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ISO week number and YYYY-Www label formula (year-boundary safe)
Calculate exact ISO-8601 week numbers (1–53) and ISO week-years ("2026-W53") using Thursday-anchor date math that works in every spreadsheet.
Read the guide →Power Electronics & Isolated AC-DC Supply DesignIsolated Flyback Converter Duty Cycle & Vds Stress Formula
Calculate Coupled-Inductor Flyback Reflected Primary Voltage V_ref = (V_out + V_f)*(N_p/N_s), CCM Duty Cycle D = V_ref / (V_in + V_ref), Peak Primary MOSFET Drain-Source Stress V_ds_pk, and 80%-Derated Breakdown Headroom.
Read the guide →Healthcare & ClinicalISTH Overt DIC Diagnostic Score Calculator (0–8 Points)
Calculate the International Society on Thrombosis and Haemostasis (ISTH) overt DIC score (0–8 points) from platelet count, D-dimer tier, PT prolongation, and fibrinogen.
Read the guide →MathIV rate unit-conversion exercises: drops/minute and mL/hour
Practice spreadsheet dimensional analysis with fictional infusion inputs. These exercises are not a validated dosing or pump-setting tool.
Read the guide →StatisticalJaccard Similarity Index & Hamming Distance formulas (SUMPRODUCT)
Compare binary feature sets and equal-length codes via Jaccard Similarity |A n B| / |A u B| (ignoring shared 0-0 absences) and Hamming Distance mismatch count.
Read the guide →Business & OperationsJackson Open Queueing Network: Total WIP & End-to-End Sojourn Time
Analyze multi-station M/M/1 manufacturing, hospital, or microservice networks with rework loops using Jackson's Theorem: L = SUM(lambda_i / (mu_i - lambda_i)) and Little's Law W = L / gamma_ext.
Read the guide →Operations Research & QueueingJackson Queueing Network Rework Traffic Equations and Lead Time
Solve Jackson’s (1957) rework traffic balance lam_eff = lam_ext / (1 - p_rework), station utilizations, total WIP, and Little’s Law customer cycle time without throughput errors.
Read the guide →Clinical Medicine & PhysiologyJackson-Pollock 3-Site Skinfold Calculator: Body Density & Siri Body Fat % (Men & Women)
Calculate caliper skinfold sum S_3 (mm), quadratic Whole-Body Density D_b (g/cm^3), and Siri Percent Body Fat using Jackson & Pollock (1978, Men: Chest + Abdomen + Thigh) and Jackson, Pollock & Ward (1980, Women: Triceps + Suprailiac + Thigh).
Read the guide →Civil, Structural & Geotechnical EngineeringJanbu Simplified Noncircular Slope Stability Formula: Correction Factor f_0 & FS_J
Analyze shallow translational and composite noncircular slip surfaces using Nilmar Janbu’s Simplified Method: compute empirical interslice shear correction f_0 = 1 + b_1 * ((d / L) - 1.4 * (d / L)^2) and corrected FS_J = f_0 * FS_0.
Read the guide →Statistical & EconometricJanoschek Growth Curve Formula: Bounded Sigmoidal Size & Inflection Age
Model nonzero-birth biological and forestry growth L(t) = L_∞ - (L_∞ - L_0) * EXP(-k * t^p) and compute exact analytical inflection age t_inf = ((p - 1) / (k * p))^(1 / p).
Read the guide →Bulk Solids Mechanics, Eurocode EN 1991-4 Grain/Cement Silo Design & Janssen TheoryJanssen Silo Wall Friction & Pressure Saturation Formula
Calculate Janssen Characteristic Screening Depth z0 (m), Saturated Vertical Floor Pressure Pv(z) (kPa), Lateral Silo Wall Hoop Pressure Ph(z) (kPa), and Naive Hydrostatic Fluid Overprediction (kPa).
Read the guide →StatisticalJarque-Bera Normality Test: Skewness & Excess Kurtosis Chi-Square P-Value
Test whether regression residuals or asset returns follow a normal distribution using the Jarque-Bera statistic JB = (n / 6) * (S^2 + (K_excess^2 / 4)) and exact df = 2 exponential p-value EXP(-JB / 2).
Read the guide →ScienceJeans Length & Jeans Mass Formula (Star-Formation Cloud Collapse)
Calculate the isothermal Jeans wavelength and the mass in a sphere of half that wavelength. Keep the linear-perturbation convention consistent and explore temperature and density scaling in a live worksheet.
Read the guide →Statistical & Clinical AnalysisJeffreys Beta(0.5, 0.5) Binomial Posterior Mean & Standard Deviation Formula
Estimate rare-event and zero-numerator binomial proportions without collapsing to 0% using Harold Jeffreys’ invariant Beta(1/2, 1/2) posterior mean (x + 0.5)/(n + 1) and exact posterior standard deviation.
Read the guide →Corporate Governance & Capital StructureJensen Free Cash Flow Agency & Debt Discipline Formula
Model Michael Jensen’s (1986) Free Cash Flow overinvestment agency loss and quantify how mandatory debt service curbs negative-NPV empire building before triggering underinvestment.
Read the guide →Corporate Governance & Agency TheoryJensen-Meckling Outside-Equity Agency Cost Formula
Calculate managerial perk extraction F* = (1 - alpha)/k_u, realized equity value, and exact residual agency deadweight loss (1 - alpha)^2 / (2*k_u) under diluted inside ownership.
Read the guide →Financial ModelingJensen’s Alpha (CAPM Abnormal Return) & Systematic Beta Return Attribution
Decompose realized portfolio return into risk-free carry, systematic market-beta exposure, and manager selection skill (Jensen’s Alpha = R_p - [R_f + beta * (R_m - R_f)]).
Read the guide →Engineering & ScienceJoback Group-Contribution Method: Boiling Point (T_b) & Critical Temp (T_c)
Estimate pure-component normal boiling point T_b = 198.2 + SUMPRODUCT(n, ΔT_b) and Lydersen-Joback critical temperature T_c = T_b / (0.584 + 0.965*ΣΔT_c - (ΣΔT_c)^2) directly from functional group counts.
Read the guide →EngineeringJohnson–Euler Column Curve: Critical Stress and Transition
Calculate a piecewise Johnson–Euler critical-stress estimate, use the unrounded transition slenderness and convert stress to load with consistent units.
Read the guide →Operations & AnalyticsJohnson’s Rule Two-Machine Flow-Shop Makespan (Cmax) & Utilization
Classify jobs into Johnson’s Rule Group 1 (M1 <= M2, sort ascending M1) vs. Group 2 (M1 > M2, sort descending M2) and compute exact 4-job flow-shop makespan Cmax and Machine 2 utilization.
Read the guide →Text & String CleaningJoin Date and Text Without Raw Serial Numbers (TEXT "yyyy-mm-dd" Formula)
Embed formatted ISO dates and rounded invoice amounts cleanly inside dynamic text sentences using TEXT(date_cell, "yyyy-mm-dd") so concatenation never prints raw serial numbers like "Due on 46157".
Read the guide →TextJoin dates with text in report headers (and auto-updating copyright years)
Prevent raw date serial numbers like 46143 when concatenating report titles by wrapping dates in TEXT(..., "yyyy-mm-dd") and YEAR.
Read the guide →Lookup & ReferenceJoin Two Tables with INDEX & MATCH (Relational SKU Enrichment & Team Review)
Perform SQL-style left joins between an order transaction log and a SKU master catalog—pulling Category and Unit Price regardless of column order while flagging unmapped SKUs.
Read the guide →Supply Chain & Inventory OptimizationJoint Replenishment Shared Major/Minor Setup Formula
Coordinate multi-SKU supplier shipments via the Joint Replenishment Problem (JRP) optimal cycle time T* = SQRT(2*(S_0 + SUM(s_i)) / SUM(D_i*H_i)) and quantify savings vs independent EOQ.
Read the guide →Nonparametric Statistics & Clinical TrialsJonckheere-Terpstra Ordered-Group Trend Statistic Formula
Test monotonic trend across independent ordered dose groups using the Jonckheere-Terpstra pairwise Mann-Whitney sum J = U_12 + U_13 + U_23 and exact null moments.
Read the guide →Macroeconomics & Innovation EconomicsJones Semi-Endogenous R&D Growth & Spillover Formula
Calculate steady-state idea growth g_A* = (lambda * n) / (1 - phi), transitional R&D surge, and permanent TFP level gain (s_R1 / s_R0)^(lambda / (1 - phi)).
Read the guide →Pore-Pressure Detection & Well Control, Jordan-Shirley (1966) d & Corrected dc ExponentJordan-Shirley Drilling d-Exponent & dc Overpressure
Calculate Bit Penetration per Revolution (ft/rev), Jordan-Shirley Raw d-Exponent, Rehm-McClendon Mud-Weight Corrected dc-Exponent, and Normal Compaction Trend Ratio (%).
Read the guide →Engineering & ScienceJosephson Junction AC Frequency (KJ) & Ambegaokar-Baratoff Critical Current (Ic)
Calculate the AC Josephson oscillation frequency f_J = 0.4835979 * V_uV in GHz using the 2019 SI Josephson constant KJ = 2e/h, plus T=0 Ambegaokar-Baratoff critical current Ic = ((PI()/2) * Delta_meV) / Rn.
Read the guide →EngineeringJoukowsky Water Hammer Pressure Surge & Piezometric Head Rise
Estimate the ideal initial pressure rise from a sudden velocity reduction, its equivalent fluid head and the pipe round-trip wave time. Compare an entered closure time without treating the result as a pipe-safety certification.
Read the guide →Operations, Logistics & EngineeringJovanović (1969) Monolayer & Multilayer Adsorption Isotherm Formula: Mechanical Contact Model
Calculate equilibrium adsorption with mechanical bulk-molecule collision knock-off corrections using Dušan S. Jovanović’s (1969) monolayer isotherm q_e = q_max * (1 - EXP(-K_J * C_e)) and multilayer extension.
Read the guide →Economics & Market MicrostructureKakwani Tax Progressivity & Reynolds-Smolensky Redistribution Index Formula
Decompose how much a tax system reduces income inequality using Nanak Kakwani’s Progressivity Index K = C_T - G_X and the Reynolds-Smolensky Net Redistribution identity RS = G_X - G_Y = (t / (1 - t)) * K - D_rerank.
Read the guide →Game Theory & Joint-Venture NegotiationKalai-Smorodinsky vs Nash Bargaining Split Formula
Allocate joint-venture surplus via Ehud Kalai and Meir Smorodinsky’s (1975) proportional ideal-point rule (u_1 - d_1)/(b_1 - d_1) = (u_2 - d_2)/(b_2 - d_2) when individual payoff caps bind.
Read the guide →StatisticalKanban Bin / Card Count & On-Time In-Full (OTIF) supply chain formulas
Calculate a simplified replenishment-container estimate and measure the share of five complete shipment records that are both on time and in full.
Read the guide →Engineering & Fluid MechanicsKandlikar Flow Boiling Correlation Formula: Convective Number Co & Two-Phase Heat Transfer
Calculate in-tube evaporator and cold-plate flow-boiling heat transfer using Satish G. Kandlikar’s 1990 Convection Number Co = ((1 - x)/x)^0.8 * (rho_g / rho_l)^0.5 and convective-dominant boiling branch h_TP = h_LO * (1.136 * Co^(-0.9) + 667.2 * Bo^0.7 * F_fl).
Read the guide →Financial ModelingKaplan-Knowles Kappa-3 Ratio & Third-Order Lower Partial Moment (LPM3)
Penalize severe left-tail crashes more strictly than Sortino’s quadratic LPM2 by dividing excess return over MAR by the cube root of third-order Lower Partial Moment LPM_3.
Read the guide →StatisticalKaplan-Meier Survival Estimator & Exponential Median Survival formulas
Calculate validated Kaplan–Meier steps with a small censored follow-up table, and distinguish them from a separate constant-hazard exponential median.
Read the guide →Engineering & ScienceKapustinskii & Born-Landé Ionic Crystal Lattice Energy Formula (kJ/mol)
Estimate ionic crystal lattice enthalpy U_L = ((-120,200 * nu * |z+ * z-|) / (r+ + r-)) * (1 - 34.5 / (r+ + r-)) in kJ/mol from Shannon/thermochemical ionic radii (pm) without needing crystal structure!
Read the guide →Healthcare & ClinicalKarnofsky Performance Status (KPS 0–100) to ECOG / Zubrod Crosswalk
Convert oncology Karnofsky Performance Status deciles (0–100 in steps of 10) into validated EORTC / Buccheri ECOG-Zubrod Performance Grades (0–5) and Phase II/III clinical-trial eligibility.
Read the guide →Clinical Medicine & PhysiologyKatch-McArdle BMR (370 + 21.6 * LBM) & Boer (1984) Lean Body Mass Calculator
Calculate sex-neutral Basal Metabolic Rate RDEE = 370 + 21.6 * LBM_kg via Frank I. Katch and William D. McArdle’s equation, paired with P. Boer’s (1984) isotope-validated Lean Body Mass formulas when DXA/skinfolds are unavailable.
Read the guide →Healthcare & Clinical CalculationsKatz Index of Independence in Activities of Daily Living (ADL 0–6)
Score Sidney Katz’s foundational 6-domain geriatric Basic ADL scale (0–6 across Bathing, Dressing, Toileting, Transferring, Continence, and Feeding) for home-care, rehab, and nursing-facility placement.
Read the guide →Platform Economics & Network EffectsKatz-Shapiro Network Compatibility Equilibrium Formula
Solve Michael Katz and Carl Shapiro’s (1985) Fulfilled-Expectations Cournot Equilibrium under open standard compatibility q* = (A - c)/(N + 1 - N*v) versus proprietary incompatibility q* = (A - c)/(N + 1 - v).
Read the guide →Powder Metallurgy, Battery Cathode Calendering & Pharma Bulk Handling, Kawakita ModelKawakita Powder Volume Reduction & Cohesiveness Formula
Calculate Kawakita Engineering Volume Strain C (%), Compressed Bed Volume V (mL), Reciprocal Yield/Cohesion Pressure 1/b (MPa), and Asymptotic Packing Realization (%).
Read the guide →Climate Policy & Energy AnalyticsKaya Identity Emissions & Decarbonization Rate Formula
Compute total CO2 via Yoichi Kaya’s (1990) 4-factor identity Pop * (GDP/Pop) * (E/GDP) * (CO2/E) and solve the required carbon-intensity decline rate to meet net-zero pathways.
Read the guide →Engineering & ScienceKeldysh Parameter (γ_K): Multiphoton vs. Tunneling Ionization Formula
Calculate Leonid Keldysh’s strong-field adiabaticity parameter γ_K = 5.1232 * E_ph * SQRT(m_eff * I_p) / F to classify ultrafast laser excitation into multiphoton (γ_K > 1) or optical tunneling (γ_K < 1) regimes.
Read the guide →FinancialKelly Criterion position-sizing formula: Full Kelly, Half-Kelly & edge guard
Explore the mathematical Kelly fraction for a repeated binary payoff model and compare a fractional allocation.
Read the guide →Quantitative Finance & TradingKeltner Channel & Volatility Squeeze Formula: True Range, ATR Envelope & Squeeze Flag
Build Linda Raschke’s ATR-based Keltner Channel (EMA +- m * ATR), compute Wilder’s gap-aware True Range, and detect Bollinger-inside-Keltner Volatility Squeezes.
Read the guide →Engineering & ScienceKelvin Equation: Nanodroplet Vapor Pressure & Capillary Condensation RH
Calculate convex aerosol nanodroplet supersaturation ratio P / P_sat = EXP(+2 * γ * V_m / (r * R * T)) and concave silica-mesopore capillary condensation relative humidity RH_cond (%) = 100 * EXP(-2 * γ * V_m / (r * R * T)).
Read the guide →StatisticalKendall's Tau (tau-a & tau-b) & Somers' D Rank Concordance formulas
Measure ordinal rating and credit-scorecard rank agreement from Concordant (C), Discordant (D), and Tied pairs via Tau-a, tie-adjusted Tau-b, and Somers' D.
Read the guide →Engineering & Fluid MechanicsKern Shell-Side Nusselt & Square-Pitch Equivalent Diameter Formula
Perform preliminary shell-and-tube exchanger sizing using Donald Q. Kern’s square-pitch hydraulic diameter De = 4*(Pt² - pi*do²/4)/(pi*do) and turbulent shell correlation Nu_s = 0.36 * Re_s^0.55 * Pr^(1/3) * (mu/mu_w)^0.14.
Read the guide →Macroeconomics & Consumption TheoryKimball Prudence & Precautionary Saving Wedge Formula
Calculate Miles Kimball’s (1990) Coefficient of Relative Prudence P = gamma + 1, precautionary equivalent income haircut psi = 0.5*(gamma + 1)*sigma^2, and log-Euler consumption growth.
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