Learn one useful thing today.
FAO-56 Penman-Monteith Reference Evapotranspiration (ET0) Formula
Calculate FAO-56 Radiation-Driven ET Term (mm/d), Wind-VPD Aerodynamic ET Term (mm/d), Total Reference Grass Evapotranspiration ET0 (mm/d), and Weekly Water Volume per Hectare (m³/ha).
Read the guide →EngineeringFaraday electrolysis yield and ideal van ’t Hoff osmotic pressure
Estimate deposited mass with a stated current efficiency and compare it with a separate ideal-solution osmotic-pressure calculation.
Read the guide →Electroplating Surface Finishing, Watts Nickel / Hard Chrome Baths & Faraday’s LawFaraday Electroplating Thickness & Cathode Efficiency Formula
Calculate Cathode Current Density J (A/dm²), Ideal 100%-Faradaic Deposited Mass (g), Cathode-Efficiency-Adjusted Metal Mass (g), and Mean Electroplated Coating Thickness (um).
Read the guide →Engineering & ScienceFaraday Magneto-Optic Rotation Angle & 45-Degree Optical Isolator Formula
Calculate non-reciprocal linear polarization rotation theta = DEGREES(V * B * L) from Verdet constant V (rad/(T*m)), axial magnetic field B (Tesla), and crystal length L (m), plus the exact field required for a 45° laser optical isolator.
Read the guide →ScienceFaraday's Law of Electrolysis Mass & Tafel Electrode Overpotential
Build a constant-current Faraday mass calculation with current efficiency, and a separate anodic Tafel approximation using a dimensionless current-density ratio.
Read the guide →Statistical & Clinical AnalysisFarrington-Manning Non-Inferiority Risk Difference Score Test Formula
Test clinical non-inferiority of response rates H_0: p_T - p_C <= -delta_0 using C. P. Farrington & G. Manning’s (1990) FDA-preferred Score Z-statistic with restricted null variance.
Read the guide →Mechanical Design & Fatigue AnalysisFatigue Notch Sensitivity (q) and Factor K_f (Peterson Formula)
Convert static elastic stress concentration K_t into reduced cyclic fatigue concentration K_f = 1 + q * (K_t - 1) using Peterson’s notch-sensitivity formula q = 1 / (1 + a_pet / r_notch).
Read the guide →Natural Resource & Forestry EconomicsFaustmann Forest Rotation & Land Expectation Formula
Calculate Martin Faustmann’s (1849) infinite-rotation Land Expectation Value LEV = (p*V(T) - C*EXP(r*T))/(EXP(r*T) - 1) and contrast optimal Faustmann, single-cycle Wicksell, and biological MAI ages!
Read the guide →Petroleum Refining, Fluid Catalytic Cracking (FCC) & Heat BalanceFCC Regenerator Coke Burn, Catalyst Circulation & Air Rate Formula
Calculate Zeolite Catalyst Circulation Rate (t/hr), Regenerator Coke Burn Rate (kg/hr), Exothermic Regenerator Heat Duty (MWth), and Main Air Blower Mass Flow (t/hr).
Read the guide →Psychometrics & BiostatisticsFeldt W Statistic and Confidence Bounds for Cronbach’s Alpha
Test observed Cronbach’s alpha against a minimum reliability benchmark using Feldt’s exact variance-ratio W = (1 - alpha_0) / (1 - alpha_hat) and Bonett’s log-complement 95% confidence interval.
Read the guide →Operations, Logistics & EngineeringFellenius Ordinary Method of Slices (Swedish Circle) Slope Stability Factor of Safety
Calculate the non-iterative circular-slip Slope Stability Factor of Safety FS = SUM(c'*l_i + MAX(0, W_i*cos(alpha_i) - u_i*l_i)*tan(phi')) / SUM(W_i*sin(alpha_i)) using Wolmar Fellenius’s (1927/1936) Ordinary Method of Slices.
Read the guide →Statistical & Clinical AnalysisFencl-Stewart Base Excess Partition Formula: Na-Cl Effect & Hypoalbuminemia Alkalosis
Uncover hidden hyperchloremic acidosis masked by hypoalbuminemic alkalosis in ICU patients using Story, Morimatsu & Bellomo’s simplified Fencl-Stewart Base Excess partition: BE_NaCl = Na - Cl - 38 and BE_Alb = 0.25 * (42 - Albumin_gL).
Read the guide →EngineeringFenske Minimum Distillation Stages (N_min) & Relative Volatility
Estimate binary total-reflux minimum equilibrium stages from mole fractions and supplied relative volatility, with input checks and explicit stage-counting assumptions.
Read the guide →Civil, Structural & Geotechnical EngineeringFerguson & Church (2004) Universal Sediment Settling Velocity Formula: Silt to Cobbles
Calculate terminal fall velocity w_s (m/s) of natural river/marine grains across ALL Reynolds numbers — bridging Stokes viscous silt (w ~ D^2) and turbulent gravel wake drag (w ~ SQRT(D)) without iteration — via R. I. Ferguson and M. Church (2004).
Read the guide →Healthcare & ClinicalFeverPAIN Acute Sore Throat Score (NICE Antibiotic Stewardship Formula)
Calculate Paul Little’s UK NICE-endorsed 0–5 FeverPAIN score (Fever in past 24h, Purulence, Attend rapidly <= 3 days, severely Inflamed tonsils, No cough or coryza) to guide no-antibiotic, back-up, or immediate prescribing.
Read the guide →Healthcare & ClinicalFIB-4 Index & APRI Score for Noninvasive Liver Fibrosis Staging
Calculate the hepatology FIB-4 Index = (Age * AST) / (Platelets * SQRT(ALT)) and AST-to-Platelet Ratio Index APRI = ((AST / AST_ULN) / Platelets) * 100 from routine CBC and liver panel labs.
Read the guide →Engineering & ScienceFiber Bragg Grating (FBG) Wavelength, Strain & Temperature Shift Formula
Calculate FBG center Bragg reflection wavelength λ_B = 2 * n_eff * Λ and coupled strain-temperature shift Δλ_B = λ_B * ((1 - p_e) * ε + (α_Λ + ξ) * ΔT) for telecom C-band structural health sensors.
Read the guide →Fiber-Laser Sheet Cutting, Nesting Cycle-Time Quoting & CNC Kerf CompensationFiber-Laser Cutting Pierce Time, Kerf & Cycle Time Formula
Calculate Total Pierce Dwell Time (s), Contour Cutting Time (s), Total Part Cycle Time Including Rapid Moves (s), Gross Parts Per Hour, and CNC Toolpath Kerf Offset (mm).
Read the guide →Telecommunications Engineering, Single-Mode Fiber & DWDM Optical LinksFiber-Optic Link Power Budget, Splice Loss & Margin Formula
Calculate Total Available Optical Power Budget (dB), Cumulative Span+Splice+Connector Attenuation (dB), Received Optical Power P_rx (dBm), and Unallocated Safety Margin (dB).
Read the guide →EngineeringFiber-Optic Numerical Aperture (NA), Acceptance Angle & V-Number
Explore an ideal circular step-index fiber: numerical aperture, a ray-model acceptance half-angle and V-number, using consistent units and an approximate higher-mode cutoff.
Read the guide →Math & TrigFibonacci sequence in spreadsheets: recursive column and direct Nth term (Binet)
Generate Fibonacci numbers row-by-row (=B2+B3) or jump directly to the Nth Fibonacci number in a single cell using Binet's Golden Ratio formula.
Read the guide →StatisticalFick Cardiac Output, Stroke Volume & Systemic Vascular Resistance (SVR) formulas
Practice a simplified Fick-model calculation, stroke-volume conversion and resistance arithmetic with fictional inputs and explicit units.
Read the guide →ScienceFick's First Law Diffusive Flux, Peclet (Pe) & Schmidt (Sc) Numbers
Compute signed one-dimensional diffusive molar flux from a linear concentration gradient, plus mass-transfer Peclet and Schmidt numbers with explicit units and input checks.
Read the guide →FinancialFIFO vs. Weighted-Average Cost inventory COGS & Ending Inventory formulas
Allocate units sold across sequential purchase cost layers with MIN/MAX clipping to compute exact FIFO COGS, Ending Inventory, and WAC comparison.
Read the guide →Hydrogen Type IV COPVs, Carbon-Fiber Filament Winding & 54.74° Netting AnalysisFilament-Wound Vessel Netting Analysis (54.74°) Formula
Calculate Exact Balanced Netting Winding Angle ATAN(SQRT(2)) = 54.74°, Axial-Governed Dry Fiber Thickness (mm), Hoop-Governed Dry Fiber Thickness (mm), and Total Composite Shell Thickness (mm).
Read the guide →Structural Steel Connections, AWS D1.1 Welding & AISC 360 LRFDFillet Weld Effective Throat & AISC/AWS LRFD Strength Formula
Calculate 45° Fillet Effective Throat t_e = w / SQRT(2) (mm), Total Effective Weld Shear Area A_w (mm²), Design Strength per Millimeter (kN/mm), and Total Connection LRFD Capacity phi*R_n (kN).
Read the guide →Media, Entertainment Finance & Film-Slate Recoupment WaterfallsFilm-Slate Recoupment Waterfall & Backend Profit Formula
Calculate Independent Film & Content-Slate Off-the-Top Distribution Fee, Post-P&A Recoupment Cash Available for Production Financing, Net Backend Profit Pool, and Equity Financier Total Cash Multiple.
Read the guide →Dynamic ArraysFilter & Flag Rows Containing Any Keyword from a Watchlist (SEARCH + FILTER)
Screen support tickets or bank-memo descriptions against multiple case-insensitive watchlist substrings using OR(ISNUMBER(SEARCH(...))) and FILTER.
Read the guide →StatisticalFilter and count values within or out of tolerance (Target ± Spec Band)
Extract passing parts inside [Target - Tol, Target + Tol] and count out-of-spec defects across manufacturing or audit logs.
Read the guide →Dynamic ArraysFilter and Sort Without Errors or Blanks (SORTBY + FILTER + ISNUMBER)
Build an error-proof leaderboard pipeline that strips blank cells and #DIV/0! formula errors via ISNUMBER(B2) flags before sorting top performers descending with SORTBY + FILTER.
Read the guide →Date & TimeFilter and Sum Records from the Last N Weeks (FILTER & SUMIFS Rolling Window)
Extract and total transactions falling within a rolling N-week lookback window anchored to a report cutoff date, excluding future-dated entries beyond the cutoff.
Read the guide →Water Treatment Hydraulics, Granular Media Filtration & FluidizationFilter Backwash Bed Expansion % & Fluidized Head-Loss Formula
Calculate Fluidized Backwash Expanded Bed Depth L_e (m), Percentage Bed Expansion (%), Constant Fluidized Buoyant Head Loss h_f (m water), and Underdrain Buoyant Pressure (kPa).
Read the guide →Dynamic Arrays & FilteringFilter Data Between Two Dates (Inclusive Boolean Multiplication & Fallback)
Extract rows whose date serials fall inclusively between Start_Date and End_Date using FILTER boolean multiplication (Date >= Start) * (Date <= End) with swap-safe MIN/MAX bounds.
Read the guide →Dynamic ArraysFilter dates expiring in the next 30 days (sorted renewal alert queue)
Extract contracts, certificates, or subscriptions expiring inside [AsOfDate, AsOfDate + 30] and sort them soonest-first with SORT + FILTER.
Read the guide →Dynamic ArraysFilter every Nth row: extract periodic intervals and audit samples
Extract every 2nd, 3rd, or Nth row from a production log into a live summary list using a relative row-index MOD flag and FILTER.
Read the guide →Dynamic arraysFILTER function: extract rows matching multiple conditions
Return every matching item dynamically instead of stopping at the first lookup match. Combine conditions with boolean multiplication and provide an if_empty message when zero rows qualify.
Read the guide →Dynamic ArraysFilter horizontal columns & sort left-to-right by row with FILTER and SORT
Filter a wide month-across-columns KPI table where revenue meets a threshold and sort matching columns highest-to-lowest using SORT(..., 2, -1, TRUE).
Read the guide →Dynamic ArraysFilter horizontally to exclude or keep specific columns (FILTER on headers)
Create a derived table that omits columns with specified header names using a horizontal FILTER mask.
Read the guide →Lookup & Dynamic ArraysFILTER Rows Matching This OR That Criteria with Boolean Addition (+)
Extract rows matching Condition A OR Condition B inside FILTER using elementwise boolean addition (condA) + (condB) > 0 instead of scalar OR().
Read the guide →Dynamic ArraysFILTER to show duplicate rows: inspect all collisions vs 2nd+ repeats
Extract every transaction row involved in a duplicate key collision (TotalCount > 1) so AP auditors can compare both copies side by side.
Read the guide →Dynamic Arrays & FilteringFilter Top N Records with Category Criteria (LARGE + FILTER vs TAKE + SORT)
Extract the Nth threshold, Top-N subtotal, and ranked leaderboard within a specific department or region using LARGE(FILTER(...), N) and TAKE(SORT(FILTER(...))).
Read the guide →Dynamic ArraysFILTER with optional criteria: treat blank filter inputs as "Match All"
Build interactive multi-dropdown FILTER dashboards where clearing any search box includes all rows instead of returning zero matches.
Read the guide →Text & String ManipulationFind and Replace Multiple Values in One Formula (Readable LET + SUBSTITUTE Pipeline)
Standardize multiple street, unit, or product abbreviations in a single formula without unreadable nested SUBSTITUTE pyramids by naming each replacement step inside LET.
Read the guide →Lookup & ReferenceFind candidate amounts within an inclusive tolerance band
Compare numeric amounts with a target and flag ambiguous matches before selecting a candidate.
Read the guide →Data Cleaning & AuditFind Common Duplicate Values Appearing in Both Columns (CRM vs ERP Audit)
Reconcile two invoice or SKU columns to flag records present in both lists versus missing from the second list using COUNTIF and dynamic FILTER.
Read the guide →Lookup & ReferenceFind First Match Between Two Ranges (Priority-Ordered List Intersection)
Return the highest-priority item from List A that also appears anywhere in List B using a COUNTIF membership flag with INDEX and FILTER, with a clean fallback when the two lists are disjoint.
Read the guide →Date & TimeFind highest & lowest value on a specific day of week (WEEKDAY, MAXIFS & MINIFS)
Use a Monday-first weekday helper to find maximum and minimum numeric readings, while distinguishing no matching dates from a genuine zero result.
Read the guide →Statistical & AggregationFind MAX & MIN Values While Ignoring All Errors (Even in Negative Ranges)
Extract the true maximum and minimum finite numbers from ranges containing #DIV/0! or #N/A errors using MAXIFS and MINIFS without failing on all-negative readings.
Read the guide →StatisticalFind maximum period-over-period jump, steepest drop & largest absolute swing
Find the largest and smallest signed adjacent-period changes, the largest absolute change, and its first matching period.
Read the guide →Lookup & ReferenceFind missing values between two lists: reconcile invoices with COUNTIF and FILTER
Flag items in List A that are absent from List B using COUNTIF or XMATCH, and spill an instant exception report with FILTER.
Read the guide →