Learn one useful thing today.
Maddrey Discriminant Function (mDF) Score for Alcoholic Hepatitis
Calculate Willis Maddrey’s modified Discriminant Function mDF = 4.6 * (PT_patient - PT_control) + Bilirubin_mg_dL to identify severe alcoholic hepatitis (mDF >= 32) eligible for prednisolone therapy.
Read the guide →OperationsMAE, WAPE & Forecast Bias for Intermittent Zero-Demand SKUs
Measure supply-chain forecast accuracy without #DIV/0! zero-actual explosions using Mean Absolute Error MAE = AVERAGE(|A - F|), Weighted Absolute Percentage Error WAPE = SUM(|A - F|) / SUM(A), and Signed Bias.
Read the guide →Semiconductor PVD & Thin-Film Vacuum Coating, Magnetron Sputtering Rate & Cosine ThrowMagnetron Sputtering PVD Deposition Rate & Throw Formula
Calculate Total Sputtered Atom Emission Rate (10¹⁹ atoms/s), Knudsen Cosine Wafer-Center Flux (10¹⁶ atoms/cm²·s), Film Deposition Rate (nm/min), and 500 nm Seed Coat Time (min).
Read the guide →Operations & LogisticsMaister’s Square-Root Law of Warehouse Centralization & Correlated Safety Stock
Project safety-stock savings when consolidating N_old regional depots into N_new hubs using David Maister’s (1976) SQRT(N_new / N_old) law plus inter-regional demand correlation rho.
Read the guide →TextMake dynamic labels singular or plural based on count (1 item vs 0 items)
Format natural summary strings ("1 pallet", "0 entries", "5 boxes") by testing ABS(Qty) = 1 for regular and irregular nouns.
Read the guide →EngineeringMalus's Law Polarizer Intensity & Brewster's Angle optics formulas
Calculate ideal analyzer transmission and the Brewster angle for two transparent dielectric media.
Read the guide →Health Actuarial & Value-Based Care FinanceManaged Care PMPM Capitation & IBNR Pool Formula
Calculate Risk-Adjusted PMPM Capitation Pool Revenue, Actuarial Completion-Factor Ultimate Incurred Claims (Paid / Completion_Factor), Medical Cost Ratio (MCR), and Net Risk Margin PMPM.
Read the guide →StatisticalMann-Whitney U test (Wilcoxon Rank-Sum) statistic & AUC effect size
Calculate a pooled-rank Mann–Whitney statistic and a descriptive pairwise superiority estimate for two independent groups.
Read the guide →Statistical & Clinical AnalysisMannheim Peritonitis Index (MPI) Formula: Secondary Intra-Abdominal Sepsis Score (0 to 47)
Predict laparotomy mortality in secondary peritonitis using Linder & Wacha’s 8-variable Mannheim Peritonitis Index (0–47 points: Age > 50, Female, Organ Failure, Malignancy, Preop > 24h, Non-Colonic Origin, Diffuse Peritonitis, Exudate Character).
Read the guide →EngineeringManning's Open-Channel Flow formula: hydraulic radius, velocity & discharge Q
Estimate velocity and discharge for a rectangular SI open channel under steady uniform-flow assumptions.
Read the guide →Econometrics & Partial IdentificationManski Worst-Case and Monotone Causal Bounds Formula
Bound Average Treatment Effects without random assignment on bounded [0, 1] or [K_0, K_1] outcomes using Manski’s (1990) worst-case bounds and MTR/MTS tightening.
Read the guide →Statistical & Mathematical FormulasMantel-Haenszel Pooled Odds Ratio: Defeating Simpson’s Paradox
Calculate the confounder-stratified Cochran-Mantel-Haenszel pooled Odds Ratio OR_MH = Σ(a_k * d_k / N_k) / Σ(b_k * c_k / N_k) across multi-center or acuity strata and contrast against biased crude pooled OR.
Read the guide →Lookup & ReferenceMap Likert Survey Text Labels to Numeric Scores (SWITCH vs XLOOKUP Table)
Convert qualitative survey responses ("Strongly Agree" through "Strongly Disagree") or risk ratings into numeric 1–5 weights using SWITCH or an XLOOKUP mapping table, while excluding "N/A" responses from averages.
Read the guide →Logical & Lookup FormulasMap Text Tiers to Arbitrary Numeric Weights (CHOOSE & MATCH vs XLOOKUP)
Assign non-linear SLA severity weights or T-shirt story points ("XS"->1, "S"->2, "M"->5, "L"->8, "XL"->13) to text categories without nested IFs using CHOOSE(MATCH(...)) or XLOOKUP.
Read the guide →Statistical & Clinical AnalysisMargalef Richness, Menhinick Index & Berger-Parker Dominance Formula
Calculate three rapid ecological bioassessment indices from species counts: Margalef Richness D_Mg = (S - 1) / LN(N), Menhinick Richness D_Mn = S / SQRT(N), and Berger-Parker Dominance d_BP = N_max / N (plus reciprocal 1 / d_BP).
Read the guide →Financial ModelingMargrabe Exchange Option Formula & Correlation-Adjusted Spread Volatility
Value a European option to exchange asset 2 for asset 1 (stock-for-stock mergers, outperformance fees, spark spreads) using William Margrabe’s (1978) risk-free-rate-independent formula.
Read the guide →Engineering & ScienceMargules Non-Ideal Liquid Activity Coefficients (gamma1 & gamma2 VLE)
Calculate asymmetric binary vapor-liquid equilibrium (VLE) activity coefficients gamma_1 = EXP((1 - x_1)^2 * (A_12 + 2*(A_21 - A_12)*x_1)) and gamma_2 = EXP(x_1^2 * (A_21 + 2*(A_12 - A_21)*(1 - x_1))) for azeotropic distillation columns.
Read the guide →Charts & Visual Data ModelingMarimekko (Mekko) Chart Formula: Variable Column Widths, Cumulative X-Spans & Cell Area Share
Construct a two-dimensional Marimekko (Mosaic) market-map table: compute Segment Horizontal Width % W_j, Cumulative X-Axis Start/End Coordinates, Within-Segment Vertical Mix %, and Rectangle Area = Grand-Total Market Share!
Read the guide →Naval Architecture, Ship Propulsion & Noon-Report PerformanceMarine Propeller Apparent vs True Wake Slip Formula
Calculate Theoretical Screw Pitch Velocity V_p (m/s), Ship Speed Over Water V_s (m/s), Bridge Noon-Report Apparent Slip (%), and Hydrodynamic True Slip (%) inside the Taylor Stern Wake.
Read the guide →Maritime Chartering & Port LogisticsMaritime Laytime, Demurrage & Despatch Formula
Calculate Total Reversible Allowed Port Laytime Q/R_load + Q/R_dis, Net Laytime Balance, Shipowner Demurrage Penalty, and Charterer Half-Rate Despatch Rebate ("Despatch Half Demurrage").
Read the guide →Maritime Economics & Shipping FinanceMaritime Time Charter Equivalent (TCE) Formula
Convert Lump-Sum or $/MT Spot Voyage Freight into Daily Time Charter Equivalent TCE = (Gross_Freight*(1 - comm) - Bunkers - Port_Dues) / Voyage_Days and Daily Vessel Cash Breakeven Margin.
Read the guide →Engineering & ScienceMark-Houwink-Sakurada Equation: Intrinsic Viscosity [eta] & Polymer Molar Mass (Mv)
Calculate dilute polymer intrinsic viscosity [eta] = K * Mv^a (dL/g) and invert Ubbelohde viscometer measurements back to viscosity-average molecular weight Mv = ([eta] / K)^(1 / a).
Read the guide →Logical & ConditionalMark, Count & Sum Rows Matching Mixed AND + OR Rules (IF + COUNTIF + SUMIF)
Flag audit rows meeting compound AND + OR criteria (e.g., Amount >= $1,000 AND Status is Urgent OR Escalated), then count and sum flagged exposure cleanly.
Read the guide →Two-Sided Marketplaces & Fintech EconomicsMarketplace GMV, Take Rate & Interchange Margin Formula
Bridge Gross Merchandise Volume (GMV) from Headline Combined Take Rate to Net Realized Take Rate and Net Contribution Margin after GMV-denominated card interchange, fraud chargebacks, and incentives.
Read the guide →Chemical, Process & Catalysis EngineeringMars-van Krevelen Redox Catalytic Rate Law & Oxidized Lattice Fraction theta_ox
Model selective hydrocarbon oxidation over reducible metal oxides (V2O5, MoO3, CeO2) using Pieter Mars and Dirk Willem van Krevelen’s (1954) redox rate law r_R = (k_red * P_R * k_ox * P_O2^n) / (nu * k_red * P_R + k_ox * P_O2^n).
Read the guide →Healthcare & Clinical FormulasMarshall Multiple Organ Dysfunction Score (MODS) & PAR Index
Calculate Marshall’s 6-organ Multiple Organ Dysfunction Score (MODS, 0–24) and Pressure-Adjusted Heart Rate PAR = HR * CVP / MAP without vasopressor-dose confounding.
Read the guide →International Macroeconomics & TradeMarshall-Lerner Condition and J-Curve Trade-Balance Formula
Test the Marshall-Lerner condition (e_X + e_M > 1), Hirschman’s initial-deficit condition ((X_0 / M_0)*e_X + e_M > 1), and J-curve trade-balance response Delta_NX = dq * (X_0*e_X + M_0*(e_M - 1)).
Read the guide →Preventive Cardiology, Clinical Lipidology & Laboratory DiagnosticsMartin-Hopkins Adjustable LDL-C vs Friedewald Bias Formula
Calculate Atherogenic Non-HDL Cholesterol (TC - HDL), Legacy Fixed-Divisor Friedewald LDL-C (TC - HDL - TG/5), ACC/AHA Guideline Martin-Hopkins Adjustable-Divisor LDL-C (TC - HDL - TG/f_MH), and Friedewald Underestimation Gap.
Read the guide →Healthcare & ClinicalMASCC Risk Index for Febrile Neutropenia (0–26 Outpatient Score)
Calculate the ASCO/IDSA-endorsed 0–26 MASCC Risk Index in chemotherapy-induced febrile neutropenia—where HIGHER scores (>= 21) identify Low-Risk patients eligible for oral outpatient antibiotics.
Read the guide →Logical & Lookup FormulasMatch First Row Not Containing Specific Text (XLOOKUP & SEARCH)
Retrieve the first order or server record that excludes an internal/test substring using an ISERROR(SEARCH(...)) helper flag with XLOOKUP and count all non-matching records with COUNTIF.
Read the guide →Lookup & ReferenceMatch Long Text Over 255 Characters (EXACT + XLOOKUP Bypass for Deep URLs & Clauses)
Bypass legacy 255-character lookup limits and prefix collisions when matching long tracking URLs, API payloads, and contract clauses that differ only after character 255.
Read the guide →Lookup & ReferenceMatch Next Highest Capacity Bracket & Dynamic Column Peak (XLOOKUP +1 & CHOOSECOLS)
Select the smallest server, container, or breaker rating that meets or exceeds required load using XLOOKUP match_mode = 1, and verify dynamic column capacity peaks with MAX(CHOOSECOLS(...)).
Read the guide →InformationMatch the first error in a column: jump straight to broken rows
Identify the first record with a formula error and list all affected records using an audit helper column.
Read the guide →Civil, Structural & Geotechnical EngineeringMatlock (1970) Soft-Clay Lateral Pile p-y Curve Formula: N_p, y_50 & Cubic Spring
Generate nonlinear lateral soil-pile spring resistance p(y) (kN/m) in submerged soft clay using Hudson Matlock’s (1970, API RP 2GEO / LPILE) bearing factor N_p = MIN(9, 3 + gamma_prime*z/c_u + J*z/D), y_50 = 2.5*eps_50*D, and cubic parabola.
Read the guide →Statistical & Clinical AnalysisMatsuda Index (ISI_comp) Formula: Whole-Body OGTT Hepatic + Peripheral Insulin Sensitivity
Capture both fasting hepatic and post-load skeletal-muscle insulin sensitivity from a 75 g Oral Glucose Tolerance Test using Masafumi Matsuda & Ralph DeFronzo’s composite index 10,000 / SQRT((G_0 * I_0) * (G_mean * I_mean)).
Read the guide →StatisticalMatthews Correlation Coefficient (MCC) & Cohen's Kappa Confusion Matrix formulas
Compute binary MCC and unweighted Cohen kappa from valid integer counts, distinguish undefined cases and compare asymmetric confusion matrices.
Read the guide →Engineering & ScienceMatthiessen’s Rule & Cryogenic Residual Resistivity Ratio (RRR)
Separate impurity/defect resistivity rho_0 from thermal phonon scattering rho_ph(T) via Augustus Matthiessen’s Rule rho_tot = rho_0 + rho_ph and grade cryogenic copper/niobium purity via RRR = rho(300 K) / rho(4.2 K).
Read the guide →Statistical & AggregationMaximum and Minimum Value by Calendar Month (MAXIFS, MINIFS & EOMONTH)
Find the peak high and trough low within any calendar month using MAXIFS and MINIFS bounded by first-of-month and EOMONTH(firstOfMonth, 0), distinguishing empty months from genuine zero readings.
Read the guide →FinancialMaximum Drawdown (MDD), High-Water Mark & recovery gain % formulas
Track running portfolio peaks MAX($B$2:B2), underwater drawdown %, worst peak-to-trough Maximum Drawdown, and asymmetric recovery % needed.
Read the guide →Operations & LogisticsMaximum Flow & Min-Cut Network Model (Node Conservation, Arc Slack & Bottleneck Cut)
Model directed logistics and pipeline networks by auditing SUMIFS transshipment flow conservation (Outflow - Inflow = 0), residual arc capacity slack, and Max-Flow = Min-Cut optimality.
Read the guide →Healthcare & Clinical CalculationsMayo Score & Non-Invasive Partial Mayo Score for Ulcerative Colitis
Calculate Kenneth Schroeder’s 4-domain Full Mayo Ulcerative Colitis Score (0–12 including Endoscopic Subscore) alongside the 3-domain Non-Invasive Partial Mayo Score (0–9) for clinic visits between colonoscopies.
Read the guide →Engineering & ScienceMayo-Lewis Copolymer Equation & Azeotropic Feed Ratio
Calculate instantaneous copolymer chain composition F_1 = (r_1*f_1^2 + f_1*f_2) / (r_1*f_1^2 + 2*f_1*f_2 + r_2*f_2^2) and drift-free azeotropic monomer feed f_1,azeo = (1 - r_2) / (2 - r_1 - r_2).
Read the guide →Engineering & ScienceMcCabe-Thiele Distillation Operating Lines & Feed q-Line Intersection Formula
Calculate the McCabe-Thiele rectifying operating-line slope R / (R + 1), intercept xD / (R + 1), and exact singularity-free feed q-line intersection coordinates (x_int, y_int) valid for ALL thermal qualities q (including q = 1!).
Read the guide →Statistical & Clinical AnalysisMcDonald’s Omega (Composite Reliability) & Fornell-Larcker AVE Formula in CFA
Replace tau-equivalent Cronbach’s alpha assumptions in Confirmatory Factor Analysis (CFA / PLS-SEM) using Roderick McDonald’s congeneric omega = (SUM(lambda))² / ((SUM(lambda))² + SUM(1 - lambda²)) and Claes Fornell & David Larcker’s Average Variance Extracted AVE = SUMPRODUCT(lambda, lambda) / k.
Read the guide →HealthcareMcIsaac and Alvarado Scores: Validated Spreadsheet Arithmetic
Practice binary-input validation, age bands and weighted sums using fictional McIsaac and Alvarado components. Return numerical totals without diagnosis or treatment instructions.
Read the guide →Packaging Mechanics, Warehousing & Supply-Chain OpsMcKee Corrugated Box Compression (BCT) & Stacking Formula
Calculate R.C. McKee’s Simplified Corrugated Box Compression Strength BCT_lbf = 5.87 * ECT_lb_in * SQRT(Flute_Caliper_in * Box_Perimeter_in), Humidity/Creep Safe Bottom-Box Load, and Maximum Safe Pallet Layers.
Read the guide →Statistical AnalysisMcNemar’s Paired-Proportions Chi-Square Test & Edwards Continuity Correction
Test before-vs-after binary treatment shifts or matched classifier error rates using discordant pairs (b and c), Edwards continuity-corrected chi-square, and matched-pair odds ratio.
Read the guide →Spreadsheet Governance & Collaborative AI WorkflowsMCP apply_changes Revision, Idempotency & Conflict Audit
Audit external connector apply_changes guardrails on cloud workbooks: Pro + editor/owner access, <= 100 cell cap, 16-80 char operation_id idempotency, base revision matching, and pendingReview concurrent peer-edit routing.
Read the guide →Spreadsheet Collaboration Governance, Comment Threading & OAuth AuditingMCP Comment Reply Parent Anchor, comment_id Retry & Alert Audit
Audit Collaborative Comment Threading Rules in Arte Sheets: Exact read_range / Parent-Thread Anchor Inheritance, Explicit User Request Gate Before Participant Notification, Identical-Retry-Only comment_id Reuse, and Scoped Thread Resolution.
Read the guide →Collaborative Spreadsheets & MCP Connector GovernanceMCP Comment Tools: 25-Entry/120KB Cap & Suggester Audit
Audit list_comments (<=25 entries, <=120 KB), add_comment, and resolve_comment permissions (Pro + owner/editor/suggester on whole-cell anchors) and 120/min rate limits without Arte AI credit burn.
Read the guide →