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Discrete Geometric Asian Option and Arithmetic Forward Moment Formula
Price discrete n-fixing Geometric Asian calls exactly via Kemna-Vorst volatility scaling and compute the Turnbull-Wakeman discrete arithmetic forward mean M1.
Read the guide →Statistical & AggregationDiscrete Probability Mass Interval, Expected Value & Variance (PROB & SUMIFS)
Validate discrete probability mass tables (sum = 1, non-negative weights), calculate interval probabilities P(L <= X <= U) via SUMIFS (PROB), and compute distribution mean and standard deviation.
Read the guide →Drinking-Water Disinfection, US EPA SWTR & Clearwell HydraulicsDisinfection CT Inactivation, Baffling Factor & Log Formula
Calculate Clearwell Theoretical Hydraulic Residence Time HRT (min), Tracer T10 Effective Contact Time (min), Effective Disinfection CT (mg·min/L), and Pathogen Log-Inactivation Credit.
Read the guide →Monetary Policy & MacroeconomicsDisinflation Sacrifice Ratio & Okun Misery Index Formula
Calculate Laurence Ball’s (1994) Disinflation Sacrifice Ratio SR = Cum_Output_Loss / (pi_peak - pi_trough), Unemployment Point-Years per 1-pp disinflation, and Arthur Okun’s Misery Index.
Read the guide →LogicalDisplay a Checkmark When Checklist Conditions Pass
Use a literal Unicode checkmark with validated reviewer text and a 0–100 score. Calculate completion from the same row-status results so badges and progress agree.
Read the guide →Industrial Wastewater, Dissolved Air Flotation & Sludge ThickeningDissolved Air Flotation (DAF) Air-to-Solids Ratio Formula
Calculate DAF Saturator Net Released Air Factor (f*P - 1), Released Microbubble Air Concentration (mg/L), Mass Air-to-Solids Ratio A/S (kg air / kg TSS), and Recycle Pump Flow (m³/hr).
Read the guide →EngineeringDistance formula: 2D and 3D Euclidean vs Manhattan grid distance
Calculate straight-line Pythagorean distance in 2D or 3D space with SQRT, and compare right-angle warehouse aisle distance with ABS.
Read the guide →EngineeringDittus–Boelter and Gnielinski: Pipe Nusselt Number and Heat Transfer
Compare two turbulent circular-tube correlations, validate their input ranges and compute h from unrounded Nusselt values.
Read the guide →Charts & Visual DataDiverging Likert Stacked Bar Chart Formula: Neutral Midpoint Split & Padding Spacer
Align 5-point Likert survey responses around a vertical zero spine on a 100% Stacked Bar Chart by splitting Neutral responses in half and computing each row’s exact left-padding spacer.
Read the guide →FinancialDividend Yield, Yield on Cost, Payout Ratio, and Sustainable Growth (g)
Evaluate dividend stocks with Current Yield, Yield on Original Cost Basis, Earnings Payout Ratio, and Sustainable Growth Rate ROE * (1 - Payout).
Read the guide →Strategic Competition & Industrial OrganizationDixit-Spence Capacity Commitment & Entry Deterrence
Calculate Avinash Dixit’s (1980) entry-deterring limit capacity K_det = (a - w - r - 2*SQRT(b*F)) / b and audit subgame-perfect credibility against K_max = (a - w + r) / (3*b).
Read the guide →Healthcare & Clinical CalculationsDLQI (Dermatology Life Quality Index 0–30) Hongbo Banding Calculator
Score Andrew Finlay and Gul Karim Khan’s 10-question Dermatology Life Quality Index (0–30 points) using Hongbo clinical severity bands and the NICE/EADV DLQI > 10 biologic "Rule of Tens" threshold.
Read the guide →5G Wireless RF Front-End & Base-Station EngineeringDoherty RF Amplifier Back-Off Efficiency & PAPR Formula
Calculate OFDM Peak-to-Average Crest Ratio P_peak / P_avg, Classical Class-B Back-Off Drain Efficiency (PI()/4)*SQRT(P_avg/P_peak), Symmetric 2-Way Doherty Load-Modulated Efficiency, and DC Heat-Loss Saving Ratio.
Read the guide →Financial & AccountingDollar-Cost Averaging (DCA) Formula: Harmonic Average Cost Basis & Unrealized Gain
Calculate exact share-weighted Dollar-Cost Averaging cost basis SUM(Invested) / SUMPRODUCT(Invested / Share_Price)—showing why fixed-dollar contributions beat the arithmetic average share price—plus unrealized P&L.
Read the guide →Quantitative Finance & TradingDonchian Channel & Turtle Position Sizing Formula: N-Bar High/Low Midpoint & 1% Risk Unit
Compute Richard Donchian’s N-period breakout channel (MAX High, MIN Low, Equilibrium Midpoint) paired with Dennis & Eckhardt’s volatility-parity 1% ATR Unit Size.
Read the guide →EngineeringDoppler Effect frequency shift & compressed sound wavelength formula
Calculate observed acoustic frequency f_obs = f_src * (c + v_obs) / (c - v_src) and wavefront wavelength for approaching vs. receding sound sources.
Read the guide →Marketing Analytics & Managerial EconomicsDorfman-Steiner Optimal Advertising-to-Sales Ratio Formula
Size profit-maximizing advertising spend A* / Revenue = e_A / |e_P| = ((P - MC) / P) * e_A using the Dorfman-Steiner theorem in Excel and Arte Sheets.
Read the guide →International Macroeconomics & FXDornbusch Exchange-Rate Overshooting Model Formula
Calculate impact FX depreciation Delta_e0 = Delta_m * (1 + 1 / (lambda * theta)), overshoot ratio, liquidity interest-rate drop, and exponential convergence path.
Read the guide →Charts & Data VisualizationDot Plot Formula: Wilkinson Vertical Stack Y-Index & Cleveland Category Dot Gap
Build Wilkinson stacked frequency dot plots using an expanding running-occurrence counter COUNTIF($B$2:B2, B2) for Scatter Y coordinates, plus William S. Cleveland’s category-comparison dot gap and relative advantage.
Read the guide →Math & EngineeringDouble Factorial n!! & Perfect-Matching Pairings (SEQUENCE & PRODUCT)
Calculate the double factorial n!! for odd and even non-negative integers using PRODUCT and SEQUENCE, and count distinct ways to pair 2k items into k unordered pairs.
Read the guide →Causal Inference & Machine LearningDoubly Robust Augmented IPW (AIPW) Treatment Effect Formula
Build Robins-Rotnitzky-Zhao doubly robust AIPW pseudo-outcomes psi_i = (m_1 - m_0) + D*(Y - m_1)/e - (1 - D)*(Y - m_0)/(1 - e) and verify consistency when either nuisance model is misspecified.
Read the guide →Charts & Visual DataDoughnut Progress Ring Formula: Clamped Fill, Remainder Arc & Over-Target Guard
Prevent broken Doughnut Progress Charts when attainment exceeds 100% by clamping the unfilled remainder slice with MAX(0, 1 - Actual/Goal) instead of raw 1 - Actual/Goal.
Read the guide →Power Magnetics, High-Frequency Planar Transformers & Eddy-Current Proximity LossDowell Transformer AC Winding Resistance (Fr) & Proximity Loss
Calculate High-Frequency Transformer Normalized Foil Thickness Δ = h / δ, Dowell Sub-Skin AC-to-DC Resistance Ratio Fr = 1 + ((5*m² - 1)/45)*Δ⁴, DC Copper Loss (W), and Total AC Winding Loss Before and After P-S-P-S Layer Interleaving.
Read the guide →Quantitative Finance & DerivativesDown-and-Out Barrier Call Formula and Knock-In/Knock-Out Parity
Price continuous zero-rebate Down-and-Out Calls (H < K, S > H) via the Merton / Reiner-Rubinstein reflection principle and verify exact Down-and-In + Down-and-Out = Vanilla parity.
Read the guide →Statistical & Clinical AnalysisDownes-Vidyasagar Score Formula: Neonatal Respiratory Distress CPAP vs. Intubation (0 to 10)
Assess preterm and term newborn respiratory distress without arterial blood gases using John Downes & Dharmapuri Vidyasagar’s 5-sign clinical score (0–10 points).
Read the guide →Tribology & Mechanical EngineeringDowson-Higginson EHL Line-Contact Minimum Film Thickness Formula
Calculate elastohydrodynamic lubrication (EHL) dimensionless speed U, materials G, load W, and minimum film thickness h_min = 2.65 * R_eq * U^0.70 * G^0.54 * W^(-0.13) in microns.
Read the guide →Statistical & Clinical AnalysisDRAGON Score Formula: Post-IV Thrombolysis Stroke 3-Month Outcome (0 to 10)
Predict 3-month functional independence vs. dismal outcome (mRS 5–6) immediately at IV alteplase initiation using Daniel Strbian’s 6-domain DRAGON score (0–10 points).
Read the guide →Deep Foundations & Seismic Underpinning, FHWA Drilled & Grouted Micropile DesignDrilled & Grouted Micropile Bond & Structural Load Formula
Calculate Ultimate Grout-to-Ground Bond Capacity (kN), Allowable Geotechnical Bond Load (FS = 2.0, kN), Composite Casing+Grout Structural Capacity (kN), and Governing Load.
Read the guide →Petroleum & Geothermal Wellbore Hydraulics, API Hole Cleaning & Equivalent Circulating DensityDrilling Annular Velocity, Cuttings Transport & ECD Formula
Calculate Open-Hole Annular Mud Velocity Va (m/min), Net Upward Cuttings Rise Velocity (m/min), Sifferman Cuttings Transport Ratio Ft (%), and Equivalent Circulating Density ECD (SG).
Read the guide →Drilling Engineering & Well ControlDrilling Kill Mud Weight, ICP & FCP Well-Control Formula
Calculate True-Vertical-Depth Hydrostatic Mud Pressure 0.052 * MW * TVD, Required Kill Mud Weight KMW = MW_orig + SIDPP / (0.052 * TVD), Initial Circulating Pressure (ICP), and Final Circulating Pressure (FCP).
Read the guide →Dynamic arraysDROP function: strip opening balances, headers, or total rows dynamically
Exclude N rows or columns from the start or end of an imported range with DROP so summary rows never double-count.
Read the guide →Engineering & ScienceDrude Free-Electron Metal Conductivity & UV Plasma Frequency Formula
Calculate DC electrical conductivity sigma = (n * e^2 * tau) / m_e in MS/m and plasmon energy hbar * omega_p (in eV) explaining both metal Ohm's Law and why metals turn transparent in the deep ultraviolet!
Read the guide →Business & OperationsDrum-Buffer-Rope (DBR) Buffer Penetration % & TOC Green/Yellow/Red Expedite Priority
Calculate Theory of Constraints (TOC) time-buffer consumption percentage 100 * (Buffer_Hours - Remaining_Hours) / Buffer_Hours and classify work orders into Region I Green (<33.3%), Region II Yellow (33.3%–66.7%), or Region III Red (>66.7%) expedite zones.
Read the guide →Health & FitnessDu Bois & Haycock Body Surface Area (BSA) & Capped mg/m^2 Dosing
Calculate physiological Body Surface Area (m^2) using the foundational Du Bois & Du Bois (1916) power law 0.007184 * W^0.425 * H^0.725, Haycock pediatric BSA, and protocol-capped mg/m^2 chemotherapy doses.
Read the guide →Healthcare & ClinicalDuke Treadmill Score (DTS): Bruce Protocol Exercise Stress Test Prognosis
Calculate Mark's Duke Treadmill Score DTS = Exercise_Minutes - (5 * Max_ST_Deviation_mm) - (4 * Treadmill_Angina_Index) to stratify 1-year and 5-year coronary mortality into Low (>= +5), Moderate (-10 to +4), and High (<= -11) risk.
Read the guide →Labor Economics & Demographic StatisticsDuncan Dissimilarity Index & Karmel-MacLachlan Formula
Calculate the Duncan Index of Dissimilarity D = 0.5 * SUM(|a_k/A - b_k/B|) and Karmel-MacLachlan replacement-preserving index I_p = 2 * p * (1 - p) * D.
Read the guide →Rotordynamics, Turbomachinery Shafts & Lateral Whirling ResonanceDunkerley Shaft Critical Whirling Speed & Margin Formula
Calculate Dunkerley Cumulative Static Deflection Equivalent (mm), Conservative First Lateral Critical Speed N_cr (RPM), Operating Speed Separation Margin (%), and Sub/Supercritical Regime.
Read the guide →FinancialDuPont ROE analysis formula: Margin x Asset Turnover x Financial Leverage
Break Return on Equity (NetIncome / Equity) into 3 diagnostic levers—Net Profit Margin, Total Asset Turnover, and Equity Multiplier—to see what drives ROE.
Read the guide →ScienceDupuit-Forchheimer Unconfined Aquifer Seepage & Parabolic Water Table
Calculate steady unconfined groundwater seepage per unit width q' = K * (h1^2 - h2^2) / (2 * L) (m^2/day) and parabolic phreatic water-table elevation h(x) between two canals or earthen dam faces.
Read the guide →Fixed Income & RatesDuration-Neutral Barbell-Bullet Butterfly Weights and Convexity Pickup
Construct cash-and-duration-neutral 2s5s10s fixed-income butterflies in Excel and Arte Sheets and quantify exact barbell convexity pickup over a bullet bond.
Read the guide →Econometrics & Causal InferenceDurbin-Wu-Hausman Control-Function Residual Endogeneity Test
Test regressor endogeneity in Excel and Arte Sheets by augmenting the structural equation with first-stage IV residuals v_hat = X - X_hat and computing the exact DWH t- and F-statistics.
Read the guide →Clinical Medicine & PhysiologyDurnin-Womersley 4-Site Skinfold Calculator: LOG10 Skinfold Sum Body Density & %BF
Calculate Whole-Body Density D_b = c - m * LOG10(Biceps + Triceps + Subscapular + Suprailiac) and Siri Percent Body Fat across adult age-sex bands using J. V. G. A. Durnin and J. Womersley’s (1974, Br. J. Nutr.) general-population reference equations.
Read the guide →Lookup & ReferenceDynamic Category and Monthly Totals With Percent-of-Total (GROUPBY, PIVOTBY & PERCENTOF Patterns)
Build live category summaries, category-by-month cross-tab totals, and share-of-grand-total ratios using UNIQUE, SORT, SUMIF, and SUMIFS.
Read the guide →Charts & Visual DataDynamic Chart Title Formula: Formatted KPI Headline & Signed YoY Delta Banner
Build a self-updating executive Chart Title cell using TEXT formatting and directional + / - variance logic so chart headlines never show stale numbers or raw floating-point decimals.
Read the guide →Lookup, Reference & Dynamic ArraysDynamic Line Chart Ignore Empty Future Months: NA() Formula vs. Zero-Cliff Drop
Stop YTD actuals line charts from plunging vertically to 0 in unrecorded future months by returning NA() instead of "" or 0—while using COUNT(B2:B7) to aggregate completed months cleanly!
Read the guide →Date & TimeDynamic monthly calendar grid formula (SEQUENCE + WEEKDAY)
Spill a complete 6-week x 7-day monthly calendar grid for any Year and Month (Sunday-start or Monday-start) with one SEQUENCE formula.
Read the guide →Lookup & ReferenceDynamic range between two matches: sum or extract rows between markers
Locate any Start milestone and End milestone with XMATCH and slice all rows inclusively between them using TAKE(DROP(...)).
Read the guide →StatisticalDynamic two-way average by row category and column header (CHOOSECOLS + FILTER)
Average rows matching a region or department while dynamically switching which quarter or metric column is aggregated via XMATCH + CHOOSECOLS.
Read the guide →Lookup & ReferenceDynamic two-way sum and average: aggregate a chosen column by row criteria
Select a monthly metric column with XLOOKUP, filter its rows, and calculate a dynamic sum or average.
Read the guide →FinancialEarned Value Management (EVM) formulas: EV, PV, CPI, SPI, and EAC
Distinguish true physical progress from raw budget burn using Cost Performance Index (CPI = EV / AC), Schedule Performance Index (SPI = EV / PV), and EAC.
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