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HVAC Sensible Heat Ratio (SHR) & Coil Tons Formula
Calculate ASHRAE Sea-Level Air-Side Sensible Cooling Q_s = 1.08 * CFM * Delta_T_F, Latent Dehumidification Q_L = 0.68 * CFM * Delta_W_grains, Total Chiller Tons (/ 12,000), and Sensible Heat Ratio SHR = Q_s / Q_total.
Read the guide →Civil, Structural & Geotechnical EngineeringHveem Stabilometer Resistance R-Value Formula (ASTM D2844) & Subgrade Modulus
Calculate ASTM D2844 / Caltrans Test 301 Hveem Stabilometer Resistance R-Value (0–100 scale) from 160-psi vertical pressure, transmitted horizontal fluid pressure P_h, and displacement turns D_2, plus AASHTO Resilient Modulus M_R.
Read the guide →Operations, Logistics & EngineeringHvorslev Slug Test Formula: Piezometer Hydraulic Conductivity & Basic Time Lag T_0
Determine in-situ aquifer horizontal hydraulic conductivity K = (r_c^2 * LN(L_e / R)) / (2 * L_e * T_0) from rising- or falling-head piezometer slug-test recovery data using M. Juul Hvorslev’s (1951) USACE equation.
Read the guide →Fluid Power Energy Storage, Nitrogen Bladder/Piston Accumulators & Emergency Fail-Safe SizingHydraulic Bladder Accumulator Polytropic Sizing Formula
Calculate Dry-Nitrogen Precharge Pressure P_0 (bar_a), Naive Isothermal Gas Shell Volume V_0,iso (L), Polytropic/Adiabatic Required Shell Volume V_0,n (L), and Adiabatic Cooling Oversize Penalty (%).
Read the guide →Fluid Power Engineering, Industrial & Mobile Hydraulic Cylinders & Regenerative ValvesHydraulic Cylinder Push/Pull Force & Regenerative Speed Formula
Calculate Full-Bore Push Force (kN), Annular Rod-End Pull Force (kN), Normal Extension Speed (mm/s), Retraction Speed (mm/s), and Regenerative Fast-Approach Speed (mm/s).
Read the guide →Mineral Comminution & Wet Classification, Plitt-Arterburn Hydrocyclone d50c & G-ForceHydrocyclone Cut Size d50c, G-Force & Slurry Flow Formula
Calculate Hydrocyclone Volumetric Slurry Capacity (m³/h), Tangential Inlet Velocity (m/s), Wall Centrifugal G-Force, and Plitt-Arterburn Corrected Cut Size d50c (um).
Read the guide →Hydropower Engineering, Fluid Turbomachinery & Renewable EnergyHydroelectric Net Head, MW Output & Pelton Jet Speed Formula
Calculate Hydropower Net Effective Head (Gross_Head - Penstock_Loss), Electrical Generation Power (rho*g*Q*H_net*eta)/10^6 (MW), Pelton Impulse Nozzle Spouting Velocity Cv*SQRT(2*g*H_net), and Optimal Bucket Pitch Speed.
Read the guide →Engineering & ScienceHydrogenic Bohr Radius (an) & Fine-Structure Relativistic Velocity (vn/c)
Calculate the quantized orbital radius a_n = a_0 * (n^2 / Z) in picometers (CODATA a_0 = 52.9177 pm) and relativistic electron velocity ratio v_n / c = (Z * alpha) / n (fine-structure constant alpha = 1 / 137.036) for hydrogen-like ions.
Read the guide →Controlled-Environment Agriculture (CEA), Hydroponics & Venturi/Dosatron FertigationHydroponic Fertigation Injector Stock Tank & ppm Formula
Calculate Dripper-Line Fertilizer Salt Concentration (mg/L), Concentrated Stock-Tank Salt Concentration (g/L), Total Dry Fertilizer Bag Charge (kg), and Cold-Water Solubility Utilization (%).
Read the guide →Catalytic Reactor Engineering, ULSD Hydrotreating & SAF HydroprocessingHydrotreater LHSV, WHSV & Catalyst Bed Inventory Formula
Calculate Required Catalyst Bed Volume V_cat (m³) from LHSV, Loaded CoMo/NiMo Catalyst Mass (metric tons), True Weight Hourly Space Velocity WHSV (hr^-1), and Apparent Space Time (min).
Read the guide →Statistical & EngineeringHyperbolic COSH, SINH & TANH via EXP: Overhead Cable Catenary Sag & Length
Evaluate exact hyperbolic cosine COSH(u) = (e^u + e^-u)/2 and hyperbolic sine SINH(u) = (e^u - e^-u)/2 using EXP to compute transmission-line catenary sag and true suspended arc length.
Read the guide →Engineering & ScientificHyperbolic Secant Envelope & Complex Hyperbolic Reciprocals (SECH, IMSECH & IMCSCH)
Model optical soliton pulse envelopes sech^2(t/tau) with SECH(x) = 2 / (EXP(x) + EXP(-x)) and compute complex hyperbolic secant and cosecant components (IMSECH & IMCSCH).
Read the guide →StatisticalHypergeometric probability formula: exact sampling without replacement via FACT
Calculate exact finite-lot inspection probabilities P(X = k) = C(K, k) * C(N - K, n - k) / C(N, n) and finite-population variance using FACT and LET.
Read the guide →Digital Infrastructure REITs, Data Centers & Project UnderwritingHyperscale Data-Center REIT $/kW Lease & PUE NOI Formula
Calculate Wholesale Data-Center REIT Annual Base $/kW Lease Revenue ($M), Metered PUE Power Pass-Through Revenue ($M), Facility Cash NOI ($M), and Development Yield-on-Cost (%).
Read the guide →Frozen Dairy & Confectionery Engineering, Ice Cream Overrun % & FDA 21 CFR 135.110Ice Cream Overrun %, Air Fraction & Gallon Weight Formula
Calculate Gravimetric Overrun (%), Dispersed Air Volume Fraction (%), Finished Gallon Net Weight (lb/gal vs FDA 4.50 lb/gal Minimum), and Continuous Freezer Volumetric Yield (L/h).
Read the guide →Health Economics & Clinical Decision AnalysisICER & Net Monetary Benefit (NMB) QALY Formula
Calculate the Incremental Cost-Effectiveness Ratio (C_1 - C_0)/(E_1 - E_0), Net Monetary Benefit lambda*Delta_E - Delta_C, and expose the South-West quadrant ICER sign trap.
Read the guide →Healthcare & ClinicalICH Score (Hemphill 0–6 Points): Intracerebral Hemorrhage Severity Formula
Calculate J. Claude Hemphill's 5-component ICH Score (0 to 6 points) from Glasgow Coma Scale (3–15), Hematoma Volume (>= 30 cm^3), Intraventricular Hemorrhage (IVH), Infratentorial Origin, and Age (>= 80 years).
Read the guide →Healthcare & Clinical CalculatorsICIQ-UI Short Form Urinary Incontinence Severity Score (0–21)
Score the International Consultation on Incontinence Questionnaire Short Form (ICIQ-UI SF, 0–21) across frequency (0–5), even-weighted volume (0/2/4/6), and QoL impact (0–10).
Read the guide →EngineeringIdeal AC transformer: voltage ratio and reflected resistive load
Calculate step-down / step-up transformer turns ratio a = Np / Ns, secondary voltage Vs = Vp / a, current Is = Vs / ZL, and reflected primary impedance Zp = a^2 * ZL.
Read the guide →EngineeringIdeal Buck, Boost and Inverting Buck-Boost Calculations
Compare ideal steady-state CCM voltage ratios and calculate boost inductor current ripple with explicit units and input checks.
Read the guide →EngineeringIdeal constant-specific-heat Brayton efficiency and compressor temperature
Explore the ideal Brayton pressure-ratio expression and isentropic compression temperature, with explicit thermodynamic assumptions.
Read the guide →EngineeringIdeal Gas Law (PV = nRT) and Combined Gas Law formulas
Solve pressure, volume, or moles with PV = nRT and scale compressed-gas states via (P1*V1)/T1 = (P2*V2)/T2 using mandatory Kelvin temperatures.
Read the guide →Electrical Power Safety & Switchgear Protection, IEEE 1584 & NFPA 70E Arc FlashIEEE 1584 Arc-Flash Incident Energy & Boundary Formula
Calculate Switchgear Arc-Flash Incident Energy (J/cm² and cal/cm²), 1.2 cal/cm² Second-Degree Burn Arc-Flash Boundary (m), and NFPA 70E Arc-Rated PPE Category Gate.
Read the guide →Power System Relaying & Substation Protection, IEEE C37.110 Transient CT SaturationIEEE C37.110 CT Knee Voltage & X/R Saturation Formula
Calculate Secondary Symmetrical Fault Current (A), Symmetrical Burden Voltage Vs (V), Transient DC-Offset Excitation Demand Vs*(1 + X/R) (V), and % of Knee Voltage Vk.
Read the guide →Architectural Illumination & MEP Electrical Design, IESNA Zonal Cavity Lumen MethodIES Zonal Cavity Lumen Method, RCR & Fixture Count Formula
Calculate IES Room Cavity Ratio RCR, Exact Fractional Luminaire Count, Rounded-Up Integer Luminaire Count, and Maintained Workplane Illuminance (Lux).
Read the guide →Logical decisionsIF in Excel: flag low stock and keep missing counts visible
Compare a stock count with a minimum level. Decide what happens exactly at the threshold, then distinguish a missing count from a real zero.
Read the guide →Logical & ValidationIF NOT This or That: Avoid the Always-True OR(<>X, <>Y) Trap
Apply surcharges or workflow rules whenever a cell equals neither X nor Y using NOT(OR(cell=X, cell=Y)) or AND(cell<>X, cell<>Y).
Read the guide →Logical & ConditionalIF with Wildcards: Pattern Matching via COUNTIF & ISNUMBER(SEARCH)
Perform wildcard pattern tests (* and ?) inside IF statements—where direct =IF(A2="*PRO*", ...) fails—by pairing IF with COUNTIF(A2, pattern) > 0 or ISNUMBER(SEARCH()).
Read the guide →Logical checks and errorsIFNA vs IFERROR: handle missing lookups without hiding broken data
A missing lookup key produces #N/A, whereas a zero pack size or broken reference produces a different error. Use IFNA so genuinely missing codes show a friendly label while real arithmetic mistakes stay visible.
Read the guide →Logical checks and errorsIFS function: assign ordered score bands without nested IFs
Evaluate checklist scores from highest to lowest threshold because IFS stops at the first TRUE condition. Guard blank cells first and finish with a TRUE catch-all.
Read the guide →Healthcare & ClinicalIIEF-5 (SHIM) Erectile Dysfunction Severity Score Calculator (5–25)
Sum the 5-item abridged International Index of Erectile Function (IIEF-5 / Sexual Health Inventory for Men, 5–25 points) across its five validated clinical severity bands.
Read the guide →FinancialIllustrate a simplified US self-employment tax cash reserve
Practice a below-wage-cap US self-employment tax illustration and a rough equal-period cash reserve, not a filing calculation.
Read the guide →StatisticalIllustrative logistic Elo expected score and one-game rating update
Calculate Arpad Elo's logistic expected match score E_A = 1 / (1 + 10^((R_B - R_A) / 400)) and post-game rating update R'_A = R_A + K * (S_A - E_A) for chess, esports, and LLM arenas.
Read the guide →FinancialIllustrative mortgage payment caps and loan principal with PV
Combine assumed housing and debt-payment caps, subtract housing costs, and model loan principal.
Read the guide →FinancialIllustrative progressive bracket calculation: base amount plus marginal rate
Learn progressive bracket arithmetic using a fictional four-bracket schedule and compare effective and marginal rates.
Read the guide →EngineeringIllustrative tidal distance scales and planetary synodic periods
Compare a simple nonrotating tidal-balance estimate with a fluid Roche approximation, and calculate the beat period of two prograde mean orbital motions.
Read the guide →Maritime Decarbonization & ESG OperationsIMO Shipping CII Rating, AER & EEOI Carbon Formula
Calculate IMO MARPOL Annex VI Attained Annual Efficiency Ratio AER (g CO2 / DWT-nm), Voluntary Operational EEOI (g CO2 / cargo-ton-nm), CII Compliance Ratio, and A-to-E Rating Band.
Read the guide →Spreadsheet Governance & Collaborative AI WorkflowsIn-App 2 MB Attachment vs MCP 200-Cell Read Audit
Choose the right inspection path in Arte Sheets: metered in-app Pro Assistant file excerpts (.xlsx/.csv/.tsv/.txt <= 2 MB, safe non-executing) versus external MCP read_range (<= 200 cells raw values/formulas + revision, 0 Arte AI credits).
Read the guide →AI Assistant & Workbook SafetyIn-App AI Plan Validator, Suggest Style Guard & Undo Audit
Audit the client-side validatePlan and applyPlan safety rules in Arte Sheets: <=100 cell changes, <=2,000-char strings, <=10,000-cell range/SEQUENCE caps, suggest-mode style rejection, and local Undo stack recording.
Read the guide →AI Assistant & Collaboration GovernanceIn-App Voice 3-Min Cap & Owner Share Preview Audit
Audit bounded WebRTC voice sessions (<=180s expiry, 15s heartbeat, barge-in turn guards) and verify why share_document requires verified-owner UI confirmation and cannot run inside execute_steps.
Read the guide →LogicalInclude and exclude text substrings with SEARCH
Flag and filter transactions that match target keywords ("Cloud" OR "SaaS") while disqualifying rows containing exclusion terms ("Refund" OR "Test").
Read the guide →FinancialIncome tax bracket formula: calculate progressive marginal and effective tax
Compute progressive multi-bracket tax in a single SUMPRODUCT formula using differential bracket rates without nested IF ladders.
Read the guide →MathIncrement a Calculation Automatically with ROW or COLUMN Step Ladders
Create arithmetic scenario ladders down rows or across columns from a base and a step. Keep full precision in rates and round only displayed cost results.
Read the guide →Lookup & ReferenceIncrement a Cell Reference Every Nth Row When Copying Down (Non-Volatile INDEX)
Extract every 3rd (or k-th) row from repeating stacked export blocks—such as stacked Vendor / Invoice / Amount triplets—using non-volatile INDEX + ROW math instead of OFFSET or INDIRECT.
Read the guide →TextIncrement a zero-padded ID number inside a text string (INV-0099 -> INV-0100)
Isolate the trailing numeric segment of a structured code, add N, and preserve leading-zero width automatically across 99-to-100 rollovers.
Read the guide →TextIncrement letters (Rev A -> Rev B) and wrap A–Z shifts with CODE & CHAR
Step engineering revision letters forward ("A" -> "B"), wrap "Z" cleanly back to "A" with MOD(..., 26), and apply symmetric ROT13 character shifts.
Read the guide →Lookup & ReferenceINDEX and MATCH with multiple criteria: boolean array lookup without XLOOKUP
Match two or more columns simultaneously with INDEX(return_range, MATCH(1, (col1=x)*(col2=y), 0)) for universal workbook compatibility.
Read the guide →LookupsINDEX and MATCH: look up a column to the left of the search key
VLOOKUP can only search the leftmost column of a range. Combine INDEX and exact MATCH when the identifier you have sits to the right of the value you need to retrieve.
Read the guide →Lookup & ReferenceINDIRECT function: turn text cell and range strings into live references
Evaluate cell or range addresses stored as text with INDIRECT so summary formulas can switch target columns dynamically.
Read the guide →StatisticalIndividuals control chart: moving-range three-sigma limits
Estimate individual-observation control limits using average adjacent moving range, then compare a new reading with the fixed baseline.
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