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Coplanar Waveguide (CPW) RF PCB Impedance Z0 Formula
Calculate CPW Elliptic Modulus k0 = w/(w + 2g), Half-Space Effective Permittivity (1 + eps_r)/2, Hilberg Characteristic Impedance Z0 (Ohms), and Phase Velocity (mm/ns).
Read the guide →Extractive Metallurgy & Precious-Metals Recovery, Electrolytic Copper Refining TankhouseCopper Electrorefining Anode Cycle, Scrap & Slime Formula
Calculate Dissolvable Anode Copper Mass (kg), Faraday Daily Cathode Plating Rate (kg/d), Anode Campaign Life Before Scrap Pull (days), and Au/Ag/Se Anode Slime Yield (kg/anode).
Read the guide →Hydrometallurgy & Electrochemical Refining, Copper SX-EW Tankhouse Faraday BalanceCopper Electrowinning Tankhouse Harvest & kWh/t Formula
Calculate Daily LME Grade-A Copper plated per Electrolytic Cell (kg/day), Total Tankhouse Cathode Harvest (t/day), Rectifier DC Bus Load (MW), and Specific DC Energy (kWh/t Cu).
Read the guide →Lookup & ReferenceCopy Value from Every Nth Row or Column into a Clean Table (INDEX)
Reshape regular vertical blocks using INDEX and a stride, or extract every Nth column from a horizontal source. Includes explicit output anchors and bounds checks.
Read the guide →Statistical & Clinical AnalysisCornfield 2x2 Odds Ratio Quadratic Expected Cell A(psi) & Score Test Formula
Evaluate Jerome Cornfield’s (1956) noncentral hypergeometric quadratic expected cell count A(psi), conditioning variance V(A), and continuity-corrected chi-square score X^2(psi) for any hypothesized 2x2 Odds Ratio psi.
Read the guide →FinancialCornish-Fisher Modified VaR (mVaR) formula: Skewness & Excess Kurtosis Tail Risk
Explore a truncated Cornish-Fisher quantile approximation and compare its illustrative loss threshold with a Gaussian calculation.
Read the guide →Debt Capital Markets, Corporate Bond Indentures & Liability ManagementCorporate Bond Make-Whole Call Price & Par Floor Formula
Calculate Investment-Grade Corporate Bond Semiannual Make-Whole Discount Rate (Benchmark Treasury + Spread), Present Value of Remaining Coupons and Principal, Contractual MAX(Par, PV) Redemption Price ($), and Make-Whole Premium %.
Read the guide →Corporate Divestitures, Carve-Out Accounting & Spin-Off ValuationCorporate Carve-Out Standalone Cost & Stranded Overhead Formula
Calculate Divisional Carve-Out GAAP EBITDA (Direct EBITDA - Allocated Parent Corporate Cost), Standalone G&A Cost Delta (Dis-Synergies vs Cost Savings), True Standalone Run-Rate EBITDA, and RemainCo Unabsorbed Stranded Overhead.
Read the guide →Corporate Finance, Net-Lease Real Estate & Sale-Leaseback StructuringCorporate Sale-Leaseback Debt-Paydown Arbitrage Formula
Calculate Industrial / Retail Sale-Leaseback Gross Valuation Proceeds (NNN Rent / Cap Rate), Net After-Tax Debt Paydown After Capital-Gain Tax on Low-Basis Real Estate, Annual Interest Saved, and Pre-Tax Annual Cash-Flow Accretion / Dilution ($M).
Read the guide →Corporate Finance, M&A Divestitures & IRC Section 355 Split-OffsCorporate Split-Off Exchange Offer Proration & EPS Formula
Calculate IRC Section 355 Split-Off Parent Shares Retired (M), Oversubscribed Tender Proration Factor (%), Post-Split RemainCo EPS ($/sh), and EPS Lift vs Pro-Rata Spin-Off (%).
Read the guide →Quantitative Finance & DerivativesCorrado-Miller Closed-Form Implied Volatility for Non-ATM Options
Extract implied volatility away from the money without Solver using the Corrado-Miller (1996) quadratic moneyness correction and spot why ATM Brenner-Subrahmanyam overstates ITM vol.
Read the guide →StatisticalCorrected QT Interval (QTc) ECG formulas: Bazett (SQRT) vs Fridericia (Cube Root)
Compare Bazett and Fridericia heart-rate corrections using QT in milliseconds and heart rate in beats per minute.
Read the guide →Health & FitnessCorrected Sodium for Hyperglycemia (DKA / HHS): Katz & Hillier Formulas
Correct dilutional hyponatremia in Diabetic Ketoacidosis (DKA) and Hyperosmolar Hyperglycemic State (HHS) using Katz's +1.6 mEq/L and Hillier's +2.4 mEq/L per 100 mg/dL serum glucose above 100.
Read the guide →StatisticalCORREL function: measure positive, negative, and zero linear correlation
Calculate the Pearson correlation coefficient (-1 to +1) between two paired metrics with CORREL, and understand why constant series return #DIV/0!.
Read the guide →Quantitative FinanceCorwin-Schultz High-Low Bid-Ask Spread Estimator Formula (2-Day vs 1-Day)
Estimate effective percentage bid-ask spreads from daily High and Low bars alone using the Corwin & Schultz (2012) two-day range decomposition.
Read the guide →MathCOS function: calculate horizontal run from sloped distance and angle
Project sloped survey or rafter lengths onto the horizontal ground plane with COS(RADIANS(angle)), and round floating-point noise at 90 degrees.
Read the guide →StatisticalCosine Similarity and Euclidean Distance between two vectors in cells
Compare embeddings, customer preference profiles, or document term vectors using SUMPRODUCT dot products and L2 vector norms.
Read the guide →FinancialCost-of-carry price model: compare a maturity price with spot
Explore Spot × EXP((financing + storage - yield) × years), with explicit continuous-rate assumptions and a comparison against spot.
Read the guide →FinancialCost-of-living adjustment (COLA): percentage raises, dollar caps, and reverse base
Calculate adjusted salaries with Base * (1 + Pct), enforce maximum raise caps with MIN, and recover pre-raise pay accurately.
Read the guide →FinancialCost-to-cost project progress: a simplified revenue and billings worksheet
Practice cost-based progress and cumulative catch-up arithmetic. Determine applicable ASC 606 or IFRS 15 accounting separately before using a project model.
Read the guide →Math & EngineeringCotangent (COT), Cosecant (CSC) & Secant (SEC) Roof Pitch & Optical Formulas
Calculate cotangent, cosecant, and secant from degree or radian angles using exact COS/SIN and 1/SIN identities while guarding 0 and 180 degree singularities.
Read the guide →Engineering & ScienceCottrell Equation: Chronoamperometry Diffusion Current i(t) & Nernst Layer Thickness
Calculate t^(-1/2) planar diffusion current i(t) = (n * F * A * C0 * SQRT(D)) / SQRT(PI() * t) in microamps and Nernst diffusion-layer thickness delta = SQRT(PI() * D * t) in electrochemical sensors.
Read the guide →EngineeringCouette Shear Stress, Viscous Heating & Rotational Viscometer Torque
Compute planar Couette shear and viscous dissipation, then compare narrow-gap torque with the ideal concentric-cylinder solution using the same inputs.
Read the guide →Retaining Wall Design, Lateral Earth Pressure & Limit EquilibriumCoulomb Active Earth Pressure Coefficient (Ka) & Thrust Formula
Calculate Coulomb Active Coefficient K_a (with Wall Friction delta, Battered Stem beta & Backfill Slope alpha), Inclined Active Thrust P_a (kN/m), Horizontal Sliding Thrust P_ah (kN/m), and Stabilizing Vertical Shear P_av (kN/m).
Read the guide →EngineeringCoulomb Active Retaining-Wall Earth Pressure (Ka) & Horizontal Thrust
Calculate Charles-Augustin de Coulomb's Active Earth Pressure Coefficient K_a (accounting for soil friction phi, wall-soil friction delta, and sloping backfill beta) and horizontal overturning thrust P_ah.
Read the guide →EngineeringCoulomb's Law Electrostatic Force & Electric Field Strength formulas
Calculate point-charge electrostatic force F = ke * |q1 * q2| / r^2, attractive/repulsive polarity, and electric field E = ke * |q1| / r^2.
Read the guide →Data Cleaning & TextCount & Audit Cells Containing Exactly N Characters (REPT "?" & LEN)
Count text codes matching an exact character length N using COUNTIF(range, REPT("?", N)) and flag truncated or padded SKU/IBAN entries row by row with LEN(TRIM(cell)).
Read the guide →Text & Regular PatternsCount & List Which Keywords Appear Inside a Single Text Cell
Score support tickets, contract clauses, or incident notes by counting how many distinct keywords from a watchlist appear inside one cell and listing every matched keyword.
Read the guide →Conditional AggregationCount & Sum Cells Ending With or Starting With Specific Text (COUNTIF / SUMIF)
Match SKU suffixes ("*" & suffix) and regional prefixes (prefix & "*") dynamically with COUNTIF and SUMIF while preventing blank-affix wildcard traps.
Read the guide →MathCount & Sum Odd vs Even Numbers in a Range (MOD, ISODD & SUMIF)
Test integer parity with MOD(n, 2) or ISODD/ISEVEN and count or sum odd-numbered vs even-numbered street addresses, lot IDs, and quantities cleanly across any spreadsheet engine.
Read the guide →Math & StatisticalCount 16+ Digit Card, IBAN & Tracking IDs Safely (Avoid COUNTIF 15-Digit Bug)
Count 16-to-22-digit card tokens, GS1 SSCC barcodes, and bank IDs accurately with SUMPRODUCT(--(A2:A6 = D2)), avoiding Excel COUNTIF's silent 15-significant-digit coercion bug.
Read the guide →Conditional AggregationCount Active Rows Not Equal to Multiple Terminal Statuses
Count non-blank records whose status does not match any item in an excluded list using SUMPRODUCT boolean inequalities or multi-criteria COUNTIFS.
Read the guide →MathCount and sum GL codes by the sixth character with positional wildcards
Use a sixth-character mask with literal target escaping, and sum matching numeric amounts.
Read the guide →Date & TimeCount Birthdays & Records by Year Cohort (Avoiding the Blank-Cell 1900 Trap)
Count birthdates or hire dates belonging to a specific calendar year or multi-year cohort using COUNTIFS date bounds and blank-guarded SUMPRODUCT + YEAR.
Read the guide →Date & TimeCount birthdays and list names by calendar month across years
Group the example birthday dates by month number while ignoring year.
Read the guide →Dates & TimeCount Calls or Log Events Inside a Specific Time-of-Day Window (COUNTIFS)
Count support calls, ER arrivals, or API requests occurring inside an intraday shift bucket (such as >= 09:00 and < 12:00) using half-open [Start, End) COUNTIFS intervals.
Read the guide →StatisticalCount category labels and calculate their share of nonblank responses
Build a literal-label frequency summary with an explicit blank policy and unrounded percentage values.
Read the guide →Math & TrigCount cells containing specific text: substrings and literal ? or * wildcards
Wrap search terms in "*" & B2 & "*" inside COUNTIF for partial matches, and escape literal question marks or asterisks with ~.
Read the guide →Conditional AggregationCount Cells Greater Than or Less Than a Cell Reference (COUNTIF & COUNTIFS)
Concatenate comparison operators with cell references—COUNTIF(range, ">" & E2), COUNTIF(range, "<" & E2), and two-sided COUNTIFS(range, ">=" & E2, range, "<=" & F2)—without falling into the literal ">E2" string trap.
Read the guide →Statistical & Conditional CountingCount Cells Not Between Two Numbers (Out-of-Tolerance Spec Gate)
Count numeric observations that fall strictly outside a [Lower, Upper] specification interval while ignoring blanks and guarding reversed min/max inputs with MIN and MAX.
Read the guide →Math & TrigCount cells not equal to a value (without counting blank cells)
Pair "<>Value" with "<>" inside COUNTIFS so empty rows in pre-allocated ranges are not counted as active orders.
Read the guide →Counting & Conditional MathCount Cells Over N Characters (REPT("?", N+1) & "*" Wildcard COUNTIF)
Count how many text cells exceed a strict character limit N (such as 60-character SEO titles or 160-character SMS messages) using wildcard COUNTIF(range, REPT("?", N + 1) & "*") without helper columns.
Read the guide →Conditional AggregationCount Cells That Contain Either X or Y Without Double-Counting Overlaps
Count text cells containing substring X or substring Y accurately by subtracting the dual-match intersection COUNTIFS("*X*","*Y*") from COUNTIF("*X*") + COUNTIF("*Y*").
Read the guide →Data Auditing & CollaborationCount Cells That Do Not Contain Errors & Sign Off Imported Sheets
Count valid non-error cells versus broken formulas across imported schedules using per-row NOT(ISERROR(...)) flags, and coordinate multi-user remediation in Arte Sheets.
Read the guide →Counting & Conditional AggregationCount Cells With Exact N Characters Using COUNTIF & REPT("?", N)
Count text codes, SKUs, ZIP codes, or IBANs that match an exact N-character length dynamically using COUNTIF(B2:B7, REPT("?", D2))—and audit mismatched lengths automatically.
Read the guide →StatisticalCount consecutive monthly orders: active retention streak across columns
Count how many unbroken trailing months a customer has ordered right up to the latest close using reverse XMATCH(0, (Row > 0)*1, 0, -1).
Read the guide →Date & TimeCount Dates & Sum Amounts in a Given Calendar Year (COUNTIFS & DATE)
Count transactions and sum revenue occurring in any target year Y using blank-safe Jan 1 to Dec 31 DATE boundaries inside COUNTIFS and SUMIFS.
Read the guide →StatisticalCount exact items in baskets and calculate an attach rate
Use delimiter-aware helper flags to count baskets containing both items and calculate P(B | A), without matching a product name inside a longer name.
Read the guide →Date & TimeCount holidays between two dates (all calendar holidays vs weekday-only)
Distinguish total listed holidays inside a window (COUNTIFS) from weekday holidays that actually reduce working days (NETWORKDAYS difference).
Read the guide →TextCount how many times a word or substring appears in a cell
Divide the characters removed by SUBSTITUTE by the length of the search word, and guard empty search terms against #DIV/0!.
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