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Samuelson Iceberg Trade Cost & CIF/FOB Wedge Formula
Convert customs CIF and FOB prices into Paul Samuelson’s (1954) iceberg factor tau = P_CIF / P_FOB >= 1, melting loss share (tau - 1) / tau, and Eaton-Kortum trade attenuation tau^(-theta).
Read the guide →Public Economics & Mechanism DesignSamuelson Public-Good Rule & Lindahl Benefit Price Formula
Sum marginal willingness-to-pay schedules vertically via Samuelson’s rule SUM(MRS_i) = MC_G, compare against free-rider voluntary provision, and solve Lindahl benefit prices.
Read the guide →Healthcare & ClinicalSan Francisco Syncope Rule (CHESS Mnemonic) for 7-Day Serious Outcome Risk
Evaluate the 5-item San Francisco Syncope Rule (CHESS: CHF history, Hematocrit < 30%, Abnormal ECG, Shortness of breath, triage Systolic BP < 90 mmHg) to flag high-risk emergency syncope.
Read the guide →Foundry Mold Engineering, Archimedes Metallostatic Core Lift & Chaplet DesignSand-Casting Core Buoyancy & Top Chaplet Load Formula
Calculate Dry Resin-Sand Core Weight (N), Upward Molten-Metal Archimedes Buoyancy (N), Net Upward Core Float Force (N), and Factored Top-Chaplet Hold-Down Load (N).
Read the guide →Healthcare & Clinical CalculatorsSAPS 3 (Simplified Acute Physiology Score 3) First-Hour ICU Mortality
Sum the three SAPS 3 ICU admission boxes (Box I Patient History, Box II Admission Circumstances, Box III First-Hour Acute Physiology) and evaluate Moreno et al.’s (2005) global mortality equation!
Read the guide →Healthcare & Clinical FormulasSAPS II Score & Le Gall Predicted ICU Hospital Mortality (%)
Sum Physiology (0–116), Age (0–18), Admission Type (0, 6, 8), and Chronic Disease (0, 9, 10, 17) points into total SAPS II (0–163) and evaluate Jean-Roger Le Gall’s log-linear mortality equation.
Read the guide →Statistical & Clinical AnalysisSARC-F Sarcopenia Screening Score (0–10) Formula: EWGSOP2 Muscle Loss Triage
Calculate the 5-item SARC-F Sarcopenia Screening Score (Strength, Assistance in walking, Rise from chair, Climb stairs, Falls; 0–2 points each, total 0–10) recommended by EWGSOP2 as the first-step case-finding screen (>= 4 positive).
Read the guide →Econometrics & Causal InferenceSargan-Hansen Overidentifying Restrictions J-Statistic Formula
Calculate Sargan’s J = N * R^2_aux overidentification statistic with df = L_excl - K_endog and catch the exact-identification trap (L_excl = K_endog -> df = 0).
Read the guide →Satellite Communications & RF Systems EngineeringSatellite EIRP, G/T & Carrier-to-Noise C/N0 Formula
Calculate Effective Isotropic Radiated Power EIRP_dBW = P_tx + G_tx - L_feed, Carrier-to-Noise Spectral Density C/N_0 = EIRP - L_path + G/T + 228.6 dB-Hz, and Digital Demodulator E_b / N_0.
Read the guide →Semiconductor Thin-Film Deposition & Vacuum MetrologySauerbrey QCM Thin-Film Mass & Frequency Shift Formula
Calculate Vacuum PVD/ALD Thin-Film Areal Mass Density (ug/cm^2 = 0.1 * t_nm * rho_g_cm3), AT-Cut Quartz Sauerbrey Sensitivity C_f = 2.264 * f_0_MHz^2, Crystal Resonance Drop Delta_f (Hz), and 2% Crystal Replacement Gate.
Read the guide →Operations Research & Inventory ManagementScarf Distribution-Free Min-Max Newsvendor Formula
Hedge unknown demand tail shapes using Herbert Scarf’s (1958) distribution-free min-max newsvendor order Q* = mu + (sigma / 2) * (SQRT(beta / (1 - beta)) - SQRT((1 - beta) / beta)).
Read the guide →Healthcare & Clinical FormulasScatchard Plot Linear Regression: Dissociation Constant Kd & Bmax
Extract equilibrium receptor-ligand dissociation constant K_d = -1 / SLOPE(B/F, B) (nM) and total receptor site density B_max = -INTERCEPT(B/F, B) / SLOPE(B/F, B) from radioligand or SPR saturation binding assays.
Read the guide →Engineering & ScienceScheibel Liquid Diffusivity Correlation (Organic Solute–Solvent Molar Volume)
Estimate dilute organic liquid molecular diffusivity D_AB = 0.0082 * T * (1 + (3 * V_B / V_A)^(2/3)) / (μ_B * V_A^(1/3)) (× 10^-5 cm^2/s) without empirical association factors!
Read the guide →Engineering & ScienceScheil-Gulliver Solidification Equation: Dendrite Coring & Non-Equilibrium Eutectic Fraction
Calculate local solid composition C_S = k * C0 * (1 - f_S)^(k - 1) during casting solidification and predict non-equilibrium interdendritic eutectic fraction f_E = (C_E / C0)^(-1 / (1 - k)).
Read the guide →Operations, Logistics & EngineeringSchmertmann Strain Influence Factor (I_z) Formula: Sand Footing Immediate & Creep Settlement
Calculate shallow foundation settlement on granular sand soils using John H. Schmertmann’s (1970/1978) strain-influence method S = C_1 * C_2 * delta_q * SUM(I_z * dz / E_s) with embedment relief C_1 and creep factor C_2.
Read the guide →Statistical & Clinical AnalysisSchoenfeld Formula: Log-Rank / Cox Survival Trial Required Events & Sample Size
Power Phase III oncology and cardiovascular time-to-event trials using David A. Schoenfeld’s 1983 asymptotic Cox/log-rank formula E = ROUNDUP((z_alpha/2 + z_beta)² / (p * (1 - p) * (LN(HR))²), 0) and total enrollment N = ROUNDUP(E / P_event, 0).
Read the guide →Clinical Medicine & PhysiologySchofield Pediatric BMR Calculator: Weight-Only & Weight-Height Equations (Ages 0–18)
Calculate infant, child, and adolescent Basal Metabolic Rate (kcal/day) across (< 3 yr, 3–10 yr, and 10–18 yr) sex-specific age bands using W. N. Schofield’s (1985) pediatric nutrition equations.
Read the guide →Financial ModelingSchwager Gain-to-Pain Ratio (GPR) & 90/10 Tail Ratio Asymmetry Formula
Evaluate CTA and hedge-fund return asymmetry without upside volatility punishment using Jack Schwager’s Gain-to-Pain Ratio SUM(r) / ABS(SUMIF(r, "<0")) and right-to-left Tail Ratio.
Read the guide →EngineeringSchwarzschild Black Hole Radius, Gravitational Time Dilation & Hawking Temp
Calculate the Schwarzschild event horizon radius R_s = 2*G*M / c^2, general-relativistic gravitational time dilation 1 / SQRT(1 - R_s / r), and Hawking radiation temperature.
Read the guide →Clinical Medicine & PhysiologySCOFF Questionnaire Calculator: 5-Item Anorexia & Bulimia Primary-Care Screen
Score John F. Morgan et al.’s (1999, BMJ) 5-question SCOFF eating-disorder screening tool (0–5 Yes responses; >= 2 cutoff flags likely anorexia nervosa or bulimia nervosa for diagnostic evaluation).
Read the guide →Healthcare & Clinical FormulasSCORAD Index & Objective oSCORAD for Atopic Dermatitis (Eczema)
Calculate total SCORAD = A/5 + 3.5*B + C (0–103) and Objective oSCORAD = A/5 + 3.5*B (0–83) from BSA extent A (0–100%), 6-sign intensity B (0–18), and pruritus + sleep-loss VAS C (0–20) to guide biologic therapy eligibility.
Read the guide →Math & TrigScore quiz or exam answers automatically against an answer key
Compare student response rows against a locked answer-key row inside SUMPRODUCT for both equal-point and weighted-question exams.
Read the guide →Psychometrics & Inter-Rater ReliabilityScott’s Pi Pooled-Marginal Agreement Formula vs Cohen’s Kappa Bias
Expose systematic rater threshold bias by comparing Scott’s (1955) pooled-marginal pi against Cohen’s (1960) separate-marginal kappa on 2x2 annotation tables.
Read the guide →TextScreen email addresses for common structural problems
Use five spreadsheet checks to flag obvious email-entry mistakes. This heuristic does not establish complete syntax validity, mailbox existence, or deliverability.
Read the guide →Bulk Solids Processing, CEMA Screw/Auger Conveyors, Grain & Cement Silo FeedingScrew Conveyor Flight Pitch & Trough Loading Capacity Formula
Calculate Net Annular Flight Area (m²), Inclined Volumetric Throughput Q_v (m³/h), Horizontal Zero-Incline Mass Rate (t/h), and Derated Inclined Mass Capacity Q_m (t/h).
Read the guide →Lookup & ReferenceSearch a 2D Table Grid for a Value & Return Its Exact Cell Address
Find a nonblank text bin ID in a rectangular grid and return its worksheet address and aisle label, preserving empty grid positions and choosing the first row-by-row match.
Read the guide →Water Desalination Engineering, Membrane Separations & Energy Recovery DevicesSeawater Reverse Osmosis (SWRO) Osmotic & ERD Energy Formula
Calculate Seawater Reverse Osmosis (SWRO) Concentrate Brine Osmotic Pressure Barrier (bar), Exit Net Driving Pressure (bar), Unrecovered Pump Specific Energy Consumption (kWh/m³), and Isobaric Pressure-Exchanger ERD Specific Energy Consumption SEC (kWh/m³).
Read the guide →Solid Mechanics & Structural DesignSecant Formula for Eccentrically Loaded Column Stress
Compute nonlinear P-Delta maximum compressive stress sigma_max = (P/A) * (1 + (e*c/r^2) / COS((L_eff/(2*r)) * SQRT(P/(E*A)))) and guard against Euler buckling.
Read the guide →Date & TimeSECOND function: extract seconds (0-59) and compute total duration in seconds
Pull the 0-59 seconds component from spreadsheet time serials with SECOND, and combine HOUR, MINUTE, and SECOND for total elapsed seconds.
Read the guide →Civil, Structural & Geotechnical EngineeringSeed-Idriss Soil Liquefaction Formula: Cyclic Stress Ratio CSR & Factor of Safety
Evaluate earthquake-induced sand liquefaction using H. Bolton Seed and I. M. Idriss’s (1971 / NCEER) Simplified Procedure: compute depth stress-reduction r_d, Cyclic Stress Ratio CSR, and Liquefaction Factor of Safety FS_liq = (CRR_7.5 * MSF) / CSR.
Read the guide →Lookup & ReferenceSelect columns with a header-driven horizontal FILTER mask
Build a smaller output view using literal header comparisons and a horizontal keep mask; source columns remain in the workbook.
Read the guide →Warehouse Structural Racking, ANSI/RMI MH16.1 Beam Deflection & Material StorageSelective Pallet-Rack Beam Deflection (L/180) Formula
Calculate Uniform Load Per Front/Rear Step Beam (kN), Midspan Elastic Beam Deflection delta (mm), ANSI/RMI MH16.1 L/180 Serviceability Limit (mm), and Deflection Utilization (%).
Read the guide →Lookup & ReferenceSelf-Contained Inline Lookup Mapping with SWITCH & CHOOSE
Map plan codes, regions, or 1..N priority integers directly to discount rates and labels inside a single self-contained SWITCH or CHOOSE formula without maintaining an external helper table.
Read the guide →Real Estate Operations, Self-Storage REITs & Revenue ManagementSelf-Storage Economic Occupancy & ECRI Rent-Roll Formula
Calculate Self-Storage REIT Move-In Concession & Bad-Debt Drag ($k), Existing Customer Rate Increase (ECRI) Lift ($k), Net Collected Rental Revenue ($k), and Economic Occupancy (%).
Read the guide →Engineering & ScienceSellmeier Refractive Index Dispersion Equation & Abbe Number (Vd) for Optical Glass
Calculate wavelength-dependent refractive index n(lambda) via the 3-term Schott Sellmeier equation SQRT(1 + SUM((Bi * lambda^2) / (lambda^2 - Ci))) and chromatic Abbe number Vd = (nd - 1) / (nF - nC).
Read the guide →Heavy-Duty Vehicle Suspension, Semi-Elliptic Multi-Leaf Springs & StiffnessSemi-Elliptic Multi-Leaf Spring Stress & Deflection Formula
Calculate Total Leaf Count n = nf + ng, Uniform-Strength Leaf Bending Stress (MPa), Central Camber Deflection (mm), and Suspension Spring Rate k (N/mm).
Read the guide →Semiconductor Manufacturing & Fab EconomicsSemiconductor Wafer DPW, Poisson & Murphy Yield Formula
Calculate Edge-Corrected Gross Dies per Wafer (DPW), Poisson Random-Defect Yield EXP(-D_0*A), Bernard Murphy’s Triangular Yield ((1 - EXP(-D_0*A))/(D_0*A))^2, Seeds Yield 1/(1 + D_0*A), and Cost per Good Die.
Read the guide →EngineeringSensible heat Q = mcΔT: convert kJ to kWh and estimate ideal heating time
Calculate thermal energy Q = m * Cp * (T_out - T_in) in kilojoules, convert to kWh (/ 3600), and solve heating recovery time at Heater kW.
Read the guide →FinancialSensitivity analysis table with formulas: mixed references ($A3 and B$1)
Build live 1-variable and 2-variable financial sensitivity grids (e.g., Interest Rate x Loan Term) with mixed $ references that recalculate instantly anywhere.
Read the guide →Dynamic arraysSEQUENCE function: generate dynamic row numbers and weekly date lists
Spill consecutive ticket numbers or 7-day inspection schedules from a single cell without dragging fill handles down the sheet.
Read the guide →Date & TimeSequence of workdays and month-end dates (holiday-aware schedule)
Generate consecutive business days skipping weekends and holidays with WORKDAY(Start - 1, Step, Holidays) alongside rolling month-end closes.
Read the guide →EngineeringSeries vs Parallel System Reliability & active redundancy formula (PRODUCT)
Compare series and active-parallel mission reliability under independent failures and a common mission horizon.
Read the guide →LogicalShade alternating groups of N rows (ISEVEN, QUOTIENT & ROW)
Calculate alternating fixed-height row-band flags and block numbers, with a positive integer band height.
Read the guide →EngineeringShaft Torsional Shear Stress (16T / pi*d^3) & Twist Angle (TL / GJ) formulas
Calculate elastic stress magnitude and signed twist for an ideal uniform solid circular shaft under pure torsion.
Read the guide →Engineering & ScienceShah In-Tube Two-Phase Condensation Heat-Transfer Correlation Formula
Calculate local annular/shear-driven condenser tube heat-transfer coefficient h_TP = h_L * ((1 - x)^0.8 + (3.8 * x^0.76 * (1 - x)^0.04) / p_r^0.38) across refrigerants and steam.
Read the guide →EngineeringShannon-Hartley channel capacity (Mbps) & RF dBm-to-milliwatt formulas
Calculate theoretical maximum wireless throughput B * LOG(1 + 10^(SNR_dB/10), 2) and convert RF link-budget power between dBm and milliwatts.
Read the guide →StatisticalShannon-Wiener Diversity Index (H'), Hill Number EXP(H') & Pielou's Evenness
Calculate ecological species diversity H' = -SUM(p_i * LN(p_i)), effective equal-abundance species EXP(H'), and Pielou's Evenness J' = H' / LN(S).
Read the guide →Labor Economics & Personnel EconomicsShapiro-Stiglitz No-Shirking Efficiency Wage Formula
Compute the Shapiro-Stiglitz No-Shirking Condition wage w_NSC(u) = b + e + (e/q)*(r + s/u) and solve involuntary equilibrium unemployment u* against MPL.
Read the guide →Economics & Market MicrostructureShapley Value Formula (3-Player Cooperative Game): Exact Coalition Marginal Allocation
Compute the fair Shapley Value payoff allocation for a 3-player cooperative game (marketing attribution, joint logistics, or R&D consortium) across all 3! = 6 arrival permutations and verify grand-coalition efficiency.
Read the guide →Cooperative Game Theory & GovernanceShapley-Shubik Weighted Voting Power Index Formula
Calculate Lloyd Shapley and Martin Shubik’s (1954) exact 6-permutation pivotal voting power index for three shareholder blocks or legislative parties against quota Q.
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