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GP-Led Continuation Vehicle (CV) Carry Rollover & Alignment
Calculate Legacy Fund Crystallized GP Carry ($M), Selling LP Cash Liquidity Payout ($M), Secondary Lead Syndicate Day-1 Check ($M), and GP Day-1 CV Ownership Alignment (%).
Read the guide →StatisticalGPA formula: calculate credit-weighted Grade Point Average
Map letter grades to 4.0 scale points with XLOOKUP and weight courses by credit hours with SUMPRODUCT(Credits, Points) / SUM(Credits).
Read the guide →Healthcare & Clinical CalculatorsGRACE ACS Risk Score: NSTEMI/STEMI Mortality & < 24h Invasive Timing
Sum the 8-predictor Global Registry of Acute Coronary Events (GRACE) point score and stratify ESC NSTEMI risk tiers (<= 108 Low, 109–140 Intermediate, > 140 High Risk < 24h angiography).
Read the guide →MathGrade multiple-choice tests against an answer key (SUMPRODUCT, FILTER & TEXTJOIN)
Score student or certification exam responses automatically with unweighted counts, custom per-question point weights, and exact missed-question lists.
Read the guide →Engineering & ScienceGraham’s Law of Gas Effusion & Knudsen Isotope Separation Factor
Calculate molecular pinhole effusion rate ratios r_1 / r_2 = SQRT(M_2 / M_1) from molar masses—comparing rapid H2 vs. O2 vacuum leaks (3.984x) against razor-thin single-stage 235UF6 / 238UF6 gaseous diffusion enrichment (alpha = 1.004303).
Read the guide →Drinking-Water Treatment, PFAS/VOC Adsorption & Mass TransferGranular Activated Carbon (GAC) EBCT & Bed-Life Formula
Calculate Granular Activated Carbon Empty Bed Contact Time EBCT (min), Superficial Hydraulic Loading Rate (m/hr), Daily Carbon Usage Rate CUR (kg/d), and Days to Breakthrough.
Read the guide →EngineeringGrashof Number (Gr) & Rayleigh Number (Ra) Natural Convection
Calculate ideal-gas Grashof and Rayleigh magnitudes with SI inputs, then compare Ra with an illustrative vertical-plate reference without treating it as a universal transition rule.
Read the guide →ScienceGreen-Ampt Wetting-Front Soil Infiltration Rate & Ponding Depth
Calculate physically based Green-Ampt soil infiltration capacity f = K_s * (1 + (psi * Delta_theta) / F) (mm/hr) and Mein-Larson Cumulative Ponding Depth F_p = (K_s * psi * Delta_theta) / (i - K_s) (mm).
Read the guide →Transportation Engineering & Operations ResearchGreenshields Traffic Flow & Queue Shockwave Formula
Calculate Greenshields (1935) highway speed v(k) = v_f*(1 - k/k_j), parabolic flow q(k) = k*v(k), maximum lane capacity v_f*k_j / 4, and Lighthill-Whitham-Richards backward queue shockwave speed.
Read the guide →Biostatistics & Survival AnalysisGreenwood Survival Standard Error and Log-Log Confidence Interval
Compute Kaplan-Meier survival S(t), Greenwood’s variance formula, and Kalbfleisch-Prentice log(-log S(t)) confidence bounds that never exceed 100% survival.
Read the guide →Statistical & Mathematical FormulasGreenwood’s Formula & Kalbfleisch-Prentice Log-Log Survival 95% CI
Calculate Kaplan-Meier survival standard error SE(S(t)) = S(t) * SQRT(Σ d_i / (n_i * (n_i - d_i))) via Major Greenwood’s 1926 formula and construct bounded [0, 1] log-log 95% confidence limits S(t)^EXP(±1.96 * SQRT(V) / |LN(S(t))|).
Read the guide →Power System Reliability & Resource AdequacyGrid N-1 Reserve & ELCC Accredited Capacity Formula
Calculate Total Accredited Unforced Capacity UCAP = Thermal_ICAP*(1 - EFORd) + VRE_Nameplate*ELCC, Planning Reserve Margin Surplus vs Target PRM, and N-1 Largest-Contingency Margin.
Read the guide →Ceramic Materials, Fracture Mechanics & Semiconductor Wafer ReliabilityGriffith Brittle Fracture & Weibull Ceramic Volume Scaling
Calculate Griffith Critical Brittle Fracture Stress SQRT((2*E*gamma_s)/(PI()*a)), Weibull Weakest-Link Effective-Volume Knockdown Factor (V_coupon / V_part)^(1/m), Full-Component Characteristic Strength, and Design Safety Factor.
Read the guide →FinancialGross margin vs markup formula: calculate profit % and target selling price
Distinguish Gross Margin ((Price - Cost) / Price) from Markup ((Price - Cost) / Cost), and price products to hit an exact target margin.
Read the guide →FinancialGross-to-net sales bridge and incremental promotional ROI example
Build a simplified sales-deduction bridge and compare estimated incremental contribution with a separately specified campaign cost.
Read the guide →Contract Theory & Corporate GovernanceGrossman-Hart-Moore Hold-Up & Ownership Formula
Calculate non-contractible relationship-specific investment e_HU = (alpha + (1 - alpha)*lambda)*(k_S/c) and quantify how asset ownership shrinks hold-up deadweight loss.
Read the guide →Asset Pricing & Information EconomicsGrossman-Stiglitz Equilibrium Informed Trader Formula
Solve Sanford Grossman & Joseph Stiglitz’s (1980) equilibrium informed-trader share lambda* and prove why costly fundamental research requires noisy market prices.
Read the guide →Lookup & ReferenceGroup arbitrary text values into P&L roll-up buckets (XLOOKUP mapping table)
Map dozens of vendor names or raw status labels into clean summary categories—with an automatic "Other" catch-all—using XLOOKUP and SUMIFS.
Read the guide →Date & TimeGroup clock times into unequal shift or restaurant daypart buckets (MOD & XLOOKUP)
Classify timestamps into uneven operational windows (Early Bird, Lunch Rush, Afternoon, Dinner, Overnight) without nested IF chains.
Read the guide →Lookup & ReferenceGroup Numbers into Pricing or Loyalty Tiers (Approximate VLOOKUP vs XLOOKUP -1)
Bucket continuous revenue, score, or age figures into named brackets without deep nested IF chains—comparing classic sorted VLOOKUP(..., TRUE) against sort-independent XLOOKUP(..., -1).
Read the guide →Lookup & ReferenceGroup numbers into uneven custom brackets (Deal size & order value cohorts)
Assign nonnegative deal values to custom lower-inclusive, upper-exclusive tiers, then summarize amounts by tier.
Read the guide →Math & TrigGroup rows into fixed-size batches (1,1,1, 2,2,2) and alternating N-row bands
Assign cohort/pallet batch IDs every N rows, cycle 1..N slot positions within each batch, and shade alternating N-row blocks.
Read the guide →Date & TimeGroup times & timestamps into unequal shift or daypart buckets (MOD & XLOOKUP)
Map irregular clock windows (e.g., 06:30 Morning, 14:00 Swing, 21:30 Night) from full date-timestamps by stripping date serials with MOD(A2, 1) and XLOOKUP(..., -1).
Read the guide →Date & TimeGroup times into 15-minute, 30-minute, or multi-hour buckets
Round call and event timestamps down to the start of any N-minute interval using FLOOR(TimeVal, Minutes / 1440).
Read the guide →International Trade & Competitiveness AnalyticsGrubel-Lloyd Intra-Industry Trade & Balassa RCA Formula
Distinguish two-way variety trade via Grubel-Lloyd Index GL_i = 1 - ABS(X_i - M_i)/(X_i + M_i) from inter-industry specialization via Bela Balassa’s (1965) Revealed Comparative Advantage RCA_ij.
Read the guide →StatisticsGumbel Return-Period Quantiles and Multi-Year Exceedance Risk
Calculate an illustrative Gumbel annual-maximum quantile from a sample mean and standard deviation, and distinguish return period from the chance of an exceedance during several years.
Read the guide →Engineering & ScienceGunn-Yamada Saturated Liquid Molar Volume Correlation (V_sat)
Calculate saturated liquid molar volume V_sat = V_sc * V_R^(0)(T_r) * (1 - ω * δ(T_r)) (cm^3/mol) across 0.2 <= T_r <= 0.8 via Gunn & Yamada’s 1971 Pitzer corresponding-states polynomial.
Read the guide →Distributed Systems & Capacity EngineeringGunther Universal Scalability Law (USL) Peak Formula
Calculate cluster relative capacity C(N) = N / (1 + alpha*(N - 1) + beta*N*(N - 1)) and exact retrograde concurrency peak N_peak* = SQRT((1 - alpha)/beta) under Neil Gunther’s USL.
Read the guide →Statistical & Clinical AnalysisGupta Perioperative MICA Risk Formula: NSQIP Myocardial Infarction or Cardiac Arrest
Calculate 30-day intraoperative/postoperative MI or cardiac arrest probability (%) using Prateek Gupta’s ACS-NSQIP 5-predictor logistic regression model (Age, ASA Class, Creatinine, Functional Status, and Procedure Site).
Read the guide →Statistical & PsychometricsGuttman’s Split-Half Lambda-4 (λ₄) Reliability Formula (Constrained-Free Variances)
Calculate Louis Guttman’s (1945) split-half test reliability λ_4 = 2 * (1 - (s_A^2 + s_B^2) / s_X^2) without Spearman-Brown’s strict equal-half-variance assumption!
Read the guide →Statistical & PsychometricsGwet’s AC1 Inter-Rater Agreement Coefficient (Solving the Kappa Paradox)
Calculate Kilem Gwet’s (2008) paradox-resistant first-order agreement coefficient AC1 = (p_a - p_eγ) / (1 - p_eγ) vs. Cohen’s κ when trait prevalence is skewed near 0% or 100%.
Read the guide →EngineeringHaaland Explicit Turbulent Pipe Friction Factor (Moody Chart Formula)
Calculate Darcy-Weisbach pipe friction factor f without iterative Colebrook-White loops using S.E. Haaland's explicit formula (-1.8 * LOG10(((eps / D) / 3.7)^1.11 + (6.9 / Re)))^(-2) with a laminar 64 / Re branch.
Read the guide →Engineering & ScientificHaaland’s Explicit Darcy Friction Factor & Laminar-Turbulent Head-Loss Gate
Calculate Darcy-Weisbach pipe friction factor f directly without Colebrook circular iteration using S. E. Haaland’s (1983) 1.11-exponent Moody equation plus a laminar 64/Re switch.
Read the guide →Chemical Reaction Engineering, Synthesis Loops & Recycle Mass BalanceHaber-Bosch Ammonia Synthesis Recycle, Purge & Conversion Formula
Calculate Synthesis-Loop Inert Purge Flow (kmol/hr), Overall Reactant Conversion (%), Ammonia Production Rate (t/hr), and Total Reactor Inlet Flow (kmol/hr) from single-pass conversion.
Read the guide →Architectural Economics, Circular Construction & Lifecycle CostingHabraken Open-Building Support vs Infill Lifecycle Cost
Compare John Habraken Open-Building Decoupled Support + Modular Infill Cumulative Lifecycle Cost against Entangled Monolithic Renovation Tear-Out Penalties, Circular Demolition Savings, and Annualized Cost.
Read the guide →Healthcare & Clinical FormulasHACOR Score (0–25) for Noninvasive Ventilation (NIV) Failure Risk
Calculate Jun Duan’s 5-component bedside HACOR Score (Heart rate 0–1, Acidosis pH 0–4, Consciousness GCS 0–10, Oxygenation P/F 0–6, Respiratory rate 0–4) at 1 hour of NIV to flag > 5 points for timely endotracheal intubation.
Read the guide →EngineeringHagen-Poiseuille Laminar Flow formula: R^4 radius law & hydraulic resistance
Calculate ideal fully developed laminar flow, hydraulic resistance and a Reynolds-number applicability check for a straight round tube.
Read the guide →Chemical, Process & Catalysis EngineeringHaider & Levenspiel (1989) Drag Coefficient C_D Formula: Spherical & Non-Spherical Particles
Calculate fluid-particle Drag Coefficient C_D across Stokes, intermediate, and Newton turbulent regimes (Re < 260,000) for spheres (phi = 1) and angular catalyst, mineral, or biomass particles (0.2 <= phi < 1) via A. Haider and Octave Levenspiel (1989).
Read the guide →ScienceHaldane Substrate-Inhibition Enzyme & Bioreactor Kinetics Formula
Explore a substrate-inhibition rate curve, its maximizing concentration and its actual peak. Distinguish the fitted rate-scale parameter from the peak and from a reactor feed concentration.
Read the guide →EngineeringHall Voltage, Single-Carrier Density & Seebeck Thermoelectric ZT
Calculate a simple transverse Hall voltage and single-carrier density estimate, then explore an independent constant-coefficient Seebeck voltage and dimensionless material ZT.
Read the guide →EngineeringHall-Petch Grain-Size Strengthening & Alloy Yield Strength Formula
Calculate polycrystalline metal yield strength sigma_y = sigma_0 + k_y / SQRT(d) (MPa) from lattice friction stress sigma_0, Hall-Petch locking coefficient k_y (MPa*m^0.5), and average grain diameter d (m).
Read the guide →FinancialHamada Equation formula: unlever peer Beta & relever to target Debt/Equity
Strip financial leverage out of comparable-company betas via Beta_U = Beta_L / (1 + (1 - Tax)*D/E) and relever to your valuation target capital structure.
Read the guide →Mass Timber & Structural Wood Design, NDS Hankinson Grain-Angle Bearing FormulaHankinson Wood Grain-Angle Bearing Strength Formula
Calculate NDS Hankinson Inclined-to-Grain Bearing Strength F_theta (MPa), Retained Parallel Strength (%), Allowable Joint Bearing Load (kN), and Naive Linear Error (MPa).
Read the guide →Economics & Market MicrostructureHannah-Kay Generalized Concentration Index HK(alpha) Formula: Numbers-Equivalent Firms
Unify Shannon Entropy (alpha -> 1), Herfindahl-Hirschman 1/HHI (alpha = 2), and large-firm dominance weighting in a single numbers-equivalent market structure formula: N_HK(alpha) = (SUM(s_i^alpha))^(1 / (1 - alpha)).
Read the guide →Asset Pricing & Macro-FinanceHansen-Jagannathan Bound & Equity Premium Puzzle
Test asset-pricing pricing kernels against Lars Peter Hansen and Ravi Jagannathan’s (1991) lower bound sigma(M) / E[M] >= ABS(E[R_e]) / sigma(R_e) and quantify Mehra-Prescott implied risk aversion.
Read the guide →Civil, Structural & Geotechnical EngineeringHantush-Jacob Leaky Aquifer Formula: Leakage Factor B, Aquitard Resistance c & Steady Drawdown
Analyze semi-confined ("leaky") pumping wells using Mahdi S. Hantush and C. E. Jacob’s (1955) Characteristic Leakage Length B = SQRT(T * b_prime / K_prime), Hydraulic Resistance c = b_prime / K_prime, and De Glee steady drawdown.
Read the guide →Date & TimeHappy Birthday & Work Anniversary Alert Formula (MONTH & DAY)
Build an annual reminder from numeric dates, with an explicit February 28 policy for leap-day anniversaries in common years and calendar-day comparisons for timestamps.
Read the guide →Public Finance & Welfare EconomicsHarberger Deadweight Loss Triangle & Marginal Cost of Funds
Calculate Harberger excess burden DWL = 0.5 * eta * tau^2 * (P_0 * Q_0), quadratic distortion scaling, and Marginal Cost of Public Funds MCPF = (1 - eta*tau) / (1 - 2*eta*tau).
Read the guide →Mechanized Tunneling & Underground Civil Engineering, CSM / NTNU Hard-Rock TBM PerformanceHard-Rock TBM Cutterhead Thrust, Torque & Daily Advance
Calculate Total Cutterhead Normal Thrust (MN), Cutterhead Drive Torque (MN·m), Net Boring Rate of Penetration ROP (m/h), and Daily Utilization-Adjusted Tunnel Advance (m/d).
Read the guide →StatisticalHardy-Weinberg Equilibrium formula: allele & heterozygous carrier frequency (2pq)
Explore two-allele genotype proportions under Hardy–Weinberg assumptions using an assumed recessive homozygote frequency.
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