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Forklift Load-Center Moment & Attachment Derating Formula
Calculate Rated Safe Overturning Moment About Front Drive Axle (kN·m), Extended Net Moment Arm (mm), Derated Safe Lifting Capacity (kg), and Retained Nameplate Capacity (%).
Read the guide →TextFormat email with display name ("Name <email>") and extract address back out
Format a simple single-recipient display string and extract an address from a controlled angle-bracket format. This is not a complete email-header parser.
Read the guide →TextFormat MAC addresses: standardize colons (00:1A:2B...) or Cisco dots
Strip mixed separators from 12-character hex MAC addresses, validate length, and format into colon-separated pairs or Cisco dot-quads.
Read the guide →TextFormat numbers as ordinals: 1st, 2nd, 3rd, 4th (including 11th–13th)
Append accurate English ordinal suffixes ("st", "nd", "rd", "th") to ranks and day numbers while handling the 11th/12th/13th teen exception.
Read the guide →Date & Time FormulasFormula to List Weekend Dates Only (Saturday & Sunday Shift Schedule)
Calculate the upcoming Saturday on or after any start date via B2 + MOD(6 - WEEKDAY(B2, 2), 7) and step strictly across consecutive Saturday/Sunday pairs using 7 * INT((N - 1) / 2) + MOD(N - 1, 2).
Read the guide →Healthcare & Clinical CalculationsForns Index Non-Invasive Liver Fibrosis Calculator (Platelets, GGT, Cholesterol)
Calculate Xavier Forns’s logarithmic hepatic fibrosis index 7.811 - 3.131*LN(Platelets_10^9/L) + 0.781*LN(GGT_IU/L) + 3.467*LN(Age) - 0.014*Cholesterol_mg/dL (< 4.2 rules out F2–F4 fibrosis with 96% NPV; > 6.9 rules in).
Read the guide →Statistical & Clinical AnalysisForrester Hemodynamic Subsets (I–IV) & Nohria-Stevenson Wet/Dry Warm/Cold Diamond
Classify acute myocardial infarction and decompensated heart failure hemodynamics across Cardiac Index CI (<= 2.2 vs > 2.2 L/min/m²) and Pulmonary Capillary Wedge Pressure PCWP (<= 18 vs > 18 mmHg).
Read the guide →Economics & Market MicrostructureFoster-Greer-Thorbecke (FGT_0, FGT_1, FGT_2) Poverty Headcount, Gap & Severity Formula
Calculate the World Bank’s unified Foster-Greer-Thorbecke (1984) poverty family P_alpha = (1/N) * SUM(MAX(0, (z - y_i)/z)^alpha): Headcount Ratio P_0, Poverty Gap Index P_1, and Distribution-Sensitive Squared Severity P_2.
Read the guide →Foundry Sand Lab & Defect Control, AFS Standard 2-Inch Specimen Permeability FormulaFoundry Green-Sand AFS Permeability & Blowhole Formula
Calculate Volumetric Air Venting Rate (cm³/min), Superficial Darcy Gas Velocity (cm/min), AFS Permeability Number P, and Iron/Steel Castings Steam-Blowhole Gate.
Read the guide →Metal Casting Gating Design, Bernoulli Mold Aspiration Prevention & Pouring TimeFoundry Tapered Sprue Choke & Aspiration Ratio Formula
Calculate Aspiration-Free Top Sprue Entry Area A1 = A2*SQRT(h2/h1) (mm²), Torricelli Choke Velocity (m/s), Volumetric Pouring Rate (cm³/s), and Mold Fill Time (s).
Read the guide →Healthcare & Clinical FormulasFOUR Score (Full Outline of UnResponsiveness) Intubated Coma Scale (0–16)
Calculate Eelco Wijdicks’ 4-domain neurocritical care FOUR Score (Eye 0–4, Motor 0–4, Brainstem Reflexes 0–4, Respiration/Ventilator Drive 0–4) to grade intubated coma, locked-in syndrome, and uncal herniation.
Read the guide →EngineeringFourier Heat Conduction formula: composite wall R-Value, U-Value & heat loss (W)
Calculate SI area-normalized resistance, transmittance and signed steady heat flow through a planar layered wall.
Read the guide →Engineering & ScienceFowler-Nordheim Quantum Field-Emission Tunneling Current Density Formula
Calculate cold-cathode quantum electron tunneling current density J = ((1.5414e-6 * E^2) / phi) * EXP((-6.8309e7 * phi^1.5) / E) in A/cm^2 for FE-SEM tips, carbon nanotubes, and flash memory.
Read the guide →Machine Learning & Cluster EvaluationFowlkes-Mallows Clustering Index Formula vs Pairwise F1 and Jaccard
Evaluate clustering partitions in Excel and Arte Sheets using the Fowlkes-Mallows geometric mean of pairwise precision and recall TP / SQRT((TP + FP) * (TP + FN)).
Read the guide →Engineering & ScienceFox Equation & Gordon-Taylor Copolymer Glass Transition Temperature (Tg)
Predict the glass transition temperature Tg (in °C via absolute Kelvin!) of random copolymers, plasticized PVC, and miscible amorphous blends using the Fox harmonic rule and Gordon-Taylor equation.
Read the guide →Healthcare & ClinicalFractional Excretion of Sodium (FENa) & Urea (FEUrea) in Acute Kidney Injury
Calculate FENa (%) = (U_Na * P_Cr) / (P_Na * U_Cr) * 100 and diuretic-resistant FEUrea (%) to differentiate prerenal azotemia from intrinsic acute tubular necrosis (ATN).
Read the guide →Healthcare & Clinical CalculationsFRAIL Scale (5-Item Geriatric Frailty & Pre-Frailty Screening)
Screen older adults in under 60 seconds without grip-dynamometers using John Morley’s 0–5 FRAIL Questionnaire (Fatigue, Resistance, Ambulation, Illnesses > 5, Loss of Weight > 5%).
Read the guide →Hydropower & Turbomachinery Engineering, Francis Reaction Turbine & Thoma Cavitation LawFrancis Turbine Specific Speed & Thoma Draft-Tube Formula
Calculate Metric Power Specific Speed Ns, Required Runner Suction Head NPSH_r (m), Maximum Safe Runner Elevation Above Tailwater Hs,max (m), and Cavitation Submergence Margin (m).
Read the guide →Engineering & ScienceFranz-Keldysh Electro-Absorption Energy (ħΘ_FK) Modulator Formula
Calculate the Franz-Keldysh photon-assisted tunneling energy ħΘ_FK = 0.72495 * (F^2 / m_r)^(1/3) (meV) governing bulk III-V electro-absorption optical modulators.
Read the guide →EngineeringFree-Space Path Loss (FSPL), Friis RF link power & Inverse-Square dB drop
Calculate wireless RF attenuation FSPL(dB) = 20*LOG10(d_km) + 20*LOG10(f_MHz) + 32.44, Friis received dBm, and acoustic -20*LOG10(d2/d1) distance attenuation.
Read the guide →Statistical & Clinical AnalysisFreedman Log-Rank Sample Size Formula: Required Events ((k*HR + 1)/(HR - 1))²
Calculate conservative log-rank survival event targets under non-null variance using Laurence S. Freedman’s 1982 Statistics in Medicine formula E = ROUNDUP((z_alpha + z_beta)² * (1 + k*HR)² / (k * (1 - HR)²), 0).
Read the guide →Statistical & Clinical AnalysisFrench TMA Score (Coppo Rule): Severe ADAMTS13 Deficiency Probability in TTP (0 to 3)
Differentiate immune Thrombotic Thrombocytopenic Purpura (iTTP, ADAMTS13 < 10%) from atypical HUS in thrombotic microangiopathy using Paul Coppo’s ISTH-endorsed French TMA Score (Platelets <= 30 × 10⁹/L + Creatinine <= 200 umol/L + ANA positive).
Read the guide →LTCC Microelectronics, Glass Frits & SLS Polymer Powders, Yakov Frenkel (1945) Viscous SinteringFrenkel Viscous Sintering Neck Ratio & Shrinkage Formula
Calculate Viscous Capillary Characteristic Time (min), Frenkel Neck-to-Particle Radius Ratio (x/r), Isotropic Linear Shrinkage (-dL/L0 %), and Frenkel-vs-Mackenzie Regime Status.
Read the guide →StatisticalFrequency distribution table: Bin Count, Relative %, and Cumulative %
Group numeric scores into custom bins with COUNTIFS and calculate Relative Frequency % and Cumulative Frequency % without legacy array entry.
Read the guide →Charts & Visual Data ModelingFrequency Polygon Chart Formula: Class Midpoints, Zero Anchor Bins & Grouped Mean
Construct a true closed Frequency Polygon line/scatter chart: calculate Class Midpoints x_m = (Lower + Upper) / 2, add zero-frequency boundary anchor bins so polygon area equals histogram area, and compute Grouped Mean.
Read the guide →EngineeringFresnel Optical Reflectance, Transmittance & Brewster's Angle formulas
Calculate uncoated glass or crystal surface reflection loss R = ((n1 - n2) / (n1 + n2))^2, single-interface transmittance 1 - R, and Brewster's polarizing angle ATAN(n2 / n1).
Read the guide →Aerospace & EV Battery Tray Solid-State Joining, Friction Stir Welding (FSW) EnergeticsFriction Stir Welding (FSW) Pitch, Heat Index & Power Formula
Calculate FSW Advance-per-Revolution Weld Pitch (mm/rev), Arbegast Pseudo-Heat Index, Mechanical Spindle Stir Power (kW), and Net Linear Heat Input (J/mm).
Read the guide →Chemical, Process & Catalysis EngineeringFriedel Two-Phase Pressure-Drop Multiplier (Phi_LO^2) Formula: Froude & Weber Pipe Flow
Calculate two-phase gas-liquid frictional pressure drop dP_TP = Phi_LO^2 * dP_LO in horizontal and vertical upward pipelines using Lutz Friedel’s (1979) 25,000-point correlation incorporating Froude (Fr_H) and Weber (We_L) numbers.
Read the guide →StatisticalFriedewald LDL-C estimate, non-HDL-C and TC/HDL: guarded spreadsheet examples
Calculate three different lipid-panel quantities with explicit mg/dL units, input checks and limits on the Friedewald estimate.
Read the guide →Nonparametric StatisticsFriedman Repeated-Measures Rank Test and Iman-Davenport F Formula
Rank repeated-measures blocks row by row in Excel and Arte Sheets, verify the rank-sum invariant, and compute Friedman’s Q alongside the sharper Iman-Davenport F statistic.
Read the guide →Engineering & ScienceFriedmann Equation: Cosmological Critical Density & Hubble H(z)
Calculate the universe’s critical closure density rho_crit = (3 * H_0^2) / (8 * PI() * G) (in 10^-27 kg/m^3) and flat Lambda-CDM expansion rate H(z) = H_0 * SQRT(Omega_m * (1 + z)^3 + Omega_Lambda) at redshift z.
Read the guide →RF & Wireless Communications EngineeringFriis Cascaded RF Noise Figure (dB) and LNA Placement Formula
Calculate 3-stage cascaded RF receiver Noise Factor F_tot = F_1 + (F_2 - 1)/G_1 + (F_3 - 1)/(G_1*G_2) and Noise Figure NF_dB = 10*LOG10(F_tot) in Excel and Arte Sheets.
Read the guide →Engineering & ScientificFriis Free-Space Path Loss (FSPL), Nyquist Noise Floor & RF Link SNR Margin
Build an end-to-end RF wireless link budget in dB/dBm combining exact speed-of-light Friis FSPL, Johnson-Nyquist k_B*T*B thermal noise floor plus receiver noise figure, and carrier-to-noise ratio (SNR).
Read the guide →EngineeringFroude Number (Fr = V / SQRT(gD)) & Weber Number (We = rho*V^2*d / sigma)
Calculate an open-channel Froude number and a separately specified Weber number with explicit length, velocity and density conventions.
Read the guide →Fluid Mechanics, Dimensional Analysis & Tow-Tank / Wind-Tunnel TestingFroude vs Reynolds Scale-Model Similitude Scaling Formula
Calculate Tow-Tank Froude-Scaled Model Speed V_proto / SQRT(Lambda), Cubic Force Scaling F_proto / Lambda^3, Propulsion Power Scaling P_proto / Lambda^3.5, and Unpressurized Reynolds-Similitude Speed V_proto * Lambda.
Read the guide →Strategic Competition & Game TheoryFudenberg-Tirole Top Dog & Puppy Dog Strategy Formula
Classify Stage-1 strategic over- vs under-investment into Drew Fudenberg and Jean Tirole’s (1984) four animal strategies (Top Dog, Puppy Dog, Fat Cat, Lean and Hungry) using Tough/Soft and Substitutes/Complements derivatives.
Read the guide →Clinical Medicine & PhysiologyFujimoto (1968) & Kurazumi (1994) Body Surface Area (BSA) Formula: Precision Drug & GFR Indexing
Calculate Body Surface Area (m^2) using Shigeki Fujimoto et al.’s (1968) Japanese/East Asian clinical standard BSA = 0.008883 * H^0.663 * W^0.444 and Yutaka Kurazumi et al.’s (1994) modern 3D-validated reference BSA = 0.00949 * H^0.655 * W^0.441.
Read the guide →Engineering & ScienceFuller-Schettler-Giddings Binary Gas Diffusivity Formula (D_AB)
Calculate binary gas-phase diffusion coefficients D_AB = 0.00143 * T^1.75 / (P * SQRT(M_AB) * (v_A^(1/3) + v_B^(1/3))^2) (cm^2/s) from atomic diffusion volumes.
Read the guide →Statistical & Clinical AnalysisFUNC Score (0–11) Formula: 90-Day Functional Independence After Intracerebral Hemorrhage
Complement the mortality-focused ICH Score by calculating Natalia S. Rost et al.’s (2008) 11-point FUNC Score (ICH Volume, Age, Location, Admission GCS, and Pre-ICH Cognitive Impairment — where HIGHER scores 0–11 predict 90-day functional independence GOS >= 4!).
Read the guide →Institutional Asset Allocation, Fund-of-Funds & Fee-Drag EconomicsFund-of-Funds Double-Layer Fee & Carry Net-TVPI Formula
Compare Direct Primary LP Net TVPI against Private Equity Fund-of-Funds (FoF) Two-Layer Fee & Carry Net TVPI, Cumulative Two-Tier Fee/Carry Leakage ($M), and End-Investor Gross-Gain Capture Ratio.
Read the guide →Quantitative FinanceFundamental Law of Active Management Formula (Grinold IR, IC, Breadth & TC)
Calculate ex-ante Information Ratio IR = IC * SQRT(Breadth) * TC and expected active alpha E[R_A] = IR * Tracking_Error under the Clarke-de Silva-Thorley extended Fundamental Law.
Read the guide →StatisticalFunnel conversion analysis: step pass-through, drop-off %, and overall conversion
Diagnose where prospects abandon a signup or checkout funnel by contrasting stage-to-stage conversion (B3 / B2) against cumulative top-of-funnel conversion (B3 / $B$2).
Read the guide →Financial analysisFV function: project future reserve balance from regular deposits
Calculate how an opening reserve plus fixed monthly contributions grows under compound monthly interest, keeping deposit signs consistent.
Read the guide →Food Dehydration & Pharmaceutical Stability, GAB Moisture Sorption IsothermGAB Food Moisture Sorption Isotherm (M0, C, K) Formula
Calculate Effective Multilayer Activity K*aw, GAB Equilibrium Moisture Content (% dry basis), Uncorrected BET Moisture Prediction (%), and High-aw BET Divergence Error (%).
Read the guide →Food & Pharmaceutical Powder StabilityGAB Moisture Sorption Isotherm & Monolayer Formula
Calculate Optimal Monolayer Water Activity a_w0 = 1 / (K * (1 + SQRT(C))), GAB Equilibrium Moisture Content M(a_w) = (M_0*C*K*a_w) / ((1 - K*a_w)*(1 - K*a_w + C*K*a_w)), and Classic BET Bias.
Read the guide →Healthcare & ClinicalGAD-7 Generalized Anxiety Disorder Scale (0–21) & Cutoff (>=10) Formula
Calculate Spitzer & Kroenke's 7-item Generalized Anxiety Disorder score (GAD-7, 0 to 21 points) and stratify anxiety severity at the validated 5-, 10-, and 15-point cutoffs.
Read the guide →Quantitative Receptor PharmacologyGaddum Competitive vs Non-Competitive Occupancy Formula
Compare J.H. Gaddum’s (1937) Competitive Orthosteric Occupancy [A] / ([A] + K_A*(1 + [B]/K_B)) against Non-Competitive Allosteric Insurmountable Occupancy ([A] / ([A] + K_A)) / (1 + [B]/K_B) and Ceiling 1 / (1 + [B]/K_B).
Read the guide →Market Design & Operations ResearchGale-Shapley Matching Blocking-Pair Audit Formula
Audit proposed hospital-resident, school-choice, or project-team assignments for David Gale and Lloyd Shapley’s (1962) stability condition by counting Blocking Pairs.
Read the guide →Clinical Medicine & PhysiologyGalveston Pediatric Burn Resuscitation Formula: 5,000 mL/m^2 Burned + 2,000 mL/m^2 Maintenance
Calculate 24-hour pediatric burn fluid resuscitation and hourly infusion rates using Shriners Burns Institute’s (Carvajal, 1988) BSA-based Galveston Formula: V_24 = 5000 * BSA_m2 * (%TBSA / 100) + 2000 * BSA_m2 (50% in first 8 hours, 50% in next 16 hours).
Read the guide →StatisticsGambler's Ruin Probability: Fair (p = 0.5) & Biased Random Walk
Calculate the probability of reaching zero before a fixed upper target in an independent unit-step random walk, including fair odds, deterministic endpoints and numerically stable near-fair evaluation.
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