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Spreadsheet arithmetic for a simplified alveolar gas equation and P/F ratio
Use fictional values to practice pressure units and ratios; this example does not diagnose respiratory disease or recommend treatment.
Read the guide →MathSpreadsheet arithmetic with fictional blood-pressure and laboratory values
Practice approximate MAP, an anion-gap subtraction and a historical albumin-adjusted calcium calculation, with explicit units and limitations.
Read the guide →Credit Analysis & Forensic AccountingSpringate S-Score & Zmijewski Distress Formula
Cross-validate private-firm credit risk without market-cap inputs using Gordon Springate’s (1978) 4-factor S-Score (0.862 cutoff) and Mark Zmijewski’s (1984) distress index.
Read the guide →Charts & Visual Data ModelingSprint Burndown Chart Formula: Ideal Remaining Line, Daily Velocity & Completion Forecast
Build an agile Sprint Burndown table and line chart: compute Ideal Remaining Story Points P_0 * (1 - d / D), Schedule Variance, Realized Daily Velocity, and Projected Days to Zero.
Read the guide →MathSQRT function: calculate square roots, diagonal distances, and standard error
Compute principal square roots for geometry, EOQ inventory sizing, and sample standard error (s / SQRT(n)) with SQRT.
Read the guide →Math & TrigonometrySquare Root of n*Pi and Gaussian Normal Density Formulas (SQRTPI)
Calculate sqrt(n * pi) normalizing constants, standard normal peak height 1 / (sigma * sqrt(2*pi)), and Gaussian bell-curve ordinates using SQRT and PI.
Read the guide →Site Reliability Engineering & Cloud OpsSRE SLO Error Budget & Burn-Rate Alert Formula
Calculate monthly SLO error-budget minutes, dimensionless Burn Rate = Error_Rate / (1 - SLO), hours to exhaustion, and Google SRE 14.4x fast-burn paging thresholds.
Read the guide →Engineering & ScienceSRH, Radiative & Auger Recombination Lifetime + Diffusion Length
Combine defect-mediated Shockley-Read-Hall (τ_SRH), band-to-band radiative (B·Δn), and three-particle Auger (C_a·Δn^2) recombination rates into effective minority-carrier lifetime τ_eff (μs) and diffusion length L = SQRT(D·τ_eff) (μm).
Read the guide →Industrial Organization & Game TheoryStackelberg Leader-Follower Duopoly Output & Profit Formula
Solve backward-induction Stackelberg leader output q_L* = (a - 2*c_L + c_F)/(2*b), follower output q_F* = MAX(0, (a - c_F - b*q_L*)/(2*b)), market price, and first-mover profit gain over Cournot.
Read the guide →Math & TrigStaffing FTE & shrinkage formula: why you divide by (1 - Shrinkage%)
Convert contact-center or back-office volume and Average Handle Time into Workload Hours, Productive FTEs, and Shrinkage-grossed Headcount.
Read the guide →Statistical AnalysisStandard Error of Measurement (SEM) & 95% Minimal Detectable Change (MDC95)
Convert baseline standard deviation and test-retest reliability (ICC) into Standard Error of Measurement SEM = SD * SQRT(1 - ICC) and two-measurement Minimal Detectable Change MDC_95.
Read the guide →Statistical AnalysisStandard Normal Cumulative Probability, GAUSS Band & Inverse Quantile (NORM.S.DIST & NORM.INV)
Compute left-tail normal probabilities Phi(z), center-to-z GAUSS intervals Phi(z) - 0.5, and inverse normal quantile cutoffs x = mu + z_p * sigma using portable rational polynomials.
Read the guide →Engineering & ScienceStanton Number (St) & Chilton-Colburn jH Heat-Momentum Analogy Formula
Calculate the dimensionless Stanton Number St = Nu / (Re * Pr) and Chilton-Colburn heat-transfer factor j_H = St * Pr^(2/3) to estimate convective heat transfer directly from Fanning skin-friction drag (j_H ~ f / 2).
Read the guide →Semiconductor Yield Engineering & VLSIStapper Negative-Binomial & Bose-Einstein Yield Formula
Calculate Charles Stapper’s Negative-Binomial Clustered Wafer Yield Y_NB = (1 + D_0 * A / alpha)^(-alpha), Bose-Einstein Single-Layer Yield (alpha = 1), and Multi-Mask Critical-Layer Bose-Einstein Yield.
Read the guide →Microvascular Physiology, Nephrology & Critical Care MedicineStarling Capillary Filtration & Oncotic Edema Formula
Calculate Microvascular Outward Hydrostatic Gradient (Pc - Pi), Staverman-Weighted Inward Oncotic Pull sigma*(pi_c - pi_i), Net Starling Filtration Pressure (mmHg), and Transcapillary Fluid Flux Jv (mL/min).
Read the guide →Descriptive statisticsSTDEV.S vs STDEV.P: measure sample variation vs full population spread
Know when to divide squared deviations by n - 1 (STDEV.S for quality samples) or n (STDEV.P for complete populations), and why a single reading returns #DIV/0!.
Read the guide →Clinical Pharmacokinetics & Dosing RegimensSteady-State Accumulation R_ac & Loading Dose Formula
Calculate repeated-dosing Accumulation Index R_ac = 1 / (1 - EXP(-k_el * tau)), Steady-State Peak C_max,ss, Steady-State Trough C_min,ss, and exact Loading Dose D_load = D_maint * R_ac.
Read the guide →Industrial Steam Systems, Boiler Water Chemistry & Energy RecoverySteam Boiler TDS Blowdown Rate & Flash Heat Loss Formula
Calculate Steam Boiler TDS Cycles of Concentration, Continuous Drum Blowdown Mass Rate (kg/hr), Unrecovered Sensible Blowdown Heat Loss (kW), and Flash-Economizer Heat Recovery (kW).
Read the guide →Petrochemical Olefins, Naphtha Steam Cracking & Pyrolysis FurnacesSteam Cracker Ethylene/Propylene (P/E) Ratio & Steam Formula
Calculate Polymer-Grade Ethylene Output (t/hr), Co-Product Propylene Output (t/hr), Cracking Severity P/E Weight Ratio, and Furnace Dilution Steam Rate (t/hr).
Read the guide →Hydrogen Engineering, Chemical Process Synthesis & Carbon CaptureSteam-Methane Reforming (SMR) H2 & Blue CO2 Intensity Formula
Calculate SMR Hydrogen Plant Total Methane Demand (t/day), Net Specific CO2 Intensity (kg CO2 / kg H2), Daily Captured CO2 Sequestered (t/day), and Residual Stack Emissions (t/day).
Read the guide →Metallurgical Heat Treatment, Gear Gas/Vacuum Carburizing & Fick’s Second LawSteel Gas Carburizing Harris Case-Depth & Time Formula
Calculate Arrhenius Carburizing Diffusion Factor KT (mm/sqrt(hr)), Required Furnace Soak Hours (t = (ECD/KT)²), Case Depth Achieved at 4 Hours (mm), and Total Cycle Minutes.
Read the guide →Structural Steel Stability, AISC 360 / Eurocode 3 Beams & LTBSteel I-Beam Lateral-Torsional Buckling (Mcr) Formula
Calculate Pure St. Venant Torsional Buckling Term (kN·m), Combined Timoshenko Elastic Critical LTB Moment M_cr (kN·m) including Flange Warping C_w, and Warping Stiffness Boost (%).
Read the guide →Charts & Data VisualizationStem-and-Leaf Plot Formula: Tens Stem Extraction, Leaf Digit & Bin Frequency
Construct John Tukey’s Exploratory Data Analysis (EDA) Stem-and-Leaf display in a spreadsheet by splitting observations into integer Stems INT(x / 10), Trailing Leaf Digits MOD(x, 10), and Per-Stem Bin Frequencies COUNTIFS.
Read the guide →Lookup & ReferenceStep across every Nth column when dragging a formula down rows (INDEX & ROW)
Pull values from every Nth horizontal column (e.g., B2, D2, F2) into a vertical summary list as you copy a formula down rows using non-volatile INDEX and ROW.
Read the guide →Charts & Visual Data ModelingStep Chart Formula: Piecewise-Constant Rate Staircase Coordinates & Time-Weighted Average
Plot discrete jumps (central-bank policy rates, SaaS pricing tiers, inventory reorders) accurately as a true Step Chart instead of misleading diagonal slopes, and calculate the exact Time-Weighted Average Rate!
Read the guide →Mechatronics, CNC Motion Control & 3D Printing, Hybrid Stepper Motor DynamicsStepper Motor Microstep Resolution & Corner Speed Formula
Calculate Microsteps per Revolution, Ballscrew Linear Microstep Resolution (um), Required Step-Pulse Frequency (kHz), and Inductive L/R Chopper Corner Speed (RPM).
Read the guide →Additive Manufacturing & Photopolymer 3D Printing, SLA Jacobs Working Curve Cure DepthStereolithography (SLA) Jacobs Cure Depth & Overcure Formula
Calculate Gaussian Centerline Peak UV Exposure Emax (mJ/cm²), Jacobs Beer-Lambert Cure Depth Cd (um), Interlayer Stitching Overcure Cd - z (um), and Cured Line Width (um).
Read the guide →Financial ModelingSterling Ratio & Burke Ratio: Multi-Drawdown Risk-Adjusted Portfolio Return
Evaluate CTA and hedge-fund drawdown resilience across multiple historical drawdown episodes using both the classical +10%-buffered Sterling Ratio and quadratic-penalty Burke Ratio.
Read the guide →Engineering & ScienceStern-Volmer Fluorescence Quenching (I0/I) & Förster FRET Energy Transfer Efficiency
Calculate collisional fluorescence quenching intensity ratio I0/I = 1 + kq * tau0 * [Q] via the Stern-Volmer equation and nanoscale Förster resonance energy transfer efficiency E = 1 / (1 + (r / R0)^6).
Read the guide →Statistical & Clinical AnalysisStewart Acid-Base Formula: Apparent Strong Ion Difference (SID_a) & Strong Ion Gap (SIG)
Unmask hyperchloremic acidosis and unmeasured anions in hypoalbuminemic ICU patients using Peter Stewart’s physicochemical SID_a, Figge-Fencl effective SID_e, and Strong Ion Gap SIG = SID_a - SID_e.
Read the guide →Engineering & ScienceStiel-Thodos High-Pressure & Supercritical Gas Residual Viscosity Formula
Calculate dense-fluid and supercritical CO₂ viscosity η = η_0 + Δη(ρ_r) (µPa·s) across pipelines and compressors using Leonard Stiel & George Thodos’s (1961) reduced-density correlation.
Read the guide →Produced-Water & Desalination Chemistry, ASTM D4582 Stiff-Davis Brine Scaling IndexStiff-Davis High-TDS Brine Scaling Index (SDSI) Formula
Calculate Molar Negative Log Calcium pCa, Molar Negative Log Bicarbonate Alkalinity pAlk, Stiff-Davis Ionic-Strength Temperature Constant K, and SDSI Scaling Index.
Read the guide →Banking, Credit Risk & Information EconomicsStiglitz-Weiss Credit Rationing Rate-Cap Formula
Calculate the Stiglitz-Weiss (1981) bank-optimal interest rate ceiling r_cap* = (R_S - u_0/p_S)/L - 1 and prove why raising loan rates above r_cap* slashes expected bank repayment.
Read the guide →Biophysics, Colloid & Nanoparticle Science & Dynamic Light ScatteringStokes-Einstein Nanoparticle Diffusion & RMS Walk Formula
Calculate Stokes-Einstein Brownian Translational Diffusion Coefficient D (µm²/s) from Temperature, Dynamic Viscosity, and Hydrodynamic Radius (nm), plus 3D and 1D Root-Mean-Square (RMS) Displacement (µm) and Characteristic Diffusive Transit Time.
Read the guide →EngineeringStokes' Law Terminal Settling Velocity & Laminar Re_p <= 1 Check
Calculate creeping-flow particle settling or rising velocity v_t = (g * d^2 * (rho_p - rho_f)) / (18 * mu) (mm/s) for clarifiers, emulsions, and falling-ball viscometers—with automatic Particle Reynolds Re_p verification.
Read the guide →Engineering & ScientificStokes’ Law Terminal Settling Velocity, Particle Reynolds Gate & Clarifier Capture
Calculate laminar gravitational settling velocity v_s = g*(rho_p - rho_f)*d^2 / (18*mu), validate creeping flow via particle Reynolds number Re_p <= 1, and check sedimentation basin capture.
Read the guide →EngineeringStokes's Law Terminal Settling Velocity & Particle Reynolds Check formulas
Calculate the ideal terminal speed of an isolated sphere in a Newtonian fluid and screen the estimated particle Reynolds number.
Read the guide →International Trade & General EquilibriumStolper-Samuelson & Rybczynski Magnification Formula
Solve Ronald Jones’s (1965) 2x2 Heckscher-Ohlin hat-algebra equations to verify Stolper-Samuelson factor-price magnification and Rybczynski endowment-output magnification.
Read the guide →Health & FitnessSTOP-BANG Obstructive Sleep Apnea (OSA) Screening Score Formula
Practice validated binary inputs and conditional formulas using the published 40-cm STOP-Bang scoring variant. Calculate the total and two-step screening category without treating missing answers as a low-risk result.
Read the guide →EngineeringStreeter-Phelps Dissolved Oxygen (DO) Sag Curve & Critical Time formulas
Model river dissolved oxygen depletion and recovery downstream of a wastewater discharge using Streeter-Phelps deficit D(t), remaining DO = DO_sat - D(t), and critical sag travel time t_c.
Read the guide →EngineeringStress, Strain, Young's Modulus & Factor of Safety formulas (PL / AE)
Calculate tensile stress (MPa = N / mm²), elastic elongation ΔL = (P · L) / (A · E), strain ε, and yield Factor of Safety.
Read the guide →Lookup & ReferenceStrict Single-Match Lookup (DGET Uniqueness Guard vs. Silent XLOOKUP First-Match)
Enforce primary-key uniqueness in lookup formulas by reproducing DGET's exact single-record behavior—returning the value when 1 row matches, NO_MATCH when 0 match, and DUPLICATE_KEY when 2+ rows collide.
Read the guide →TextStrip all numeric digits (0–9) from a text string (TEXTSPLIT & TEXTJOIN)
Remove digits 0–9 from display text, or replace digit and separator boundaries with spaces. Keep the original identifiers.
Read the guide →TextStrip HTML tags from text with a single formula (TEXTSPLIT + FILTER)
Extract text from simple balanced angle-bracket markup with TEXTSPLIT and FILTER; learn the limitations of this formula approach.
Read the guide →Engineering & ScienceStrömgren Sphere Radius (RS) & H II Nebula Recombination Timescale
Calculate the ionization-bounded H II region Strömgren radius RS = ((3 * Q_H) / (4 * PI() * n_H^2 * alpha_B))^(1/3) in parsecs and hydrogen recombination time t_rec = 1 / (n_H * alpha_B) in years.
Read the guide →ScienceStrong Allee Effect Population Growth & Critical Extinction Threshold
Calculate cubic strong Allee population growth rate dN/dt = r * N * (1 - N / K) * (N / A - 1), per-capita growth rate, and extinction-vortex vs carrying-capacity trajectory.
Read the guide →EngineeringStrouhal Number & Karman Vortex-Shedding Frequency Formula
Estimate stationary-cylinder shedding frequency and nominal frequency-match speed from a supplied Strouhal number, with a configurable comparison band that does not certify structural safety.
Read the guide →Operations & AnalyticsStudent Course Enrollment Tracker: Open Seats, Waitlist & Fill Rate
Tally live course registrations from a student roster using COUNTIF, calculate remaining open seats via MAX(0, Cap - Enrolled) and waitlist overflow via MAX(0, Enrolled - Cap), and classify section status.
Read the guide →Financial ModelingStutzer Performance Index: Skewness-Adjusted Sharpe & Cumulant Decay Rate
Adjust the Sharpe ratio for third-moment crash skewness using Michael Stutzer’s (2000) large-deviations information decay rate I_P and Sharpe-equivalent SQRT(2 * I_P).
Read the guide →TextSubstitute multiple values at once: template placeholders and mixed delimiters
Replace Name and Plan placeholders sequentially, or normalize the example’s mixed separators.
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