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Revised Five-Factor Score (2011 FFS) Formula: Systemic Necrotizing Vasculitis Prognosis
Calculate Loïc Guillevin’s 2011 Revised Five-Factor Score (FFS) across PAN, MPA, EGPA, and GPA—including the protective ENT absence (+1 when ENT manifestations are absent in GPA/EGPA).
Read the guide →Healthcare & Clinical CalculationsRevised Geneva Score for Pulmonary Embolism (Objective Pretest Risk)
Calculate Grégoire Le Gal’s 100% objective Revised Geneva Score (0–25 points across Age > 65, Prior DVT/PE, Surgery/Fracture, Active Cancer, Unilateral Leg Pain, Hemoptysis, Heart Rate tiers, and Deep-Vein Palpation Pain) to guide D-dimer vs. CTPA.
Read the guide →Healthcare & ClinicalRevised Trauma Score (RTS) Weighted Physiological Formula (TRISS)
Convert raw Glasgow Coma Scale (GCS 3–15), Systolic Blood Pressure (SBP), and Respiratory Rate (RR) into 0–4 Champion coded values and compute the weighted Revised Trauma Score RTS = 0.9368*GCSc + 0.7326*SBPc + 0.2908*RRc.
Read the guide →EngineeringReynolds Number (Re) formula: Laminar vs Turbulent pipe flow regime
Calculate dimensionless Reynolds Number Re = (ρ · v · D) / μ in SI units and classify Laminar (< 2,300), Transitional, and Turbulent (> 4,000) flow.
Read the guide →RF & Wireless Transceiver Design, Receiver Linearity & Dynamic RangeRF Receiver IIP3, IMD3 & Spurious-Free Dynamic Range Formula
Calculate RF Front-End Input-Referred Two-Tone Third-Order Intermodulation Product IMD3 (dBm = 3*Pin - 2*IIP3), Carrier-to-Intermod Suppression (dBc), Two-Thirds-Slope Spurious-Free Dynamic Range SFDR (dB), and Noise-Floor Headroom.
Read the guide →EngineeringRF VSWR, Reflection Coefficient (Gamma) & Return Loss (dB) formulas
Calculate RF transmission-line impedance mismatch using Gamma = ABS((Z_L - Z_0) / (Z_L + Z_0)), Voltage Standing Wave Ratio VSWR = (1 + Gamma) / (1 - Gamma), Return Loss -20*LOG10(Gamma), and reflected power.
Read the guide →LogicalRFM (Recency, Frequency, Monetary) customer scoring & CRM segment formula
Score customers 1–5 on Recency (lower days = higher score!), Frequency, and Monetary spend, build 3-digit RFM codes ("555", "155"), and assign lifecycle segments.
Read the guide →Statistical & Mathematical FormulasRichards Generalized Logistic Curve: Asymmetry Parameter (ν) & Inflection
Model asymmetric epidemic, crop, and market S-curves via F. J. Richards’ 4-parameter generalized logistic equation Y(t) = K * (1 + ν * EXP(-r * (t - t_m)))^(-1 / ν) and inflection height Y_inf = K * (1 + ν)^(-1 / ν).
Read the guide →Engineering & ScienceRichardson-Dushman Thermionic Emission Current Density Formula (SEM, X-Ray & Klystron Cathodes)
Calculate thermionic electron emission current density J = A_G * T^2 * EXP(-phi_eV / (kB_eV * T)) in A/cm^2 across tungsten, thoriated tungsten, and LaB6 electron-microscope cathodes.
Read the guide →Engineering & ScienceRichardson-Zaki Hindered Settling Velocity & Kynch Gravity Thickener Solids Flux
Calculate concentrated slurry hindered settling velocity v_h = v_t * ((1 - C_v) ^ n) and batch gravity-thickener solids flux G_s = C_v * v_h for mineral tailings, wastewater clarifiers, and fluidized beds.
Read the guide →Engineering & ScienceRiedel Parameter (αc): Critical Vapor-Pressure Slope & dPsat/dT at Tc
Calculate L. Riedel’s dimensionless critical saturation slope α_c = 5.808 + 4.93 * ω and dimensional critical pressure-temperature derivative (dP_sat / dT)|_Tc = α_c * (P_c / T_c) (bar/K).
Read the guide →Cleaning imported dataRIGHT function: extract trailing serial digits with leading zeros
Pull a fixed-width suffix from the end of invoice or voucher IDs while preserving leading zeros as text, and handle short or blank cells cleanly.
Read the guide →Public Choice & Political EconomyRiker-Ordeshook Calculus of Voting Formula
Calculate Expected Instrumental Pivotal Payoff p * B, Downsian Net Voting Return p * B - C, Riker-Ordeshook Expressive Turnout Utility R = p * B - C + D, and Breakeven Pivotal Probability.
Read the guide →Healthcare & ClinicalRIPASA Appendicitis Score Calculator (Half-Point 2.0–16.5 Scale)
Calculate the Raja Isteri Pengiran Anak Saleha Appendicitis (RIPASA) score (2.0 to 16.5 points) across demographics, symptom duration, Rovsing/guarding signs, WBC, and negative urinalysis.
Read the guide →EngineeringRLC Circuit formulas: Resonant Frequency, Reactance (XL, XC), Impedance Z & Q-Factor
Calculate series RLC resonant frequency f0 = 1 / (2*PI()*SQRT(L*C)), total AC impedance Z = SQRT(R^2 + (XL - XC)^2), and circuit Quality Factor Q.
Read the guide →EngineeringRLC Resonant Frequency (f0), Quality Factor (Q) & -3 dB Bandwidth
Calculate LC tank resonant frequency f_0 = 1 / (2 * PI() * SQRT(L * C)) (Hz), Series RLC Quality Factor Q = (1 / R) * SQRT(L / C), and half-power -3 dB Bandwidth BW = f_0 / Q.
Read the guide →Healthcare & ClinicalRockwood Clinical Frailty Scale (CFS 1–9): Geriatric IADL/ADL Triage Formula
Assign Kenneth Rockwood's revised 9-level Clinical Frailty Scale (CFS 1 Very Fit to CFS 9 Terminally Ill) from baseline 2-week pre-illness terminal status, basic BADL dependence, IADL dependence, and symptom limitation.
Read the guide →Statistical AnalysisRogan-Gladen True Prevalence Estimator Correcting False Positives & Negatives
Recover true population prevalence from apparent screening-test positivity via Rogan and Gladen’s (1978) identity (p_app + Spec - 1) / (Sens + Spec - 1) with [0, 1] boundary clamping.
Read the guide →Quantitative FinanceRogers-Satchell Drift-Independent OHLC Volatility Estimator Formula
Estimate unbiased intraday and annualized return volatility on trending assets using the Rogers-Satchell (1991) Open-High-Low-Close variance v_RS = ln(H/C)*ln(H/O) + ln(L/C)*ln(L/O).
Read the guide →Engineering & ScienceRohsenow Nucleate Pool Boiling Correlation: Wall Superheat ΔT_e Formula
Calculate boiler tube wall superheat ΔT_e = T_wall - T_sat (K) for nucleate pool boiling at heat flux q″ via Warren Rohsenow’s 1952 bubble-agitation correlation.
Read the guide →FinancialROI, ROAS, Break-Even ROAS, and Annualized ROI formulas
Distinguish Return on Ad Spend (Revenue / Spend) from true Gross-Profit ROI, solve for Break-Even ROAS (1 / GrossMargin), and annualize multi-year returns.
Read the guide →FinancialROIC, NOPAT, and Economic Value Added (EVA) formulas
Calculate Net Operating Profit After Tax (NOPAT), Operating Invested Capital, ROIC %, and dollar Economic Value Added above WACC.
Read the guide →Quantitative FinanceRoll (1984) Implied Effective Bid-Ask Spread Formula (Serial Autocovariance)
Infer the hidden effective dollar and basis-point bid-ask spread from transaction prices alone using Roll’s (1984) first-order price-change autocovariance S_Roll = 2 * SQRT(-Cov(dP_t, dP_{t-1})).
Read the guide →Market Microstructure & Quantitative FinanceRoll Serial-Covariance Implicit Bid-Ask Spread Formula
Estimate effective bid-ask spread s_Roll = 2 * SQRT(-Cov(Delta_P_t, Delta_P_{t-1})) from transaction prices alone without quote data via Richard Roll’s (1984) bounce formula.
Read the guide →Date & TimeRoll weekend or Monday dates to Friday / Monday (nearest workday rules)
Apply illustrative weekend shifts or calculate the previous Monday–Friday working date.
Read the guide →Financial ModelingRoll’s Implied Effective Bid-Ask Spread from First-Order Price Autocovariance
Estimate hidden transaction bid-ask spreads from trade-only price tapes using Richard Roll’s (1984) microstructure formula Spread = 2 * SQRT(MAX(0, -Cov(Delta_P_t, Delta_P_{t-1}))).
Read the guide →StatisticalRolled Throughput Yield (RTY = PRODUCT) & Hidden Factory DPU formulas
Multiply sequential step First-Pass Yields with PRODUCT(B2:B5) to expose multi-step "Hidden Factory" rework loss and Poisson Defects per Unit (-LN(RTY)).
Read the guide →Mechanical Drives, Roller Chains & Sprocket KinematicsRoller Chain Sprocket Pitch Diameter & Chordal Ripple Formula
Calculate Exact Polygon Sprocket Pitch Diameter D_p (mm), Chordal Speed Variation Ripple (%), Mean Linear Chain Velocity (m/s), and Chain Strand Tension (N) from kW.
Read the guide →Metallurgical Rolling Mills, Hot/Cold Strip Pass Schedules & Roll Separating ForceRolling Mill Draft, Max Friction Bite & Roll Force Formula
Calculate Pass Thickness Draft Delta_h (mm), Friction-Limited Maximum Self-Entry Draft mu^2*R (mm), Projected Roll-Bite Contact Length L_p (mm), Plane-Strain Roll Separating Force (kN), and Bite Status.
Read the guide →Cloud Infrastructure & AI Systems EngineeringRoofline Model Compute vs Memory-Bound Formula
Diagnose LLM inference vs training bottlenecks via Samuel Williams, Andrew Waterman, and David Patterson’s (2009) Roofline ceiling MIN(Peak_TFLOPS, Operational_Intensity * HBM_Bandwidth) and Ridge Point.
Read the guide →Urban Economics & Regional Labor MarketsRosen-Roback Spatial Equilibrium Wage & Rent Formula
Invert Sherwin Rosen (1979) and Jennifer Roback’s (1982) spatial equilibrium conditions to extract unobserved Household Consumption Amenities (s_R*d_ln_r - d_ln_w) and Firm Agglomeration Productivity (theta_L*d_ln_w + theta_R*d_ln_r).
Read the guide →Causal Inference & Sensitivity AnalysisRosenbaum Sensitivity Bounds (Gamma) for Matched-Pair Studies
Calculate Rosenbaum hidden-bias probability bounds p_plus = Gamma / (1 + Gamma) and worst-case McNemar discordant-pair Z-scores to find the exact confounding odds Gamma that tips significance.
Read the guide →Economics & Market MicrostructureRosenbluth / Hall-Tideman Index (HTI) Formula: Rank-Weighted Market Concentration
Measure antitrust market concentration with full sensitivity to small-fringe competitors using Gideon Rosenbluth (1955) and Marshall Hall & Nicolaus Tideman’s (1967) rank-weighted index HTI = 1 / (2 * SUM(i * s_i) - 1).
Read the guide →Statistical & Clinical AnalysisROSIER Scale Formula: Recognition of Stroke in the Emergency Room (-2 to +5)
Distinguish acute stroke/TIA (ROSIER > 0) from seizure or syncope mimics using Azlisham Mohd Nor’s 7-item emergency triage score (-2 to +5 points) after excluding hypoglycemia.
Read the guide →Engineering & Fluid MechanicsRosin-Rammler (RRSB) Particle Size Distribution Formula: Cumulative Retained & Passing %
Model pulverized coal, cement clinker, pharmaceutical sprays, and cyclone dusts using Rosin & Rammler’s 1933 Weibull sieve law R(d) = 100 * EXP(-(d / d_63.2)^n) and cumulative passing P(d) = 100 - R(d).
Read the guide →Engineering & ScienceRossby Number (Ro), Coriolis Parameter (f) & Geostrophic Wind Speed
Calculate the planetary Coriolis parameter f = 2 * Omega * SIN(phi), atmospheric/oceanic Rossby number Ro = U / (|f| * L), and geostrophic wind speed Ug = (dP / dn) / (rho * |f|).
Read the guide →Pneumatic Conveying, Powder Handling, Rotary Airlock Valves & Flour/Cement MillsRotary Airlock Feeder Displacement & Solids Loading Formula
Calculate Theoretical Rotor Swept Volume (m³/h), Pocket-Fill-Adjusted Volumetric Feed (m³/h), Powder Mass Feed Rate (kg/h), and Dilute-Phase Solids-to-Air Mass Loading Ratio mu.
Read the guide →Lithium-Battery Dry-Room HVAC, Silica-Gel Desiccant Wheels & Psychrometric Mass BalanceRotary Desiccant Wheel Moisture Removal & Regen Formula
Calculate AHRI 940 Moisture Removal Capacity MRC (kg/h), Process Latent Heat of Sorption Released (kW), Reactivation Heater Thermal Input (kW), and Specific Regeneration Energy (kWh/kg).
Read the guide →Cement, Lime & Mineral Pyroprocessing, USBM Sullivan Rotary Kiln Residence TimeRotary Kiln Sullivan Residence Time & Fill % Formula
Calculate USBM Sullivan Solids Mean Residence Time (min), Axial Bed Advance Velocity (m/min), In-Kiln Solids Holdup Inventory (tonnes), and Volumetric Fill Degree (%).
Read the guide →Mineral Processing, Composting & Recycling Separation, Rotary Trommel Screen KineticsRotary Trommel Screen Critical RPM & Bed Fill Formula
Calculate Drum Critical Centrifuging Speed Ncrit (RPM), Operating % Critical Speed, Cascade Helix Residence Time (s), and Cross-Sectional Bed Holdup Fill (%) for Undersize Screening.
Read the guide →Charts & Visual DataRotate Pie Chart Formula: Exact First-Slice Angle to Center Callout at 3 O’Clock
Calculate the exact Angle of First Slice in degrees MOD(90 - 180 * Share + 360, 360) so a highlighted pie wedge or Bar-of-Pie connector centers symmetrically on the 3 o’clock horizontal axis.
Read the guide →Hollow Polymer Processing, Rotational Molding Powder Shot Weight & Cavity Tumbling FillRotational Molding Powder Shot Weight & Bulk Fill Formula
Calculate Required Pulverized PE Charge Weight (kg), Unmelted Powder Loose Volume (L), Cold-Mold Volumetric Fill Fraction (%), and Solid-to-Powder Compaction Ratio.
Read the guide →Biostatistics & EpidemiologyRothman Additive Interaction: RERI, AP, and Synergy Index (S)
Calculate Relative Excess Risk due to Interaction (RERI = RR_11 - RR_10 - RR_01 + 1), Attributable Proportion (AP), and Rothman’s Synergy Index (S) to detect public-health synergy missed by multiplicative models.
Read the guide →Actuarial Economics & Asymmetric InformationRothschild-Stiglitz Insurance Screening Deductible Formula
Solve the incentive-compatible Low-risk partial coverage deductible D_L* and test Rothschild-Stiglitz separating equilibrium existence lambda_H >= lambda_H*.
Read the guide →Master Production Scheduling & Factory Capacity PlanningRough-Cut Capacity Planning (RCCP) & Overtime Formula
Validate a Master Production Schedule (MPS) using APICS Rough-Cut Capacity Planning (RCCP): Required Standard Hours, Demonstrated Capacity (Machines * Clock_Hours * Utilization_Efficiency), Load-to-Capacity Ratio, and Clock Overtime Hours.
Read the guide →Math & TrigRound a number to N significant figures (scientific and lab precision)
Dynamically compute ROUND's decimal-places argument from INT(LOG10(ABS(x))) to round large integers, tiny decimals, and negatives to N sig figs.
Read the guide →Numbers and totalsROUND in Excel: why rounded rows can disagree with the total
Compare rounding each amount with rounding the final sum. Use a three-row example, check negative midpoint values, and separate number formatting from changing a value.
Read the guide →Math & TrigRound order quantity up to case-pack / MOQ bundle size (CEILING & excess units)
Enforce supplier Minimum Order Quantity (MOQ) and case-pack multiples, calculate sealed cases to order, and track overage buffer units.
Read the guide →Math & RoundingRound Retail Prices to End in .45 or .95 with Minimum-Margin Floor Guard
Snap raw cost-plus catalog prices to the nearest .45 or .95 psychological charm ending—or force upward rounding when nearest-step rounding would dip below your target floor price.
Read the guide →Math & TrigRound retail prices to end in .99 or .95 (charm pricing formulas)
Convert calculated cost-plus prices to nearest .99, margin-safe upward .99, or $5-increment .95 retail price points.
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