaro’s (1970) expected-wage migration equilibrium w_R = (L_M / L_U)*w_M, urban unemployment rate u* = 1 - w_R/w_M, and the Todaro job-creation paradox.
Read the guide →Macroeconomics & Development FinanceHarrod-Domar ICOR Growth & Financing Gap Formula
Calculate Harrod-Domar warranted GDP growth g_w = (s / ICOR) - delta, required gross investment share (g_target + delta) * ICOR, and Chenery-Strout external financing gap.
Read the guide →Game Theory & Strategic CoordinationHarsanyi-Selten Risk Dominance (Stag Hunt) Formula
Calculate the Critical Trust Threshold p* = (D - C)/((A - B) + (D - C)) and Harsanyi-Selten (1988) risk-dominance margin in symmetric 2x2 Stag Hunt coordination games.
Read the guide →Statistical & Clinical AnalysisHartung-Knapp-Sidik-Jonkman (HKSJ) Random-Effects Standard Error Formula
Eliminate anti-conservative DerSimonian-Laird false positives in small-k meta-analyses using the Röver-Knapp truncated HKSJ variance factor q = MAX(1, [1/(k-1)] * Σ w_i*(y_i - μ_RE)²) and SE_HKSJ = SQRT(q / Σw_i*).
Read the guide →Macroeconomics & Sustainable DevelopmentHartwick Rule & Genuine Saving (ANS) Formula
Calculate World Bank Adjusted Net Saving GNS - D_cap + E_edu - R_dep - D_pol and test John Hartwick’s (1977) wealth-sustainability reinvestment rule.
Read the guide →Healthcare & Clinical CalculationsHarvey-Bradshaw Index (HBI) for Crohn’s Disease Activity & Remission
Calculate R. F. Harvey and J. M. Bradshaw’s single-day clinical Crohn’s Disease activity score across Well-Being (0–4), Abdominal Pain (0–3), Daily Liquid Stools, Abdominal Mass (0–3), and Extraintestinal Complications (< 5 Remission).
Read the guide →StatisticalHAS-BLED spreadsheet exercise: nine validated risk-factor flags
Practice summing nine binary flags and comparing a historical HAS-BLED review threshold, without making treatment decisions.
Read the guide →Market Microstructure & Quant FinanceHasbrouck Information Share Bounds for Two-Venue Price Discovery
Calculate Hasbrouck (1995) Cholesky upper, lower, and midpoint price-discovery information shares across two cointegrated trading venues and audit correlation sensitivity.
Read the guide →Engineering & ScienceHausen Laminar Thermal Entry-Length Formula: Graetz Number & Pipe Nusselt
Calculate length-averaged laminar tube Nusselt number Nu_D = 3.66 + 0.0668*Gz / (1 + 0.04*Gz^(2/3)) from Graetz number Gz = (D/L)*Re*Pr for constant wall temperature.
Read the guide →Panel Data & EconometricsHausman Fixed-vs-Random-Effects Specification Test Formula
Test correlation between unobserved unit effects alpha_i and regressors X_it using Hausman’s (1978) H = (b_FE - b_RE)^2 / (SE_FE^2 - SE_RE^2) chi-square statistic.
Read the guide →Corporate Investment Theory & MacroeconomicsHayashi Marginal q & CapEx Adjustment-Cost Formula
Calculate Hayashi’s CRS Marginal/Average q Ratio V / K, Optimal Investment-to-Capital Rate I / K = delta + (q - 1) / phi, Optimal Gross CapEx, and Convex Installation Friction Cost.
Read the guide →Engineering & ScienceHayduk-Laudie Aqueous Liquid Diffusivity Correlation (EPA VOC Standard)
Calculate the U.S. EPA recommended aqueous diffusivity D_AB = 13.26 / (μ_w^1.14 * V_A^0.589) (× 10^-5 cm^2/s) for VOC air-strippers, carbon adsorbers, and groundwater remediation.
Read the guide →EngineeringHazen-Williams Water Pipe Head Loss formula: 10.67 * L * Q^1.852 / (C^1.852 * D^4.8704)
Estimate straight-pipe friction head loss for turbulent water flow with SI inputs and an assumed Hazen-Williams coefficient.
Read the guide →Hydrometallurgy, Gold ADR / Copper SX-EW & Heap Leach OperationsHeap Leach Irrigation Flux, PLS Flow & Metal Recovery Formula
Calculate Pregnant Leach Solution (PLS) Volumetric Flow (m³/hr), ADR/SX Stripping Efficiency (%), Daily Net Recovered Metal Mass (kg/d), and Daily Gold Equivalent (troy oz/d).
Read the guide →HealthcareHEART Score Spreadsheet: Validate and Sum Five Subscores
Practice input validation, SUM and IFS with five fictional HEART subscores. Calculate a total from 0 to 10 and a numerical score band without generating treatment or discharge instructions.
Read the guide →EngineeringHeat Exchanger Effectiveness-NTU Method (Counterflow & Condenser)
Calculate counterflow effectiveness, its balanced-capacity limit, an ideal isothermal phase-change comparison and heat duty, with explicit units and stable near-limit evaluation.
Read the guide →EngineeringHeat Exchanger LMTD (Log-Mean Temperature Difference) & Area sizing formula
Calculate counter-current heat exchanger Log-Mean Temperature Difference LMTD = (dT1 - dT2) / LN(dT1 / dT2) with L'Hopital equal-pinch guard and required surface area.
Read the guide →EngineeringHeat Pump & Chiller COP (Cooling vs Heating) & EER HVAC formulas
Calculate cooling Coefficient of Performance COP_cool = Q_cold / W_in, heating COP_heat = (Q_cold + W_in) / W_in = COP_cool + 1, and Energy Efficiency Ratio EER = 3.41214 * COP.
Read the guide →Engineering & ScienceHeating Degree Days (HDD) & Cooling Degree Days (CDD) Weather Energy Formula
Calculate daily and cumulative Heating Degree Days HDD = MAX(0, T_base - (T_max + T_min) / 2) and Cooling Degree Days CDD = MAX(0, (T_max + T_min) / 2 - T_base) for HVAC energy normalization and weather derivatives.
Read the guide →Pharmaceutical Solid-Dosage Engineering, Rotary Tablet Press Heckel Yield PressureHeckel Pharmaceutical Tablet Compaction Yield Formula
Calculate Tablet Relative Density D, Residual Porosity (%), Heckel Log-Porosity Value LN(1/(1-D)), and Excipient Mean Yield Pressure Py = 1/K (MPa).
Read the guide →Biostatistics & Meta-AnalysisHedges’ g Small-Sample Bias Correction and Glass’s Delta Formula
Correct upward small-sample bias in Cohen’s d using Hedges’ J(df) = 1 - 3 / (4*df - 1) factor and switch to Glass’s Delta when treatment alters group variance.
Read the guide →Quantitative Finance & TradingHeikin-Ashi Candlestick Formula: Smoothed HA-OHLC Recursion & Wickless Trend Filter
Transform noisy raw OHLC price bars into Munehisa Homma’s smoothed Heikin-Ashi ("Average Bar") coordinates HA_Open, HA_High, HA_Low, HA_Close and detect pure wickless trend candles.
Read the guide →Engineering & ScienceHeisenberg Uncertainty Principle: Momentum Spread & Natural Linewidth
Calculate minimum quantum momentum spread delta_p*c >= hbar*c / (2 * delta_x) (using hbar*c = 197.327 eV*nm) and excited-state / ultrafast-laser energy linewidth delta_E >= hbar / (2 * tau) (using hbar = 658.212 meV*fs).
Read the guide →Wind Energy & Atmospheric EngineeringHellmann Wind Shear Hub-Height Power Formula
Extrapolate meteorological mast wind speed to turbine hub height via Gustav Hellmann’s Power Law v_hub = v_ref * (z_hub / z_ref)^alpha and compute the Cubic Wind Power Density Multiplier (z_hub / z_ref)^(3*alpha).
Read the guide →Engineering & ScienceHelmholtz Resonator Frequency Formula (With Flanged Neck End Correction)
Calculate the resonant frequency f_H = (c / (2 * PI())) * SQRT(A_neck / (V_cavity * L_eff)) in Hz of bass-reflex speaker ports, engine intake resonators, and acoustic absorbers including neck end correction L_eff = L + 1.7 * r.
Read the guide →Healthcare & ClinicalHEMORR2HAGES Bleeding Risk Score in Atrial Fibrillation (0–12 Points)
Calculate Brian Gage’s Medicare-derived HEMORR2HAGES major bleeding score (0–12 points, weighting Rebleeding history at 2 points) to stratify anticoagulated atrial fibrillation patients.
Read the guide →EngineeringHenderson-Hasselbalch equation: Buffer pH & Conjugate Base/Acid ratio
Estimate buffer pH from a weak-acid/conjugate-base concentration ratio, and invert the approximation for a target pH.
Read the guide →Healthcare & Clinical FormulasHendrich II Fall Risk Model (HIIFRM) Inpatient Nursing Score
Calculate Ann Hendrich’s 8-factor inpatient fall-risk score (0–16) combining intrinsic CNS/medication risk factors (confusion +4, depression +2, elimination +1, dizziness +1, male +1, antiepileptics +2, benzodiazepines +1) and Get-Up-and-Go rising ability (0–4), flagging >= 5 as High Risk.
Read the guide →FinancialHerfindahl-Hirschman Index (HHI) formula for market & supplier concentration
Calculate revenue-share HHI on the 0–10,000 scale and the equivalent number of equal-sized firms for a defined market or supplier set.
Read the guide →Engineering & ScienceHerning-Zipperer Rule: Multicomponent Natural Gas Mixture Viscosity Formula
Calculate multicomponent hydrocarbon & flue-gas mixture viscosity μ_m = Σ(y_i * μ_i * SQRT(M_i)) / Σ(y_i * SQRT(M_i)) using square-root molecular weights.
Read the guide →Non-Newtonian Fluid Mechanics, API 13D Herschel-Bulkley & Bingham Plug FlowHerschel-Bulkley Yield Stress & Pipe Plug-Flow Formula
Calculate Herschel-Bulkley Total Shear Stress tau (Pa), Apparent Viscosity (mPa·s / cP), Unsheared Central Plug Radius Ratio rp/R, and Sheared Flowing Area (%).
Read the guide →EngineeringHertzian Contact Stress: Ball-on-Flat Contact Radius & Max Pressure
Calculate reduced contact modulus E*, circular contact-patch radius a = ((3 * F * R) / (4 * E*))^(1/3), and peak Hertzian bearing stress p_max = (3 * F) / (2 * PI() * a^2) (MPa).
Read the guide →Healthcare & Clinical FormulasHestia Criteria for Outpatient Pulmonary Embolism (PE) Disposition
Evaluate all 11 binary Hestia exclusion criteria (hemodynamics, thrombolysis, active bleeding, >24h oxygen, breakthrough PE, IV opioids, CrCl <30, severe liver disease, pregnancy, HIT, social support) to clear low-risk PE patients for direct home DOAC therapy.
Read the guide →StatisticalHHI market concentration, Gini Impurity, and Shannon Entropy formulas
Quantify market concentration (HHI = SUM(s^2)*10000), classification Gini Impurity (1 - SUM(p^2)), and information Shannon Entropy in bits.
Read the guide →Statistical & Clinical AnalysisHick-Hyman Law Formula: Choice Reaction Time RT = a + b * log2(n + 1)
Quantify menu-navigation and cockpit decision latency across n equally probable choices using William Edmund Hick (1952) and Ray Hyman’s (1953) logarithmic law RT = a + b * LOG(n + 1, 2).
Read the guide →Engineering & ScienceHigbie Penetration & Danckwerts Surface-Renewal Mass Transfer (kL)
Calculate liquid-side gas-absorption mass-transfer coefficients k_L (mm/s) using Ralph Higbie’s unsteady penetration model 2*SQRT(D_AB / (π * t_e)) and Peter Danckwerts’ random surface-renewal theory SQRT(D_AB * s).
Read the guide →Statistical & Clinical AnalysisHiggins I² & H² Meta-Analysis Heterogeneity Formula from Cochran’s Q
Quantify percentage between-study inconsistency I² = MAX(0, (Q - (k - 1)) / Q) * 100% and variance-inflation factor H² = MAX(1, Q / (k - 1)) in Cochrane meta-analyses.
Read the guide →Data Validation & AuditingHighlight & Audit Numbers Stored with Embedded Unit or Currency Symbols (ISTEXT)
Catch imported entries like "125 kg", "approx 90", or "EUR 400" that masquerade as numbers and silently drop out of SUM() using --AND(B2 <> "", ISTEXT(B2)).
Read the guide →Conditional Formatting & RulesHighlight & Count Duplicate Columns in a Matrix (TEXTJOIN Signature + COUNTIF)
Detect accidentally duplicated import columns across a multi-row table by serializing each column vector with TEXTJOIN("|", FALSE, A2:A4) and flagging signatures with COUNTIF($A$5:$D$5, A5) > 1.
Read the guide →Conditional Formatting & RulesHighlight & Count Values Between Two Bounds: Order-Safe MIN/MAX & COUNTIFS
Test whether numbers or dates fall inside [Lower, Upper]—even if a user types Upper before Lower—using AND(B2 >= MIN($E$2,$E$3), B2 <= MAX($E$2,$E$3)) and COUNTIFS.
Read the guide →Conditional Formatting & AuditsHighlight Cells Matching Any Value in a Watchlist Range (COUNTIF Membership Rule)
Replace brittle 10-way OR formulas with a table-driven COUNTIF($D$2:$D$5, TRIM(A2)) > 0 rule that highlights any row matching an editable watchlist or priority code table.
Read the guide →Conditional Formatting & AuditsHighlight Cells That End With a Specific Suffix (RIGHT & LEN Exact Suffix Rule)
Flag filenames, SKUs, or email domains ending with a target suffix like ".csv" or "-TEMP" using TRIM, RIGHT, and LEN—avoiding wildcard false positives on "?" and "*".
Read the guide →Conditional Formatting & AuditsHighlight Entire Rows by Day of Week or Incomplete Required Fields
Apply column-locked row formatting rules using WEEKDAY($B2, 2) = $G$2 to spotlight Friday/Monday cutoffs and AND(COUNTA($A2:$D2) > 0, COUNTBLANK($A2:$D2) > 0) to catch half-entered rows.
Read the guide →Logical & ConditionalHighlight Every Other Row & N-Row Zebra Bands (ISEVEN, ROW & MOD)
Generate TRUE/FALSE zebra-striping flags for alternating single rows using ISEVEN(ROW(A2)) or header-anchored MOD(ROW(A2) - ROW($A$2), 2) = 1, and group N-row visual blocks via MOD(INT((ROW(A2) - ROW($A$2)) / N), 2) = 1.
Read the guide →Conditional Formatting & AuditsHighlight Strictly Unique (Once-Only) Values with Blank-Safe COUNTIF Rules
Flag single-occurrence IDs, unmatched reconciliation entries, or one-time buyers using COUNTIF($A$2:$A$7, A2) = 1 while preventing blank rows from highlighting.
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