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Preston Equation CMP Material Removal Rate (MRR) Formula
Calculate CMP Material Removal Rate MRR (nm/min) from Slurry Preston Coefficient, Downforce Pressure (kPa) & Relative Velocity (m/s), Polish Time (sec), and WIWNU Thickness Spread (nm).
Read the guide →Bridge & Structural Engineering, Post-Tensioned & Pre-Tensioned ConcretePrestressed Concrete Tendon Kern Point & Fiber Stress Formula
Calculate Section Kern Radius k = S / A (m), Top-Fiber Concrete Service Stress f_top (MPa, Compression +), Bottom-Fiber Service Stress f_bot (MPa), and Class U Uncracked Status.
Read the guide →Data Validation & CleaningPrevent Duplicate Entries (Normalized TRIM + UPPER Uniqueness Rule vs. Plain COUNTIF)
Block both exact and whitespace-padded stealth duplicates ("INV-101" vs. " inv-101 ") by pairing UPPER(TRIM(A2)) canonical keys with COUNTIF uniqueness rules.
Read the guide →Data Validation & AuditPrevent Split Allocations from Exceeding Total Pool or 100% Cap
Audit equity splits, cost-center allocations, and grant distributions so SUM($B$2:$B$6) never exceeds the master pool $E$2, reporting exact unallocated headroom or over-allocation excess.
Read the guide →Reliability Engineering & Maintenance OptimizationPreventive Age vs Block Replacement Renewal Cost Formula
Compare Barlow-Proschan Age Replacement C(T)/mu(T) against Block Replacement (c_p + c_f*M(T))/T and Run-to-Failure cost rates for increasing-hazard Erlang-2 lifetimes.
Read the guide →FinancialPrice Elasticity of Demand (Midpoint / Arc formula) & revenue impact check
Calculate symmetric Arc Price Elasticity ((Q2-Q1)/AvgQ) / ((P2-P1)/AvgP) to classify Elastic vs Inelastic demand and revenue change.
Read the guide →Engineering & SciencePriestley-Taylor Potential Evapotranspiration (PET) Radiation Formula
Calculate daily radiation-driven crop/watershed Potential Evapotranspiration PET = alpha_PT * (Delta / (Delta + gamma)) * ((R_n - G) / lambda_v) (mm/day) using the FAO-56 Tetens vapor-pressure slope Delta.
Read the guide →LogicalPrioritize example shipping workflow rules with IFS
Use an illustrative IFS decision tree to route special-handling flags before express requests and package-weight bands.
Read the guide →Statistical & Clinical AnalysisPRISM III Score Formula: Pollack Pediatric Risk of Mortality PICU Severity
Calculate Murray Pollack’s 5-subscore PRISM III physiological severity score (0–74 points across Cardiovascular/Neurologic, Acid-Base/Blood Gas, Chemistry, and Hematology) for 12-hour and 24-hour PICU benchmarking.
Read the guide →Healthcare & Clinical FormulasPRISMA-7 Frailty Screening Questionnaire (With Reverse-Scored Item 6)
Calculate the 7-item PRISMA-7 geriatric frailty screening score (0–7)—properly reverse-scoring Question 6 ("Can you count on someone close to you?": No = +1 point!)—to flag >= 3 for Comprehensive Geriatric Assessment.
Read the guide →Quantitative Finance & Backtest AuditingProbabilistic Sharpe Ratio (PSR) Formula with Skewness and Kurtosis
Audit backtested Sharpe ratios against negative skewness, fat tails, and multiple-testing benchmarks SR_0 using Bailey and López de Prado’s Probabilistic Sharpe Ratio.
Read the guide →Market Microstructure & Quantitative TradingProbability of Informed Trading (PIN) & Spread Formula
Calculate Easley, Kiefer, O’Hara, and Paperman’s (1996) Probability of Informed Trading PIN = (alpha * mu) / (alpha * mu + epsilon_b + epsilon_s) and Bayesian opening bid-ask quotes.
Read the guide →StatisticalProcess capability Cp and Cpk: spread and centering
Measure manufacturing spread Cp = (USL - LSL)/(6*SD) and off-center capability Cpk = MIN((USL - Mean)/(3*SD), (Mean - LSL)/(3*SD)).
Read the guide →Geotechnical Earthwork QA/QC, ASTM D698 / D1557 Proctor Compaction & Zero-Air-VoidsProctor Soil Compaction Dry Density & ZAV Curve Formula
Calculate In-Situ Dry Unit Weight gamma_d = gamma_m/(1+w) (kN/m³), Theoretical 100%-Saturated Zero-Air-Voids Ceiling gamma_ZAV (kN/m³), Relative Proctor Compaction (%), and >= 95% Spec Gate.
Read the guide →MathPRODUCT function: multiply chained yield factors and sequential discounts
Multiply an entire column of growth multipliers or manufacturing stage yields with PRODUCT while skipping blank and text cells.
Read the guide →Math & TrigProject completion percentage: task count vs effort-weighted progress
Avoid false progress spikes on small chores by weighting each task's % complete by budgeted hours with SUMPRODUCT.
Read the guide →Date & TimeProject midpoint date and % schedule time elapsed (calendar vs workdays)
Find a calendar-date midpoint and an inclusive workday schedule ratio.
Read the guide →Behavioral Economics & Decision AnalysisProspect Theory Value & Prelec Weighting Formula
Evaluate reference-dependent gains and losses via Kahneman and Tversky’s (1992) asymmetric value function v(x) and Drazen Prelec’s (1998) inverse-S probability weight w(p) = EXP(-((-LN(p))^gamma)).
Read the guide →Healthcare & ClinicalPSI / PORT Pneumonia Severity Index (Fine Score Classes II–V) Formula
Compute Michael Fine’s Pneumonia Severity Index (PSI / PORT score) from age, sex (-10 female adjustment), nursing-home residency, comorbidities, vitals, and labs to stratify CAP into Risk Classes II–V.
Read the guide →Engineering & SciencePsychrometric Humidity Ratio (g/kg) & Moist Air Specific Enthalpy (ASHRAE / Arden Buck)
Calculate saturation vapor pressure Pws via the Arden Buck equation, humidity ratio W = 0.621945 * Pw / (Patm - Pw) in g/kg dry air, and moist-air specific enthalpy h in kJ/kg dry air.
Read the guide →Industrial Dust Collection, Fabric Filtration & Fan SizingPulse-Jet Baghouse Gross vs Net Air-to-Cloth Ratio Formula
Calculate Pulse-Jet Baghouse Single-Bag Area (ft²), Gross Air-to-Cloth Velocity (fpm), Net (N-1 Compartment Offline) Air-to-Cloth Velocity (fpm), and Filter Cake Pressure Drop (in. w.g.).
Read the guide →Autonomous Sensing, Photonics & LiDAR SystemsPulsed ToF LiDAR Power & Unambiguous Range Formula
Calculate Laser Time-of-Flight Round-Trip Delay (ns), Extended-Target Lambertian Received Power P_rx = P_pk * rho * (D^2 / (4 * R^2)) * eta, and Maximum Unambiguous PRF Range.
Read the guide →Composites Manufacturing, Pultrusion Heated-Die Residence Time, Pull Force & Line SpeedPultrusion Composite Die Residence Time & Pull Force Formula
Calculate Heated-Die Cure Residence Time (s), Net Fiber Cross-Section Area (mm²), Viscous-Gelation Die Wall Pull Force (kN), and Continuous Profile Mass Output (kg/h).
Read the guide →EngineeringPump NPSHa (Net Positive Suction Head Available) & Cavitation Margin formula
Estimate available suction head from a large reservoir and compare it with a supplied pump requirement and an explicit illustrative margin.
Read the guide →Grid-Scale Long-Duration Storage, Hydropower Engineering & Power MarketsPumped-Storage Hydro Reservoir MWh & Grid Arbitrage Formula
Calculate Pumped-Storage Hydropower (PSH) Upper-Reservoir Gravitational Potential Energy (MWh = 2.725 * Mm³ * Head_m), Generated MWh Delivered, AC-to-AC Round-Trip Efficiency, and Full-Cycle Duck-Curve Arbitrage Margin ($).
Read the guide →Engineering & SciencePurcell Factor (F_P) & β-Factor Spontaneous Emission Enhancement Formula
Calculate Edward Purcell’s cavity QED spontaneous emission enhancement F_P = (3 / (4 * π^2)) * (Q / V_norm) and single-photon waveguide coupling efficiency β = F_P / (F_P + 1).
Read the guide →FinancialPurchasing Power Parity (PPP) implied FX rate & currency over/under-valuation
Compare an illustrative matched-basket price ratio with a spot rate and model an inflation-ratio scenario. These are not forecasts of fair market exchange rates.
Read the guide →Analytical Chemistry & Pharmaceutical QCPurnell Chromatography Peak Resolution Rs Formula
Calculate Retention Factor k_2 = (t_R2 - t_0) / t_0, Selectivity Factor alpha = k_2 / k_1, Purnell Master Resolution R_s = (SQRT(N)/4) * ((alpha - 1)/alpha) * (k_2 / (1 + k_2)), and USP R_s >= 1.5 Separation Gate.
Read the guide →TextPut double quotes inside a formula: "" escaping vs CHAR(34)
Generate quoted CSV fields, JSON payloads, and HTML attributes cleanly using doubled "" quotes or readable CHAR(34).
Read the guide →Financial analysisPV function: find the maximum loan a monthly budget can support
Discount a fixed monthly repayment stream back to today’s affordable loan principal with PV, and verify how rising interest rates shrink borrowing capacity.
Read the guide →Math & Everyday CalculationsPythagorean Theorem Formula: Hypotenuse, Missing Leg & 3D Box Diagonal
Calculate right-triangle hypotenuse c = SQRT(a^2 + b^2), solve for an unknown leg b = SQRT(c^2 - a^2) with triangle-inequality validation, and find 3D shipping-crate space diagonal d = SQRT(L^2 + W^2 + H^2).
Read the guide →StatisticalPythagorean Win Expectation formula (Bill James Sports Analytics)
Compare observed wins with a scoring-based Pythagorean model estimate, using an explicitly chosen exponent.
Read the guide →Restaurant & Retail Operations, Multi-Unit Franchising & Unit EconomicsQSR Franchise Royalty, Four-Wall EBITDA & Cash-on-Cash Formula
Calculate Quick-Service Restaurant (QSR) Franchise Gross-Sales Royalty + National Brand Ad-Fund Assessment ($), Net Franchisee Four-Wall EBITDA ($), Unlevered Buildout Cash-on-Cash Return, and Simple Capex Payback Period (Years).
Read the guide →Charts & Data VisualizationQuadrant Chart (2x2 Matrix) Formula: Crosshair-Centered XY & Quadrant Classifier
Build a 2x2 Strategic Quadrant Scatter Chart (BCG Growth-Share, Value-vs-Effort, Price-vs-Quality) by centering coordinates at origin (X - X_cut, Y - Y_cut) so plot axes form natural crosshairs and classifying items into Q1–Q4.
Read the guide →Industrial Organization & Spatial PricingQuadratic Hotelling Maximal Differentiation Price Formula
Calculate d’Aspremont, Gabszewicz, and Thisse’s (1979) quadratic-transport spatial Nash equilibrium prices p_1* = c + t*(1 - a - b)*(1 + (a - b)/3) and prove maximal product differentiation.
Read the guide →Mergers & Acquisitions, Financial Due Diligence & Quality of EarningsQuality of Earnings (QoE) Adjusted & Pro-Forma EBITDA Formula
Calculate Buy-Side/Sell-Side Quality of Earnings (QoE) Normalized EBITDA (Reported EBITDA + Non-Recurring Add-Backs - Non-Operating Gains + Excess Owner Compensation), Full-Year Pro-Forma Run-Rate EBITDA, Implied Headline EV, and Add-Back Reliance Share.
Read the guide →Engineering & ScienceQuantum Barrier Tunneling (STM & Flash Oxide WKB Transmission Formula)
Calculate the evanescent wavefunction decay constant kappa = 5.12317 * SQRT((m_eff / m_0) * (V_0 - E)) (nm^-1) and exponential tunneling transmission probability T_WKB = EXP(-2 * kappa * L) across Scanning Tunneling Microscope (STM) vacuum gaps and gate oxides.
Read the guide →Thin-Film Optics, Camera Lenses, Solar PV Glass & PhotonicsQuarter-Wave Anti-Reflection (AR) Coating Thickness & R% Formula
Calculate Ideal Zero-Reflection Index SQRT(n_0 * n_s), Physical Quarter-Wave Film Thickness d (nm), Bare-Substrate Fresnel Reflectance (%), and Coated Quarter-Wave Reflectance (%).
Read the guide →RF & Microwave EngineeringQuarter-Wave Impedance Transformer (Z_T) and Off-Frequency VSWR
Size a quarter-wave matching section Z_T = SQRT(Z_0 * R_L) and compute exact off-frequency reflection |Gamma(f/f_0)| and VSWR across fractional bandwidths.
Read the guide →StatisticalQUARTILE.INC function: split salaries or deal sizes into Q1, median, and Q3 bands
Calculate the 25th, 50th, and 75th inclusive quartile cutoffs and interquartile range (IQR) with QUARTILE.INC.
Read the guide →Reinsurance & Insurance AccountingQuota-Share vs Surplus-Share Reinsurance Formula
Compare fixed Quota-Share cession against risk-sized First-Surplus-Share cession MIN(Max_Lines * Line, MAX(0, Sum_Insured - Line)) / Sum_Insured, Ceding Commission, and Net Retained Cash Flow.
Read the guide →MathQUOTIENT function: calculate full cases or whole hours without remainders
Return only the integer portion of division with QUOTIENT, and pair it with MOD to split totals into full packs plus leftovers.
Read the guide →Statistical & Clinical AnalysisR-ISS Multiple Myeloma Staging Formula: IMWG Beta-2-Microglobulin, Albumin, FISH & LDH
Stage newly diagnosed Multiple Myeloma using Antonio Palumbo’s IMWG Revised International Staging System (R-ISS I, II, III) combining Greipp’s ISS (B2M & Albumin) with high-risk interphase FISH [del(17p), t(4;14), t(14;16)] and serum LDH.
Read the guide →StatisticalR-Squared (R^2) and linear regression residuals formula
Measure how much variance an OLS trendline explains with CORREL(X, Y)^2 and compute fitted values and residuals Y - Y_hat.
Read the guide →Quantitative Finance & RiskRachev Ratio Formula: Upper Expected Tail Gain vs Lower Expected Tail Loss
Calculate the Rachev tail-asymmetry ratio in Excel and Arte Sheets by dividing upper beta-tail expected excess gain (right-tail ETL) by lower alpha-tail expected excess loss (CVaR).
Read the guide →Chemical, Process & Catalysis EngineeringRachford-Rice Isothermal VLE Flash Formula: Bubble/Dew Check & Objective f(V/F)
Test multicomponent feed phase stability (Subcooled Liquid SUM(z_i * K_i) <= 1, Superheated Vapor SUM(z_i / K_i) <= 1, or Two-Phase Flash) and evaluate H. H. Rachford and J. D. Rice’s (1952) monotonic flash residual f(psi).
Read the guide →Engineering & ScienceRackett Equation: Saturated Liquid Molar Volume & Density
Predict saturated liquid molar volume V_sat = V_c * Z_c^((1 - T / T_c)^(2/7)) (cm^3/mol) and mass density ρ_L = MW / V_sat (g/cm^3) for LPG storage tanks and pressurized liquid pipelines.
Read the guide →Charts & Data VisualizationRadar (Spider) Chart Formula: 0–100 Multi-Axis Normalization & Polygon Area
Normalize incommensurate KPI units (dollars, milliseconds, percentages) onto a common 0–100 Radar / Spider Chart spoke scale (with polarity inversion for lower-is-better metrics) and compute enclosed K-spoke polygon area.
Read the guide →MathRADIANS function: convert degree angles before SIN, COS, and TAN
Convert compass bearings and incline angles from degrees to radians with RADIANS so spreadsheet trigonometry produces accurate ratios.
Read the guide →Industrial Radiography (RT), Ir-192 / X-Ray Weld Inspection & ASME Sec V Article 2Radiographic NDT Geometric Unsharpness (Ug) & SFD Formula
Calculate Source-to-Object Distance D_o = SFD - t (mm), Penumbra Geometric Unsharpness U_g = F*t/(SFD - t) (mm), Minimum Code Source-to-Film Distance SFD_min (mm), and ASME Sec V Compliance.
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