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1-2 Shell-and-Tube LMTD Correction Factor (Ft) Formula
Calculate Heat-Capacity Ratio R, Cold-Side Thermal Effectiveness P, Exact Bowman-Mueller-Nagle 1-Shell / 2-Tube-Pass LMTD Correction Factor F_t, and Effective Mean Temperature Difference (°C).
Read the guide →Math & Statistical100% Stacked Column & Bar Mix Matrix Formula: Mixed-Reference Period Shares (B$2:B$4)
Normalize multi-quarter revenue or headcount tables into a 100% composition matrix using column-row-locked mixed references ROUND(B2 / SUM(B$2:B$4) * 100, 2) and measure mix shift percentage-point changes.
Read the guide →Financial2/10 Net 30 formula: implied annualized cost of skipping trade discounts
Annualize the illustrative cost of foregoing an early-payment discount using simple and compounded conventions.
Read the guide →Statistical & Clinical Analysis2012 SLICC Lupus Classification Criteria: Dual-Pathway SLE Decision Formula
Evaluate Michelle Petri’s 2012 SLICC Systemic Lupus Erythematosus classification rule: (>= 4 of 17 criteria with >= 1 Clinical AND >= 1 Immunologic) OR Biopsy-Proven Lupus Nephritis + ANA/anti-dsDNA.
Read the guide →Healthcare & Clinical Calculators2019 ACR/EULAR SLE Classification Criteria (ANA >= 1:80 Gate & >= 10 Score)
Evaluate Martin Aringer et al.’s 2019 ACR/EULAR Systemic Lupus Erythematosus classification rule enforcing ALL THREE gates: ANA reciprocal titer >= 80, >= 1 clinical criterion, and weighted score >= 10!
Read the guide →Health & Fitness2021 CKD-EPI Creatinine eGFR and GFR Categories in Excel
Practice the adult 2021 race-free creatinine equation, validate units and inputs, and classify the unrounded estimate without treating it as a CKD diagnosis.
Read the guide →Lookup & Reference2D Matrix Dynamic Row Sum, Column Sum & Two-Way Lookup (SUMPRODUCT)
Sum an entire dynamically matched row, sum an entire dynamically matched column, or retrieve a two-way matrix intersection across a 2D table using boolean-broadcast SUMPRODUCT.
Read the guide →Statistical Analysis2x2 Association Coefficients: Pearson Phi, Yule’s Q & Yule’s Y Colligation
Measure binary 2x2 contingency association on [-1, +1] with Pearson’s Phi coefficient and marginal-prevalence-invariant Yule’s Q and Yule’s Y formulas.
Read the guide →Math & Trigonometry3x3 Matrix Determinant and Cramer's Rule Linear System Solver (MDETERM & MINVERSE)
Calculate exact 2x2 and 3x3 matrix determinants, test for singular zero-determinant systems, and solve simultaneous linear equations A*x = b via cofactor expansion.
Read the guide →Healthcare & Clinical Calculations4Ts Score for Heparin-Induced Thrombocytopenia (HIT) Pretest Probability
Calculate Theodore Warkentin’s 0–8 ASH guideline 4Ts Pretest Score (Thrombocytopenia, Timing of platelet fall, Thrombosis, oTher causes) to rule out HIT (0–3, NPV ~99.8%) or immediately switch to non-heparin anticoagulation.
Read the guide →Finance5-Factor DuPont ROE: Tax Burden, Interest Burden & EBIT Margin
Decompose ROE into five accounting ratios, reconcile their unrounded product to net income over average equity, and distinguish undefined factors from a still-defined direct ROE.
Read the guide →Lookup & Reference5x5 risk matrix formula: score Likelihood x Impact and assign severity
Convert qualitative Likelihood and Impact ratings into 1–5 scores with XMATCH, compute the 1–25 risk score, and classify Low/Medium/High/Critical.
Read the guide →Lookup & Reference5x5 Risk Score Buckets & Step-Based Tier Lookup (Sorted INDEX & MATCH)
Compute Likelihood x Impact risk scores (1–25) and map them into editable Low / Moderate / High / Critical governance tiers using sorted step-threshold lookup.
Read the guide →Clinical Medicine & PhysiologyA Body Shape Index (ABSI) Calculator: Krakauer Allometric Waist-BMI-Height Formula
Calculate Nir Y. Krakauer and Jesse C. Krakauer’s (2012) BMI-independent allometric A Body Shape Index ABSI = WC_m / ((BMI^(2/3)) * (Height_m^(1/2))) and standardized ABSI z-score for premature mortality risk.
Read the guide →StatisticalA/B test conversion lift and statistical significance (two-proportion Z-score)
Calculate relative conversion lift, pooled standard error, and two-proportion Z-score to test 95% statistical significance.
Read the guide →Biostatistics & Survival AnalysisAalen-Johansen Competing-Risks Cumulative Incidence vs Naive 1 - KM
Calculate cause-specific Cumulative Incidence CIF_1(t) = SUM(S_all(t_{j-1}) * d_{1j} / n_j) and prove why censoring competing deaths inflates naive 1 - KM above 100% total risk.
Read the guide →Public Economics & Actuarial PensionsAaron-Samuelson PAYGO vs Funded Pension Formula
Compare Pay-As-You-Go social security’s Samuelson biological rate of return g_bio = (1 + n)*(1 + g_w) - 1 against funded capital return r and compute equilibrium replacement rates.
Read the guide →Civil, Structural & Geotechnical EngineeringAASHTO 1993 Flexible Pavement Structural Number (SN) Formula: Layer & Drainage Design
Calculate composite asphalt highway Structural Number SN = a_1*D_1 + a_2*D_2*m_2 + a_3*D_3*m_3 and minimum required layer thicknesses using the AASHTO (1993) Guide for Design of Pavement Structures.
Read the guide →Civil & Transportation Engineering, Highway Geometric Design (AASHTO)AASHTO Curve Superelevation Radius & Stopping Sight Distance
Calculate AASHTO Green Book Minimum Horizontal Curve Radius V^2 / (127*(e + fs)), Perception-Reaction Distance 0.278*V*tr, Grade-Adjusted Braking Distance, and Total Stopping Sight Distance (SSD).
Read the guide →Causal Inference & Policy EvaluationAbadie Synthetic Control Convex Weights and Post/Pre RMSPE Ratio
Audit convex donor-pool weights (w_j >= 0, SUM w_j = 1), pre-intervention fit, and Abadie’s post-to-pre RMSPE permutation test ratio in Excel and Arte Sheets.
Read the guide →TextAbbreviate names into initials: 1-, 2-, and 3-word names
Extract uppercase initials from mononyms, two-part names, and full middle-name strings using TRIM, LEFT, and TEXTAFTER.
Read the guide →Lookup & ReferenceAbbreviate state or country names to 2-letter postal codes (mixed-input safe)
Standardize columns that mix full state names ("California", "New York") and 2-letter abbreviations ("tx", "CA") into clean uppercase postal codes.
Read the guide →Healthcare & ClinicalAbbreviated Burn Severity Index (ABSI) Tobiasen Survival Tier Formula
Calculate Joyce Tobiasen’s 5-variable Abbreviated Burn Severity Index (ABSI, 2 to 18 points) summing Female sex (+1), 20-year Age bracket (1–5), Inhalation Injury (+1), Full-Thickness 3rd-Degree Burn (+1), and 10% TBSA bracket (1–10).
Read the guide →StatisticalABC–XYZ inventory example: cumulative spend share and demand variation
Combine a chosen cumulative-spend classification with population CV of four demand observations. Thresholds are example policy choices, not universal stocking rules.
Read the guide →Healthcare & ClinicalABCD2 Score for TIA Early Stroke Risk (0–7 Point Clinical Rule)
Compute the 0–7 point ABCD2 transient ischemic attack (TIA) score across Age (>=60), Blood pressure (>=140/90), Clinical features, Duration, and Diabetes to stratify 2-day ischemic stroke risk.
Read the guide →Quantitative Finance & Market MicrostructureAbdi-Ranaldo Close-High-Low (CHL) Bid-Ask Spread Formula
Estimate effective proportional bid-ask spreads from daily OHLC bars using Abdi and Ranaldo’s (2017) two-day zero-floored formula s_t = 2 * SQRT(MAX(0, (c_t - eta_t) * (c_t - eta_{t+1}))).
Read the guide →Commercial Credit, Working Capital & Asset-Based LendingABL Borrowing Base, Dilution Reserve & Availability Formula
Calculate Asset-Based Lending (ABL) Effective AR Advance Rate 0.85 - MAX(0, 2*(Dilution - 0.05)), Capped Borrowing Base MIN(Commitment, AR_Adv + 0.85*Inventory_NOLV), Excess Availability, and Springing Cash-Dominion Covenant Gate.
Read the guide →Non-Traditional Machining, Cold-Cutting Abrasive Waterjet (AWJ) & UHP Intensifier PumpsAbrasive Waterjet (AWJ) Jet Velocity & Pump Power Formula
Calculate Supersonic Ruby/Diamond Orifice Waterjet Velocity (m/s), Vena-Contracta Orifice Water Flow (L/min), Hydraulic Jet Power (kW), and Garnet-to-Water Mass Loading Ratio.
Read the guide →MathABS function: measure budget variance distance and tolerance bands
Strip minus signs with ABS so over-budget and under-budget variances do not cancel each other out and symmetric tolerance checks stay concise.
Read the guide →Cell referencesAbsolute and relative cell references: lock constants with $ when copying formulas
Copied formulas adjust row and column coordinates automatically unless you lock them with dollar signs. Calculate wholesale pack prices from one shared pack size and handling fee without breaking rows below.
Read the guide →HealthcareAbsolute Neutrophil Count (ANC) & Reticulocyte Production Index (RPI)
Practice ANC, corrected reticulocyte percentage and RPI calculations with explicit units, a configurable reference hematocrit and a supplied maturation factor.
Read the guide →EngineeringAC & RF Skin Depth formula: delta = SQRT(rho / (pi * f * mu0 * mur))
Estimate skin depth for a good conductor with positive resistivity and a real permeability, keeping the DC case separate.
Read the guide →Health Insurance Regulation & Actuarial FilingACA Medical Loss Ratio (MLR) & Rebate Formula
Calculate Statutory Health Insurer Adjusted Premium Denominator, HCQI-Adjusted Medical Loss Ratio (Claims + Quality_Improvement) / (Premiums - Regulatory_Assessments), and Mandatory Policyholder Rebate.
Read the guide →Spreadsheet Governance & Collaborative AI WorkflowsAcademy MCP Lesson Gate, Locale & Progress Audit Formula
Audit academy:read lesson access across free vs Pro-gated catalog metadata, transparent locale fallback without fabricated official translations, and read-only server-verified progress boundaries.
Read the guide →LogicalAccounts receivable aging buckets: classify invoices into Current, 1-30, 31-60, 61-90, and 90+
Assign standard AR aging bands with ordered IFS thresholds and summarize dollar exposure per bucket with SUMIF.
Read the guide →Labor Economics & Human CapitalAcemoglu-Pischke Firm-Sponsored General Training Formula
Calculate Daron Acemoglu and Jorn-Steffen Pischke’s (1998, 1999) optimal firm-paid general training intensity tau* = (theta_comp * p_skill) / c_tr under compressed wage structures versus Gary Becker’s (1964) zero-sponsorship benchmark.
Read the guide →Structural Engineering, ACI 318 Reinforced Concrete & Flexural DesignACI 318 Whitney Stress Block Concrete Beam Moment Formula
Calculate Whitney Compression Block Depth a (mm), Net Tensile Rebar Strain epsilon_t, Nominal Flexural Capacity M_n (kN·m), and Tension-Controlled Design Moment phi*M_n (kN·m).
Read the guide →Civil, Structural & Geotechnical EngineeringAckers-White (1973) Sediment Transport Formula: Mobility Number F_gr & Concentration
Calculate Peter Ackers and W. Rodney White’s (1973, HR Wallingford / ASCE) Transition-Exponent Sediment Mobility Number F_gr and Mass Flux Concentration X_ppm across fine transitional sand to coarse gravel.
Read the guide →Mechanical Actuators, Acme Lead Screws & Lifting JacksAcme Power Screw Raising/Lowering Torque & Efficiency Formula
Calculate Acme Thread Raising Torque T_R (N·m) including Thrust Collar Friction, Load-Lowering Torque T_L (N·m), Overall Screw+Collar Efficiency (%), and Overhauling Check.
Read the guide →MathACOS function: find roof or vector angles from adjacent-over-hypotenuse ratios
Calculate arccosine angles in [0, 180] degrees using DEGREES(ACOS(ratio)), and guard ratios outside [-1, 1].
Read the guide →Architectural & Noise-Control Acoustics, Sound Isolation & PartitionsAcoustic Mass Law Wall Transmission Loss & Coincidence Formula
Calculate Partition Surface Mass Density m_s (kg/m²), Field-Incidence Mass-Law Sound Transmission Loss TL (dB), Critical Bending-Wave Coincidence Frequency f_c (Hz), and STC Speech-Band Warning.
Read the guide →Engineering & ScienceAcousto-Optic Modulator (AOM) Acoustic Wavelength & Bragg Deflection Angle
Calculate the ultrasonic grating period Lambda = v_a / f_RF (um) and external Bragg angle theta_B ~ (lambda_0 * f_RF) / (2 * v_a) (milliradians) for TeO2 and fused-silica laser acousto-optic deflectors.
Read the guide →Clinical Medicine & PhysiologyACR TI-RADS Thyroid Nodule Calculator: TR1–TR5 Point Sum & FNA Biopsy Size Threshold
Score thyroid ultrasound nodules using Franklin N. Tessler et al.’s (2017) American College of Radiology TI-RADS 5-feature point system (TR1 to TR5) and determine size-based Fine-Needle Aspiration (FNA) vs Surveillance recommendations.
Read the guide →Biological Wastewater Treatment, Nitrification & Sludge WastingActivated-Sludge SRT (MCRT), F/M Ratio & WAS Flow Formula
Calculate Aeration Bioreactor Biomass Inventory (kg MLVSS), Food-to-Microorganism F/M Ratio (d^-1), Required Daily Waste Activated Sludge Mass (kg/d), and WAS Pump Flow (m³/d).
Read the guide →Hydronic HVAC Systems, DOAS + Active Chilled Beams & Sensible Cooling EngineeringActive Chilled Beam Induction Ratio & Cooling Formula
Calculate Induced Room Secondary Airflow Q_sec (L/s), Primary DOAS Ventilation Sensible Cooling (W), Secondary Hydronic Coil Sensible Cooling (W), and Total Chilled-Beam Sensible Capacity (W).
Read the guide →Actuarial Life Contingencies & Insurance MathematicsActuarial Commutation Dx, Nx, Mx & Life Premium Formula
Calculate Life Annuity-Due a_ddot_x = N_x / D_x, Death-Benefit Commutation M_x = D_x - (i / (1 + i)) * N_x, Whole-Life Net Single Premium Face * (M_x / D_x), and Net Level Annual Premium Face * (M_x / N_x).
Read the guide →FinancialActuarial Pure Premium (Frequency x Severity) & Credibility Factor Z
Explore observed loss cost, a simplified variable-load calculation and a separate limited-fluctuation claim-frequency credibility illustration.
Read the guide →Industrial Organization & Pricing StrategyAdams-Yellen Pure vs Mixed Bundling Profit Formula
Compare Separate Component Pricing, Pure Bundling, and Mixed Bundling profits across negatively correlated customer segments and verify Adams & Yellen’s Sub-Cost Exclusion Theorem.
Read the guide →EngineeringADC Effective Number of Bits (ENOB), SINAD & Ideal SNR (6.02N + 1.76)
Compare a rounded ideal full-scale sine-wave SNR formula with SINAD-derived ENOB, and calculate nominal LSB size from the full input-voltage span.
Read the guide →Lookup, Reference & Dynamic ArraysAdd an Average Line to a Chart: Constant Helper Column, Variance & +1 SD Control Band
Plot a horizontal mean benchmark line across any column or line chart by anchoring =AVERAGE($B$2:$B$7) in a helper series, plus compute point-vs-mean variance and +1 SD upper control limits.
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