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Earned Value TCPI & Lipke Earned Schedule Formula
Audit unrecoverable cost overruns via To-Complete Performance Index TCPI = (BAC - EV) / (BAC - AC) and fix late-project SPI = 1.00 convergence distortion with Walt Lipke’s Earned Schedule SPI(t) = ES / AT.
Read the guide →International Trade & Quantitative MacroeconomicsEaton-Kortum Trade Share & ACR Gains-from-Trade Formula
Compute multi-country Eaton-Kortum Fréchet import shares pi_ni = T_i*(c_i*d_ni)^(-theta) / Phi_n and Arkolakis-Costinot-Rodríguez-Clare welfare gain pi_nn^(-1/theta).
Read the guide →Structural Mechanics, Column Stability & Non-Linear P-Delta BendingEccentric Column Secant Formula Max Compressive Stress
Calculate Eccentric Column Direct Axial Stress P/A (MPa), Stability Secant Angle (rad), Exact Secant Maximum Fiber Compressive Stress (MPa), and Naive Linear Stress Without P-Delta (MPa).
Read the guide →Chemical, Process & Catalysis EngineeringEckert GPDC Packed-Column Flooding Formula: Flow Parameter F_LV & Tower Diameter
Size random and structured packed absorption, stripping, and distillation towers using Sherwood-Eckert Generalized Pressure Drop Correlation (GPDC) Flow Parameter F_LV = (L / G) * SQRT(rho_G / rho_L), Flooding Gas Velocity u_flood, and Column Diameter.
Read the guide →OperationsEconomic Production Quantity (EPQ) Finite-Rate Lot-Size Formula
Calculate an idealized finite-rate production lot, peak inventory and annual setup-plus-holding cost, deriving daily demand from annual demand on a consistent operating-day basis.
Read the guide →FinanceEconomic Value Added (EVA), NOPAT & ROIC vs WACC Economic Spread
Calculate Net Operating Profit After Tax NOPAT = EBIT * (1 - Tax), Economic Value Added EVA = NOPAT - (Invested_Capital * WACC), and the ROIC - WACC value-creation spread.
Read the guide →Dates and reportingEDATE function: add calendar months and handle month-end clipping
Schedule monthly equipment checks from a start date with EDATE, and see why anchoring offsets to the original start date preserves the 31st after February.
Read the guide →ScienceEddington Luminosity Limit & Black-Hole Accretion Rate Formula
Compute a hydrogen electron-scattering Eddington luminosity and the associated rest-mass inflow at a chosen radiative efficiency, using consistent luminosity units and retaining very small nonzero rates.
Read the guide →Powertrain Test Cells & Driveline Braking, Eddy-Current Dynamometer & Retarder PhysicsEddy-Current Dynamometer Torque, Critical RPM & Cooling
Calculate Speed Ratio (N / Ncrit), Kloss-Type Skin-Effect Braking Torque (N·m), Absorbed Rotor Thermal Power (kW), and Required Cooling-Water Flow at 25 K Rise (L/min).
Read the guide →Healthcare & Clinical CalculationsEdinburgh Postnatal Depression Scale (EPDS) & Item-10 Safety Override
Score the 10-item Edinburgh Postnatal Depression Scale (0–30) for antepartum and postpartum mood screening while enforcing an immediate Item-10 self-harm safety override regardless of total score.
Read the guide →Power Electronics, Ultracapacitor Energy Storage & Pulse-Power SizingEDLC Supercapacitor 75% Usable Energy & ESR Drop Formula
Calculate Electric Double-Layer Supercapacitor (EDLC) Usable Extractable Energy (Wh) Between V_max and Converter Cutoff V_min, Usable Energy Fraction (75% at 0.5*V_max), Instantaneous ESR Voltage Sag (V), and Matched-Impedance Peak Power (kW).
Read the guide →Statistical & Clinical AnalysisEdmonton Frail Scale (EFS 0–17) Formula: 9-Domain Perioperative & Geriatric Frailty Tier
Calculate Darryl B. Rolfson et al.’s (2006) 17-point Edmonton Frail Scale across all 9 clinical domains (Cognition clock-draw, General health, Functional independence, Social support, Medication polypharmacy/adherence, Nutrition, Mood, Continence, and Timed Up & Go performance) to stratify Fit (0–5), Vulnerable (6–7), and Mild/Moderate/Severe Frailty (8–17).
Read the guide →FinancialEFFECT function: convert stated APR into effective annual interest rate (APY)
Compare loan or savings offers with different compounding frequencies on an apples-to-apples annual basis using EFFECT.
Read the guide →FinanceEffective Duration & Key-Rate Duration (Callable Bond Finite Difference)
Calculate effective duration, convexity and individual key-rate sensitivities from supplied repriced bond values, with a reproducible three-tenor example and input validation.
Read the guide →Lookup & ReferenceEffective-Date Rate & Price Lookup by Transaction Date (XLOOKUP Mode -1 & VLOOKUP)
Resolve the historical price, billing rate, or FX rate in effect on any transaction date using XLOOKUP with match_mode = -1 (exact or next earlier effective date) while guarding dates prior to contract inception.
Read the guide →Statistical & Clinical AnalysisEgger’s Linear Regression Test: Funnel Plot Asymmetry & Small-Study Publication Bias
Detect small-study publication bias in meta-analysis by regressing Standardized Normal Deviate SND_i = θ_i / SE_i on Precision P_i = 1 / SE_i via INTERCEPT and SLOPE.
Read the guide →Consumer Panel Analytics & Brand Growth ScienceEhrenberg NBD Brand Penetration & Double Jeopardy Formula
Calculate Andrew Ehrenberg’s Negative Binomial Distribution (NBD) Non-Buyer Share P_0 = (1 + m/k)^(-k), Household Penetration b = 1 - P_0, Average Purchase Frequency per Buyer w = m/b, and Duplication of Purchase D*b_Y.
Read the guide →Engineering & ScienceEinstein Quantum Solid Molar Heat Capacity (CV) vs. Dulong-Petit 3R Limit
Calculate quantized lattice molar heat capacity C_V = 3 * R * (theta_E / T)^2 * EXP(theta_E / T) / (EXP(theta_E / T) - 1)^2 (J/(mol*K)) and % of the classical Dulong-Petit 3R = 24.943 J/(mol*K) limit.
Read the guide →Civil, Structural & Geotechnical EngineeringEinstein-Brown Bedload Transport Formula: Stochastic Low-Shear & 40 * theta^3 Law
Calculate river and coastal bedload transport intensity Phi across stochastic incipient saltation (theta < 0.18) and sheet-flow high-shear transport (Phi = 40 * K_R * theta^3) using Hans Albert Einstein (1942) and Carl B. Brown (1950).
Read the guide →Healthcare & Clinical CalculationsEl-Ganzouri Multivariate Airway Risk Index (EGRI) for Difficult Intubation
Calculate Abdel Raouf El-Ganzouri’s 7-variable preoperative airway score (0–12 points across Mouth Opening, Thyromental Distance, Mallampati Class, Neck Mobility, Jaw Protrusion, Body Weight, and Prior Difficult Intubation).
Read the guide →Fluid-Power Sealing, Parker / AS568 Elastomer O-Ring Glands, Squeeze & ExtrusionElastomer O-Ring Squeeze % & Gland Fill Swell Formula
Calculate Linear Diametral Interference Squeeze (mm), Percentage Cross-Sectional Squeeze (%), Swollen-Elastomer Rectangular Gland Fill (%), and Parker Static Gland Compliance.
Read the guide →EngineeringElectricity kWh and utility cost calculator formula (Watts to $ bill)
Estimate energy use and the energy component of a bill from average input power, operating hours and a flat tariff.
Read the guide →Turbine-Blade Superalloy Non-Traditional Machining, ECM Faraday Equilibrium Gap & Joule BoilElectrochemical Machining (ECM) Gap & Brine Boiling Formula
Calculate Anodic Dissolution Current Density J (A/cm²), Self-Regulating Equilibrium Inter-Electrode Gap heq (mm), Total Rectifier Current (A), and Brine Joule Temperature Rise (°C).
Read the guide →Engineering & ScienceElectron-Positron Pair & Triplet Production Gamma Threshold Formula
Evaluate gamma-ray nuclear pair-production threshold (2 * m_e * c^2 = 1.022 MeV), atomic-electron triplet-production threshold (4 * m_e * c^2 = 2.044 MeV), and total lepton kinetic energy K_e- + K_e+ = E_gamma - 1.022 MeV.
Read the guide →Nanomaterials, HEPA Filtration & Tissue Scaffolds, Taylor-Cone ElectrospinningElectrospinning Taylor-Cone Critical Voltage & GSM Formula
Calculate G. I. Taylor Critical Cone-Jet Onset Voltage Vc (kV), Mean Inter-Electrode Field Vc/H (kV/cm), Dry Nanofiber Production Rate (g/h), and Nonwoven Mat GSM (g/m²).
Read the guide →Chemical, Process & Catalysis EngineeringEley-Rideal Catalytic Rate Law Formula & Apparent Reaction Order Diagnostic
Compute Daniel Eley and Eric Rideal’s (1940) gas-surface collision rate r_ER = k_ER * K_A * P_A * P_B / (1 + K_A * P_A) and Apparent Reaction Order n_app,A = 1 / (1 + K_A * P_A) to distinguish Eley-Rideal from Langmuir-Hinshelwood kinetics.
Read the guide →VLSI Physical Design & Semiconductor InterconnectsElmore RC Wire Delay & Repeater Insertion Formula
Calculate Distributed-Line Elmore RC Time Constant tau_D, 50% Propagation Delay t_p50 = 0.69 * tau_D, Naive Lumped-RC Overprediction Error, and Bakoglu Optimal CMOS Repeater Count.
Read the guide →Operations, Logistics & EngineeringElovich (Roginsky-Zeldovich) Chemisorption Kinetics Formula: Uptake q(t) & Rate Decay
Model activated chemisorption on energetically heterogeneous catalysts, biochars, and soils using the integrated Elovich kinetic equation q(t) = (1 / beta) * LN(1 + alpha * beta * t) and instantaneous rate dq/dt = alpha * EXP(-beta * q).
Read the guide →CRM Lifecycle Marketing & Growth AnalyticsEmail Deliverability, CTOR vs CTR & List Churn Formula
Calculate Delivered Rate, Open Rate on Delivered, Click-to-Open Rate (CTOR = Unique_Clicks / Unique_Opens) vs Unique CTR, Opt-Out Rate, and Net Subscriber List Growth.
Read the guide →HR & Payroll AnalyticsEmployee Salary Band Lookup, Compa-Ratio & Pay-Range Penetration Formulas
Join employee grades to compensation band minimums, midpoints, and maximums with XLOOKUP to compute Compa-Ratio, Range Penetration %, and Green-Circle / Red-Circle outlier flags.
Read the guide →Civil, Structural & Geotechnical EngineeringEngelund-Hansen (1967) Total Alluvial Sand-Bed Sediment Transport Formula
Calculate total bed-material sediment load (bedload + suspended sand across dunes and upper-plane beds) via Frank Engelund and Eggert Hansen’s (1967, DTU) energy-balance law f_EH * Phi = 0.1 * theta^2.5 (Phi = 0.05 * (V^2 / (g * R_h * S)) * theta^2.5).
Read the guide →Statistical & Clinical AnalysisEngland-Fraser & Shine-Lal Formulas: Automated Coulter Counter Thalassemia Screening
Screen microcytic CBCs for beta-thalassemia carrier status using England & Fraser’s linear discriminant DF = MCV - RBC - 5*Hb - 3.4 (< 0 Thalassemia vs. > 0 IDA) and Shine & Lal’s high-sensitivity index 0.01 * MCV² * MCH (< 1530).
Read the guide →FinancialEnterprise value bridge, EBITDA multiple and a simplified Tobin’s Q proxy
Calculate a simplified enterprise-to-equity bridge and compare total claim value with estimated replacement assets, with explicit units and assumptions.
Read the guide →Dates and reportingEOMONTH function: find the last day of any reporting month
Calculate month-end closing dates from any mid-month transaction date, handling 28-day and 29-day Februaries as well as December-to-January year rollovers.
Read the guide →Operations & Supply ChainEOQ with Planned Backorders: Optimal Lot Size, Peak On-Hand & Max Shortage
Extend classical Wilson EOQ when customers tolerate backorders at finite annual shortage cost b, computing critical fill fraction b/(h+b), expanded lot size Q*, peak inventory, and annual cost savings.
Read the guide →Mechanical Machine Design, Gearboxes & EV Powertrain KinematicsEpicyclic Planetary Gear Willis Speed Ratio & Torque Formula
Calculate Coaxial Mesh Planet Tooth Count N_p, Fixed-Ring Sun-to-Carrier Speed Reduction Ratio (1 + N_r / N_s), Carrier Output Speed (RPM), and Carrier Output Torque (N·m).
Read the guide →Supply Chain & Inventory OptimizationEppen Inventory Risk Pooling & Square-Root Law Formula
Calculate centralized safety stock z * sigma * SQRT(N * (1 + (N - 1)*rho)) via Gary Eppen’s (1979) risk-pooling formula and quantify how demand correlation erodes Square-Root Law savings.
Read the guide →Healthcare & ClinicalEpworth Sleepiness Scale (ESS): 8-Item Daytime Somnolence Score (0–24)
Sum the 8 situational dozing probabilities (0 = would never doze to 3 = high chance of dozing, total 0 to 24 points) of Murray Johns's Epworth Sleepiness Scale and stratify normal vs. mild, moderate, and severe excessive daytime sleepiness.
Read the guide →EngineeringErgun Packed-Bed Pressure Drop Formula (Catalyst & Filter Columns)
Build a guarded SI-unit spreadsheet for Ergun fixed-bed pressure loss, separating viscous and inertial contributions and testing sensitivity to flow, particle size and porosity.
Read the guide →OperationsErlang B Trunk Blocking & Erlang C Multi-Server Call Center Delay (M/M/c)
Calculate Agner Krarup Erlang's exact c=3 server Blocking Probability B(3, A), queueing Delay Probability C(3, A) = 3*B / (3 - A*(1 - B)), and Average Speed of Answer (ASA in seconds) from offered traffic Erlangs A = lambda / mu.
Read the guide →Energy Systems & Sustainability AnalyticsEROI & Net Energy Cliff Buffered Grid Formula
Calculate raw and storage-buffered Energy Return on Investment EROI = E_out*(1 - f_curt)/(E_inv + E_stor) and expose Charles Hall’s nonlinear Net Energy Cliff 1 - (1 / EROI).
Read the guide →Formula Auditing & LogicError-Proof a Complex Formula Chain: Targeted Stage Gates vs. Blanket IFERROR
Harden multi-step lookup, multiplication, and division pipelines by isolating missing lookup keys (IFNA), non-numeric text inputs (ISNUMBER), and zero denominators separately instead of masking bugs with IFERROR(..., 0).
Read the guide →Engineering & ScienceEucken & Modified Eucken Polyatomic Gas Thermal Conductivity Formula
Estimate dilute polyatomic gas thermal conductivity k = (μ / M) * (C_v + 2.25 * R) and Modified Eucken k_mod = (μ / M) * (1.32 * C_v + 1.77 * R) (mW/(m·K)) from gas viscosity and molar heat capacity.
Read the guide →EngineeringEuler Column Buckling Load formula: P_cr = PI()^2 * E * I / (K * L)^2
Explore the ideal elastic Euler buckling load and its dependence on effective length, without treating it as a structural design rating.
Read the guide →Portfolio Construction & RiskEuler Portfolio Risk Decomposition: Marginal and Component Volatility
Decompose multi-asset portfolio volatility into exact additive Component Risk CR_i = w_i * (Sigma * w)_i / sig_p and Percentage Risk Contribution in Excel and Arte Sheets.
Read the guide →Healthcare & Clinical CalculatorsEuroSCORE II Cardiac Surgery In-Hospital Mortality Logistic Formula
Convert EuroSCORE II patient, cardiac, and operative log-odds β coefficients into predicted surgical mortality (%) = 100 / (1 + EXP(-(-5.324537 + Σ β_i x_i))).
Read the guide →Statistical & Clinical AnalysisEUTOS & Sokal CML Risk Scores: Chronic Myeloid Leukemia TKI Prognosis
Calculate the European Treatment and Outcome Study score EUTOS = 7 * Basophils_% + 4 * Spleen_cm (<= 87 Low vs. > 87 High Risk) alongside Sokal’s exponential hazard ratio in newly diagnosed chronic-phase CML.
Read the guide →Semiconductor Photolithography & OpticsEUV Lithography Rayleigh CD & Depth of Focus Formula
Calculate Photolithography Minimum Printable Half-Pitch CD = k_1 * (lambda / NA), Rayleigh Depth of Focus DOF = k_2 * (lambda / NA^2), Minimum Pitch 2 * CD, and Transistor Area Scaling.
Read the guide →Electric Vehicle Battery Packs, BMS Hardware & LFP/NMC Cell BalancingEV BMS Passive Bleed Resistor Balancing Time & Heat Formula
Calculate Excess Imbalance Charge Delta_Q (Ah), Peak Shunt Bleed Current I_bleed (mA), Duty-Cycle Average PCB Resistor Heat P_avg (mW), and Full Top-Balancing Time (hours).
Read the guide →EV Battery Pack Architecture, Cell-to-Pack (CTP) Integration & Energy DensityEV Cell-to-Pack (CTP) Gravimetric & Volumetric Efficiency Formula
Calculate Nominal Pack Energy (kWh), Gravimetric Cell-to-Pack Mass Ratio GCTP (%), Volumetric Cell-to-Pack Space Utilization VCTP (%), and Pack-Level Specific Energy (Wh/kg).
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