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Lapple Cyclone Cut-Diameter (d50) & Grade Efficiency Formula
Calculate Lapple Reverse-Flow Cyclone 50% Cut-Size Diameter d_p50 (µm), Fractional Grade Collection Efficiency (%), Dust Penetration (%), and 8-Velocity-Head Pressure Drop (Pa).
Read the guide →StatisticalLARGE and SMALL with criteria: Nth highest or lowest value by group
Combine LARGE or SMALL with FILTER to retrieve the 2nd largest deal or 2nd fastest time inside a category—beyond MAXIFS and MINIFS.
Read the guide →Descriptive statisticsLARGE, SMALL, and RANK.EQ: extract Nth values and handle ties
Pull the 1st, 2nd, or 3rd highest and lowest numbers without sorting the table, see how tied scores repeat in LARGE and skip ranks in RANK.EQ, and catch #NUM! bounds.
Read the guide →High-Temperature Metallurgy, Gas Turbine Superalloys & Creep MechanicsLarson-Miller Creep-Rupture Life & Monkman-Grant Formula
Calculate Superalloy Log10 Creep-Rupture Hours from the Larson-Miller Parameter LMP = (T_K / 1000)*(C_LM + LOG10(t_r)), Predicted Rupture Life t_r (hours), Monkman-Grant Steady-State Creep Rate, and Overhaul Life Margin.
Read the guide →Additive Repair & Surface Hardfacing, Coaxial Laser Cladding / DED Dilution & CatchmentLaser Cladding Dilution Ratio & Powder Catchment Formula
Calculate Metallographic Clad Dilution Ratio (%), Deposited Alloy Mass Rate (g/min), Coaxial Powder Catchment Efficiency (%), and Specific Laser Energy (J/mm²).
Read the guide →CNC Turning, Carbide Insert Nose Geometry & Surface Metrology (ISO 4287)Lathe Turning Surface Roughness Ra & Rz Nose-Radius Formula
Calculate Schmaltz Kinematic Peak-to-Valley Roughness R_z (um), Exact Parabolic Arithmetic Average Roughness R_a (um), Finish Cut Cycle Time (s), and ISO N-Grade Finish Check.
Read the guide →Cardiovascular Biomechanics, Cardiology & Vascular SurgeryLaw of Laplace Cardiac & Aneurysm Wall Stress Formula
Calculate Spherical Left-Ventricular Myocardial Afterload Wall Stress (P*r)/(2*h), Cylindrical Aortic Aneurysm Circumferential Hoop Stress (P*r)/h in mmHg and kPa, and Geometric Stress Amplifier r/(2*h).
Read the guide →Healthcare & Clinical CalculationsLawton-Brody Instrumental Activities of Daily Living (IADL 0–8)
Assess executive community-living independence (0–8 points across Telephone, Shopping, Food Preparation, Housekeeping, Laundry, Transportation, Medication Responsibility, and Finances) to detect early dementia and care needs.
Read the guide →Personnel Economics & Executive CompensationLazear Deferred Seniority Wage & Performance Bond Formula
Calculate Edward Lazear’s (1979) incentive-compatible senior wage w_2* = w_alt + s_shirk, junior underpayment performance bond VMP_1 - w_1*, and mandatory buyout/retirement surplus gap.
Read the guide →Personnel Economics & Executive CompensationLazear-Rosen Tournament Prize Spread & Effort Formula
Design rank-order promotion tournaments via Edward Lazear and Sherwin Rosen’s (1981) optimal prize spread W_1 - W_2 = p / g(0), equilibrium effort, and participation-constrained pay levels.
Read the guide →Private Equity & Leveraged BuyoutsLBO Value-Creation Bridge, MoIC & Gross IRR Formula
Calculate Private Equity LBO Sponsor Entry/Exit Equity, Multiple on Invested Capital (MoIC), Gross IRR = MoIC^(1/T) - 1, and exact EBITDA-Growth / Multiple-Expansion / Debt-Paydown value attribution.
Read the guide →MathLCM function: find shared maintenance intervals and common denominators
Calculate the smallest positive cycle where two or more repeating schedules align simultaneously using LCM.
Read the guide →Process Safety Management, Combustion Engineering & Hazard AnalysisLe Chatelier Flammable Gas Mixture LEL & NFPA 69 Formula
Calculate Mixed Combustible-Gas Concentration in Air (vol%), Le Chatelier Mixture Lower Explosive Limit LEL_mix (vol%), Stream %LEL Fraction, and NFPA 69 25% LEL Interlock Status.
Read the guide →Business & OperationsLean Heijunka Pitch & Every Part Every Interval (EPEI) Level-Scheduling Formula
Calculate Toyota Production System Heijunka box Pitch = (Takt_Time * Pack_Qty) in minutes and mixed-model Every Part Every Interval EPEI = Total_Changeover_Min / (Available_Min - Daily_Run_Min) in days.
Read the guide →Learn with AILearn a formula with AI hints, then test it yourself
Practise order totals by finding a missing row, predicting the result and checking a changed input. Ask AI for a hint before asking it to solve the task.
Read the guide →FinancialLease vs. Buy NPV calculator: Net Advantage to Leasing (NAL) after taxes
Explore a simplified annual lease-versus-purchase cash-flow model with assumed usable tax relief, zero residual value and end-of-year payments.
Read the guide →LogicalLeave Inline Comments in Formulas (+ N("Note") & Self-Documenting LET)
Document complex audit logic directly inside spreadsheet formulas using the classic + N("Inline comment") zero-addition trick or modern LET(doc_note, "...", ...) named variables.
Read the guide →Portfolio Construction & RiskLedoit-Wolf Constant-Correlation Shrinkage Covariance Formula
Stabilize noisy sample covariance matrices in Excel and Arte Sheets using Ledoit-Wolf convex shrinkage Sigma_LW = (1 - delta)*S + delta*F toward a constant-correlation prior.
Read the guide →Econometrics & Randomized ExperimentsLee Trimming Bounds Formula for Differential Sample Attrition
Correct selective follow-up attrition in randomized trials using David Lee’s (2009) excess-observer trimming fraction p_trim = (s_T - s_C) / s_T and sharp quantile-trimmed bounds.
Read the guide →Cleaning imported dataLEFT function: extract a fixed-width prefix from structured codes
Pull a three-letter depot code from the start of consistent identifiers like NTH-014, and check what happens on shorter strings, blanks, and variable-length prefixes.
Read the guide →Credit Risk & Corporate FinanceLeland Endogenous Default Barrier, Debt Value, and Credit Spread Formula
Price perpetual risky corporate debt, equity-chosen endogenous bankruptcy threshold V_B, and levered firm value under Leland’s (1994) structural trade-off model.
Read the guide →Corporate Finance & Asymmetric InformationLeland-Pyle IPO Equity Retention Signaling Formula
Value Hayne Leland & David Pyle’s (1977) separating IPO valuation schedule V(alpha) = V_min - b*sigma^2*(LN(1 - alpha) + alpha) from insider ownership retention.
Read the guide →Healthcare & ClinicalLEMON Difficult Airway Score (0–10) & Mallampati Intubation Triage
Calculate Reed’s 0–10 point Emergency Department LEMON airway assessment score (Look externally, Evaluate 3-3-2, Mallampati >= III, Obstruction, Neck mobility) to anticipate Cormack-Lehane Grade III–IV difficult laryngoscopy.
Read the guide →Cleaning imported dataLEN function: count characters and expose hidden trailing spaces
Measure exact string length—including spaces and punctuation—to diagnose why two visually identical bin codes fail to match.
Read the guide →LogicalLET function: name intermediate calculations once inside a formula
Store repeated sub-expressions in readable local names with LET so tiered pricing and margin formulas run cleaner and faster.
Read the guide →Engineering & ScienceLevenspiel CSTR vs. PFR Reactor Volume Ratio (1st & 2nd Order)
Calculate the isothermal CSTR-to-Plug-Flow-Reactor volume penalty V_CSTR / V_PFR across target conversion X (0 < X < 1) for first-order ((X / (1 - X)) / (-LN(1 - X))) and second-order (1 / (1 - X)) kinetics.
Read the guide →Employee Ownership, Corporate Succession & ERISA / IRC §4975 Leveraged ESOPsLeveraged ESOP Suspense-Share Release & Repurchase Formula
Calculate ERISA / IRC §4975 Leveraged ESOP General Principal-Plus-Interest Suspense-Share Release Fraction, Shares Allocated to Employee Accounts, IRC §404(a)(9) Principal + Interest Tax Shield ($M), and IRC §409(h) Share Repurchase Obligation ($).
Read the guide →Biostatistics & EpidemiologyLevey-Jennings QC Chart Formula: z-Score (1_2s / 1_3s), SDI & Peer CV Ratio (CVR)
Monitor daily clinical laboratory quality-control runs on a Levey-Jennings chart via QC z-score (x_QC - Mean) / SD (flagging 1_2s warning and 1_3s rejection) and inter-laboratory proficiency SDI & CVR.
Read the guide →Engineering & ScienceLevich Equation: Rotating Disk Electrode (RDE) Limiting Current vs RPM
Calculate steady-state convective-diffusion limiting current iL = 0.620 * n * F * A * D^(2/3) * omega^(1/2) * nu^(-1/6) * C0 in microamps as a function of RDE rotation speed (RPM).
Read the guide →Statistical AnalysisLevin’s Population Attributable Fraction (PAF) & Prevented Fraction Formula
Quantify public-health and operational defect impact using Morton Levin’s (1953) Population Attributable Fraction p_e*(RR - 1) / (1 + p_e*(RR - 1)) and protective Prevented Fraction p_cov*(1 - RR).
Read the guide →Mechanical Design & Power TransmissionLewis Gear-Tooth Bending Stress and Barth Velocity Factor Formula
Size spur-gear module m and face width b in Excel and Arte Sheets using Wilfred Lewis’s (1892) cantilever tooth root bending stress sigma_b = K_v * W_t / (b * m * Y).
Read the guide →ScienceLife Table R0, Cohort Generation Time and a Leslie Projection
Calculate lifetime recruitment, a cohort-weighted generation interval and an approximate growth rate, then project three age classes using an explicit discrete census convention.
Read the guide →Financial Statement Analysis, US GAAP vs IFRS Inventory & LIFO ConformityLIFO Reserve to FIFO Inventory, COGS & Tax Shield Formula
Convert US GAAP LIFO Financial Statements to IFRS-Comparable FIFO: FIFO Ending Inventory (LIFO + Reserve), FIFO COGS (LIFO COGS - ΔReserve), Cumulative Cash Tax Saved, and LIFO Liquidation Phantom Profit Detection.
Read the guide →Healthcare & ClinicalLight's Criteria for Pleural Effusion (Exudate vs Transudate)
Classify thoracentesis pleural fluid as Exudate or Transudate using Light's 3-rule OR logic: Pleural/Serum Protein > 0.5, Pleural/Serum LDH > 0.6, or Pleural LDH > (2/3) * Serum LDH ULN.
Read the guide →Affordable Housing Finance, IRC Section 42 LIHTC & Real EstateLIHTC Section 42 Qualified Basis, DDA Boost & Equity Formula
Calculate IRC Section 42 Low-Income Housing Tax Credit (LIHTC) Boosted Qualified Basis ($M), Annual Tax Credit ($M), 10-Year Credit Allocation ($M), and Syndicated Investor Equity Proceeds ($M).
Read the guide →Healthcare & Clinical CalculationsLille Model Score (Day-7 Steroid Response in Severe Alcoholic Hepatitis)
Calculate Alexandre Louvet’s Day-7 Lille Score (0–1) from Age, Day-0 Albumin (g/L), Day-0 & Day-7 Bilirubin (umol/L), Renal Insufficiency, and PT (sec) to stop futile prednisolone when Lille >= 0.45.
Read the guide →Statistical & EconometricLin’s Concordance Correlation Coefficient (CCC, ρ_c) Formula
Calculate Lawrence Lin’s Concordance Correlation Coefficient ρ_c = (2 * r * s_x * s_y) / (s_x^2 + s_y^2 + (x̄ - ȳ)^2) and bias correction factor C_b = ρ_c / r to measure 45° identity-line assay agreement.
Read the guide →Statistical AnalysisLin’s Concordance Correlation Coefficient (CCC): Precision vs. 45-Degree Accuracy
Evaluate method-comparison and clinical assay reproducibility along the 45-degree identity line Y = X by factoring Lin’s CCC into Pearson precision (r) and bias correction accuracy (C_b).
Read the guide →Engineering & ScienceLindemann Melting Criterion & Thermal RMS Vibration Ratio
Estimate crystalline melting temperature T_m = 0.00229054 * M * Θ_D^2 * c_L^2 * d^2 (K) from Debye temperature Θ_D, atomic mass M (g/mol), nearest-neighbor spacing d (Å), and Lindemann constant c_L (~0.10–0.12).
Read the guide →Charts & Visual DataLine of Best Fit & Equation Formula: Exact OLS Slope, Intercept & R² via SUMPRODUCT
Extract the exact Scatter-Chart Line of Best Fit equation y = m*x + b and R-Squared directly into cells using closed-form SUMPRODUCT moments — so downstream forecasts reference live trendline coefficients.
Read the guide →Engineering & ScienceLinear & Quadratic Stark Effect Atomic Electric-Field Splitting Formula
Calculate Johannes Stark’s n = 2 hydrogen first-order linear electric-field energy splitting delta_E = 3 * e * a_0 * E (meV) and ground-state polarizability second-order quadratic Stark shift.
Read the guide →Engineering & ScientificLineweaver-Burk & Hanes-Woolf Enzyme Kinetics: Vmax, Km & Inhibitor Diagnosis
Extract catalytic maximum velocity V_max and Michaelis constant K_m from substrate-velocity assays using double-reciprocal Lineweaver-Burk (1/v vs 1/[S]) and Hanes-Woolf ([S]/v vs [S]) OLS regression.
Read the guide →FinancialLintner Dividend Smoothing Model formula: partial adjustment to target payout
Explore a simplified, zero-intercept dividend partial-adjustment model with explicit parameter bounds.
Read the guide →Clinical Medicine & PhysiologyLipid Accumulation Product (LAP) Calculator: Kahn Sex-Specific Waist-Triglyceride Formula
Quantify ectopic lipid overaccumulation and MASLD / hepatic steatosis risk using Henry S. Kahn’s (2005) sex-specific Lipid Accumulation Product: LAP = (WC_cm - 65) * TG_mmol_L in men and (WC_cm - 58) * TG_mmol_L in women.
Read the guide →Dynamic ArraysList all combinations from two lists (Cartesian product with TOCOL)
Generate every Size x Color SKU variant or Region x Quarter pair into a single spilled column using TOCOL(List1 & "-" & TRANSPOSE(List2)).
Read the guide →Dates, Time & SchedulesList All Dates in a Month Dynamically with SEQUENCE & EOMONTH
Generate a self-resizing vertical calendar column of every date in any Year + Month (automatically adjusting for 28-, 29-, 30-, or 31-day months) using SEQUENCE(DAY(EOMONTH(DATE(Y, M, 1), 0)), 1, DATE(Y, M, 1), 1).
Read the guide →Date & TimeList all holidays falling between two project dates (FILTER holiday schedule)
List and count records from a supplied holiday table within an inclusive date window.
Read the guide →Statistical AnalysisList Most Frequently Occurring Numbers & Bimodal Ties (UNIQUE, COUNTIF & SORTBY)
Extract every tied numeric mode, rank distinct numbers by occurrence count, and compute modal frequency share without MODE.SNGL hiding bimodal clusters.
Read the guide →TextList team members by group in alphabetical order (TEXTJOIN, SORT & FILTER)
Roll up vertical employee-to-squad assignments into sorted, comma-separated roster strings per team with graceful empty-team fallbacks.
Read the guide →Alternative Credit, Commercial Litigation Finance & Settlement WaterfallsLitigation Finance Non-Recourse Funding Waterfall Formula
Calculate Commercial Litigation Finance Non-Recourse Senior Funder Return + Multiple Payout, Remaining-Pool Capped Trial Counsel Contingency Fee, Claimant Net Settlement Proceeds, and Claimant Recovery Share.
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