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Theatrical Box-Office 90/10 Split & P&A Formula
Calculate Distributor Theatrical Film Rentals MAX(Floor_Pct * GBO, 0.90 * MAX(0, GBO - House_Nut)), Effective Cinema Exhibitor Retention, Post-Fee Studio Receipts, and Net Producer P&A Recoupment.
Read the guide →Forecasting & Demand PlanningTheil MSE Bias-Variance-Covariance and Mincer-Zarnowitz Formula
Decompose Mean Squared Forecast Error into exact additive Bias Share U_M, Variance Share U_S, and Unsystematic Covariance Share U_C = 1 - U_M - U_S alongside Mincer-Zarnowitz slope beta_MZ.
Read the guide →Financial & Economic AnalysisTheil T & Theil L (Mean Log Deviation) Entropy Inequality Indices
Quantify revenue, wage, or regional resource concentration using Theil’s GE(1) T index, GE(0) Mean Log Deviation L, and normalized [0, 1] Shannon inequality share.
Read the guide →Economics & Market MicrostructureTheil T Index GE(1) & Theil L Mean Log Deviation GE(0) Income Inequality Formula
Calculate Henri Theil’s (1967) information-theoretic inequality measures — income-weighted Theil T = (1 / N) * SUM((y_i / mu) * LN(y_i / mu)) and population-weighted Mean Log Deviation Theil L = (1 / N) * SUM(LN(mu / y_i)).
Read the guide →StatisticalTheil–Sen median pairwise slope and a separate-median intercept
Compare a median pairwise slope with ordinary least squares in a five-point example containing one large deviation.
Read the guide →Equity Capital Markets & Corporate ActionsTheoretical Ex-Rights Price (TERP) & Rights Formula
Calculate the Theoretical Ex-Rights Price TERP = (N * P_cum + M * P_sub) / (N + M), Nil-Paid Right Value per new share, Right Value per existing share, and lapsed-rights dilution loss.
Read the guide →Engineering & ScienceThermal Bremsstrahlung Plasma Radiation Loss & Z_eff Impurity Scaling
Calculate free-free thermal bremsstrahlung volumetric power loss P_br = 1.42e-40 * g_ff * Z_eff^2 * n_e^2 * SQRT(T_K) (in kW/m^3) for magnetic fusion plasmas and X-ray galaxy clusters.
Read the guide →Architectural & Automotive Glazing Engineering, ASTM C1048 Thermal Glass TemperingThermal Glass Tempering Quench Stress & ASTM C1048 Formula
Calculate Half-Plate Air-Quench Biot Number Bi, Parabolic Surface Compressive Residual Stress (MPa), Mid-Plane Core Tensile Stress (MPa), and ASTM C1048 / EN 12150 Safety Glass Class.
Read the guide →Engineering & Fluid MechanicsThermal Marangoni Number (Ma) Formula: Thermocapillary Surface-Tension Convection
Calculate the dimensionless thermal Marangoni number Ma = |dsigma/dT| * L * deltaT / (mu * alpha) governing laser weld-pool Penetration, crystal melt growth, thin-film Bénard-Marangoni cells, and microgravity boiling.
Read the guide →Heat Transfer, Cryogenic Engineering & Spacecraft Thermal ControlThermal Radiation Foil Shields & Emissivity Resistance Formula
Calculate Oppenheim Radiative Resistance Between Parallel Enclosures (1/eps1 + 1/eps2 - 1), Unshielded Radiative Heat Flux, Multi-Foil Shielded Heat Flux with N Low-Emissivity Shields, and Fractional Heat-Leak Suppression.
Read the guide →Food Process Engineering & Pharma SterilizationThermal Sterilization D-Value, z-Value & F0 Formula
Calculate Temperature-Shifted Decimal Reduction Time D_T = D_ref * 10^((T_ref - T) / z), Bigelow Equivalent Lethality F_0 = t_hold * 10^((T - T_ref) / z), Log-Spore Reduction, and FDA 12D Commercial Sterility.
Read the guide →Engineering & ScienceThermoelectric Figure of Merit (ZT) & Ioffe Maximum Generator Efficiency
Calculate the dimensionless thermoelectric figure of merit ZT = (S^2 * sigma * T_avg) / kappa and Abram Ioffe’s maximum solid-state heat-to-electricity conversion efficiency eta_max (%) relative to Carnot.
Read the guide →Math & StatisticalThermometer Goal Chart Formulas: Capped Fill Percentage, Remaining Gap & Stretch Surplus
Prepare clean 0–100% fundraising and sales thermometer column charts using MIN(1, Raised / Goal) * 100, remaining gap MAX(0, Goal - Raised), and overachievement surplus MAX(0, Raised - Goal).
Read the guide →Microelectronics Assembly & IC Interconnects, MIL-STD-883 Thermosonic Wire BondingThermosonic Wire Bonding FAB & MIL-STD-883 Pull Formula
Calculate EFO Free-Air Ball Diameter (um), Bonded Mashed-Ball Diameter (um), Nominal Wire Breaking Force (gf), and Vector-Resolved Axial Wire Tension (gf).
Read the guide →Engineering & ScienceThiele Modulus (phi) & Catalyst Pore Diffusion Effectiveness Factor (eta)
Calculate the isothermal first-order catalyst Thiele modulus phi = L * SQRT(k / D_eff) and internal pore-diffusion effectiveness factor eta = tanh(phi) / phi (%) using exact exponential hyperbolic tangent.
Read the guide →EngineeringThiem Equilibrium Aquifer Pumping Test: Transmissivity (T) & K
Estimate confined transmissivity and conductivity from two steady observation-well drawdowns, then compare a separate unconfined calculation using saturated heights above the aquifer base.
Read the guide →EngineeringThiessen and Isohyetal Area-Weighted Rainfall in Excel
Estimate basin rainfall and rainfall volume using polygon areas or isohyetal bands, with working spreadsheet examples and input checks.
Read the guide →EngineeringThin-Lens Equation (1/f = 1/do + 1/di), Magnification & Diopter formulas
Solve image distance di = (f * do) / (do - f), transverse magnification M = -di / do, optical power (Diopters), and Real vs Virtual image type.
Read the guide →EngineeringThin-Walled Pressure Vessel Stress formulas: Hoop (Pr/t) vs Axial (Pr/2t)
Calculate pressure-only membrane stresses in an ideal thin-walled closed cylinder and distinguish a yield-to-hoop ratio from a design safety assessment.
Read the guide →International Macroeconomics & Development GrowthThirlwall Balance-of-Payments Growth Law Formula
Calculate Structural Export Growth epsilon_x * z_world, Thirlwall’s Balance-of-Payments Constrained GDP Growth Rate y_B = (epsilon_x * z_world) / pi_m, Import-Export Drift Gap, and External Sustainability.
Read the guide →Hydropower Civil & Transient Hydraulics, Dieter Thoma (1910) Surge-Tank Stability CriterionThoma Hydropower Surge-Tank Area & Upsurge Formula
Calculate Thoma Critical Surge-Tank Area Ath (m²), Governor Stability Factor (As / Ath), Rigid-Column Mass-Oscillation Period T (s), and Frictionless Full-Rejection Upsurge Zmax (m).
Read the guide →Engineering & ScienceThomson Electron Scattering Optical Depth (tau_es) & Photon Mean Free Path
Calculate electron-scattering optical depth tau_es = n_e * sigma_T * L and photon mean free path l_mfp = 1 / (n_e * sigma_T) using the exact classical Thomson cross section sigma_T = 6.6524587e-29 m^2.
Read the guide →EngineeringThree-phase AC power (kW, kVA, kVAR) & Power Factor capacitor sizing
Calculate balanced 3-phase Apparent Power (kVA), Real Power (kW = SQRT(3)*V*I*PF/1000), and capacitor bank kVAR required to raise lagging Power Factor.
Read the guide →Operations & Supply ChainThree-Point Beta-PERT Expected Duration, Critical-Path Variance & P95 Buffer
Estimate asymmetric task durations with Beta-PERT weighted mean (O + 4M + P)/6 and variance ((P - O)/6)^2, then aggregate critical-path standard deviation via root-sum-of-squares.
Read the guide →Statistical & Clinical AnalysisTHRIVE Score Formula: Endovascular Stroke Thrombectomy 90-Day Outcome (0 to 9)
Predict 90-day functional independence (mRS 0–2) and mortality in large-vessel occlusion ischemic stroke using Alexander Flint’s 0–9 THRIVE score (NIHSS + Age + Chronic Disease Scale: HTN, DM, AF).
Read the guide →Statistical & Clinical AnalysisThurstone Case V Law of Comparative Judgment Formula: Probit Scale Separation
Convert empirical paired-comparison win proportions p_AB into Thurstone Case V psychological/sensory scale distances S_A - S_B = SQRT(2) * z(p_AB) using high-precision rational inverse-normal conversion.
Read the guide →StatisticalTie-Averaged Fractional Rank vs. Competition Rank (RANK.AVG & RANK.EQ Formula)
Assign midpoint fractional ranks (such as 2.5 for a two-way tie at 2nd and 3rd place) using RANK_EQ plus a COUNTIF tie-span adjustment so rank sums stay invariant.
Read the guide →Public Economics & Municipal FinanceTiebout Capitalization & Median Voter Spending Formula
Calculate majority-rule local public spending via the Bowen-Black Median Voter Theorem, derive equilibrium municipal millage rates, and value Tiebout-Oates house-price capitalization.
Read the guide →FinancialTiered volume discounts: all-units XLOOKUP vs marginal block pricing
Calculate wholesale order totals under both all-units volume discounts (XLOOKUP match_mode -1) and progressive marginal slab tiers (SUMPRODUCT).
Read the guide →Dates, Time & SchedulesTime Duration With Days, Hours & Minutes (Multi-Day SLA & Outage Timestamps)
Calculate multi-day elapsed duration between start and end timestamps as "Xd Yh Zm" and total decimal hours using INT(end - start), HOUR(end - start), and MINUTE(end - start) without 24-hour rollover bugs.
Read the guide →Date & TimeTIME function: build valid clock times from hour, minute, and second columns
Assemble numeric hour, minute, and second fields into spreadsheet time fractions with TIME, including automatic 60-minute rollover.
Read the guide →Financial & Business FormulasTime Needed to Reach a Savings Goal (NPER Months & Years)
Calculate the exact number of monthly contributions and calendar years needed to grow a starting balance to a target savings goal using NPER with cash-flow sign guards.
Read the guide →Charts & Visual DataTimeline Chart Formula: 4-Tier Alternating Callout Stem Heights Without Label Overlap
Stage collision-free horizontal Milestone Timeline Charts by cycling vertical error-bar/scatter stem heights across four alternating tiers (+H, -H, +0.5H, -0.5H) using MOD(Index - 1, 4).
Read the guide →Date & TimeTimesheet formula with breaks: calculate net hours including overnight shifts
Use MOD(End - Start, 1) * 24 - (BreakMinutes / 60) so day shifts and midnight-crossing night shifts both calculate accurately.
Read the guide →Math & TrigTimesheet overtime formula: split regular, 1.5x overtime, and 2x double-time
Cap regular hours at 40, isolate 1.5x overtime hours in a middle band, and calculate 2.0x double-time and gross pay with MIN and MAX.
Read the guide →StatisticalTIMI UA/NSTEMI spreadsheet exercise with seven validated flags
Calculate the seven-item UA/NSTEMI TIMI total from fictional pre-assessed inputs and display completion only when every flag is valid.
Read the guide →Mechanical & Structural EngineeringTimoshenko Deep-Beam Deflection Formula: Bending Plus Transverse Shear
Add transverse shear deformation F*L / (4*kappa*G*A) to Euler-Bernoulli bending F*L^3 / (48*E*I) for short deep beams and sandwich cores in Excel and Arte Sheets.
Read the guide →Healthcare & Clinical FormulasTinetti Balance & Gait Assessment (POMA) Fall Risk Score (0–28)
Combine Tinetti Balance Subscore (9 maneuvers, 0–16 pts) and Gait Subscore (7 parameters, 0–12 pts) into total 28-point POMA and classify High (<=18), Moderate (19–23), or Low (>=24) geriatric fall risk.
Read the guide →Fermentation Science, Brewing & Recipe FormulationTinseth Hop Utilization & IBU Bitterness Formula
Calculate Kettle Added Alpha Acids (mg/L), Glenn Tinseth’s Wort-Gravity & Boil-Time Utilization 1.65*(0.000125^(SG - 1))*((1 - EXP(-0.04*t))/4.15), International Bitterness Units (IBU), and BU:GU Balance Ratio.
Read the guide →Fixed Income Markets, US Treasury TIPS & Inflation-Linked BondsTIPS Index Ratio, Deflation Par Floor & Coupon Formula
Calculate US Treasury Inflation-Protected Securities (TIPS) CPI Index Ratio, Maturity Deflation-Floored Principal ($), Semiannual Inflation-Indexed Coupon ($), and Exact Fisher Breakeven Inflation Rate.
Read the guide →Dynamic arraysTOCOL function: flatten a 2D schedule grid into a single clean column
Unroll a multi-column table into one vertical list with TOCOL, remove blank slots with FILTER, and switch to column-major order with TRANSPOSE.
Read the guide →Date & TimeTODAY function: calculate live invoice days overdue and rolling deadlines
Compare due dates against TODAY() for live accounts-receivable aging without time-of-day fraction bugs.
Read the guide →API Gateways, Networking & Rate LimitingToken Bucket Max Burst Duration & Volume Formula
Calculate exact unthrottled burst duration T_burst = B / (P - r), total passed burst requests M_max = (B * P) / (P - r), and full recovery time B / r for API token-bucket limiters.
Read the guide →Statistical & Clinical AnalysisTokyo Guidelines (TG18) Acute Cholangitis Formula: Diagnosis & Grade I–III ERCP Triage
Apply the 2018 Tokyo Guidelines (TG18, Kiriyama et al.) diagnostic rule across Systemic Inflammation (A), Cholestasis (B), and Biliary Imaging (C) alongside Grade I, II, and III urgent ERCP biliary-drainage severity grading.
Read the guide →Servo & CNC Motion Control, HTD/GT Toothed Timing Belts & Teeth-in-Mesh (TIM)Toothed Timing Belt Pitch Diameter & Teeth-in-Mesh Formula
Calculate Driver & Driven Timing-Pulley Pitch Diameters (mm), Small-Pulley Engaged Teeth-in-Mesh TIM, and Exact Belt Tooth Count Lp/p across Center Distance C.
Read the guide →Charts & Visual Data ModelingTornado Sensitivity Chart Formula: Base-Centered Downside/Upside Deviations & Swing Share %
Build a DCF / project-finance Tornado Diagram: center Low-Case and High-Case NPV outputs around Base Case (Y - Y_base), calculate Total Swing |Y_high - Y_low|, and compute Squared-Swing Variance Contribution %.
Read the guide →Dynamic arraysTOROW function: flatten a 2D block into a single horizontal header or tag row
Convert a multi-row grid of SKU codes or tags into one horizontal row with TOROW and TRANSPOSE.
Read the guide →Engineering & ScientificTorricelli Orifice Jet Velocity, Vena-Contracta Flow & Tank Drain Time
Compute sharp-edged orifice efflux velocity, contracted discharge rate Q = C_d * A_o * SQRT(2*g*h), and exact falling-head cylindrical tank drain time between two liquid levels.
Read the guide →EngineeringTorricelli's Law tank orifice velocity SQRT(2gh) & discharge flow (L/s)
Calculate ideal gravity efflux velocity SQRT(2*g*h) and real orifice volumetric discharge Cd * Area * SQRT(2*g*h) in liters per second.
Read the guide →Derivatives, Prime Brokerage Synthetic Financing & Total Return SwapsTotal Return Swap (TRS) Equity Leg & SOFR Settlement Formula
Calculate ISDA Total Return Swap (TRS) Quarterly Total-Return Leg (Price Return + Dividend Pass-Through), ACT/360 SOFR + Spread Financing Leg, Net Periodic Cash Settlement ($M), and Return on Initial Margin (Independent Amount).
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