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Formula Library

Searchable knowledge base of formulas — each with its own page, linked tools, and related formulas.

22 formulas

All (22)

22 matches

General

9
  • Percentage proportionamount = (percent / 100) × wholeRelate a percent, a whole, and an amount — solve for any one when two are known.Math
  • Percent errorpercent error = |observed − true| / |true| × 100%Measure how far an observed value is from a known true value, as a percentage.Math
  • Ratio and proportionA:B = C:D → A×D = B×CTwo ratios are equivalent when their cross-products are equal.Math
  • Roundinground(value × 10^p) / 10^p · or nearest k/nReplace a number with a nearby simpler approximation.Math
  • Exponentiationbase^exponent = resultRelate a base, an exponent, and a power — fill any two to solve for the third.Math
  • Nth rootⁿ√a = b ⇔ bⁿ = aFind b such that b raised to n equals a.Math
  • Fraction arithmetica/b ± × ÷ c/d → reduced formOperate on fractions and reduce the result to lowest terms.Math
  • Long divisiondividend = quotient × divisor + remainderDivide integers with a quotient and remainder (or decimal expansion).Math
  • Order of operations (PEMDAS)PEMDAS: ( ) then × ÷ then + −Evaluate expressions in standard operator precedence.Math

Statistics

1
  • Arithmetic and weighted meanmean = sum / count · weighted = Σ(x w) / ΣwFind the central value of a list, with optional weights.Math

Cooking & apparel

1
  • Clothing size chartsLookup region size charts (approximate — brands vary)Map apparel sizes between regional labeling systems.Specialty

Data & digital

2
  • Color model conversionParse hex / RGB / HSL channels and convert between color modelsMove the same color between common digital color representations.Specialty
  • Paper size standardsMap ISO / North American paper size names to standard width × heightLook up physical dimensions from a paper size name.Specialty

Electricity & magnetism

2
  • Wavelength and frequencyf = c / λ, with c ≈ 299,792,458 m/s (speed of light in vacuum)Convert between electromagnetic frequency and wavelength in free space.Specialty
  • AWG wire gauge diameterd_mm = 0.127 × 92^((36 − AWG) / 39)Map AWG number to conductor diameter in millimeters.Specialty

Encodings & numbers

5
  • Number base conversionRead digits in the source base, then rewrite the same integer in the target baseChange how an integer is written without changing its value.Specialty
  • Roman numeralsMap Roman symbols (I, V, X, L, C, D, M) with subtractive pairs (IV, IX, XL, …)Encode integers with Roman symbols and subtractive pairs.Specialty
  • ASCII and Unicode code pointsMap characters to Unicode/ASCII code points (and the reverse)Translate between text characters and numeric code points.Specialty
  • Scientific notationRewrite as significand × 10^exponent (normalized scientific form)Express large or small numbers as a significand times a power of ten.Specialty
  • IPv4 address formsTreat IPv4 as a 32-bit integer (or dotted octets) and convert between formsRewrite an IPv4 address as dotted decimal or a single integer.Specialty

Date & time

2
  • Time zone conversionInterpret the instant in the source IANA zone, then format it in the target zoneShow the same universal instant as local time in another zone.Specialty
  • Date and time formatsParse the timestamp, then reformat it for the selected date/time representationChange how a date-time is written without inventing a new instant (unless zone rules apply).Specialty

Popular

  • Percentage proportionamount = (percent / 100) × whole
  • Arithmetic and weighted meanmean = sum / count · weighted = Σ(x w) / Σw
  • Exponentiationbase^exponent = result
  • Fraction arithmetica/b ± × ÷ c/d → reduced form
  • Number base conversionRead digits in the source base, then rewrite the same integer in the target base
  • Wavelength and frequencyf = c / λ, with c ≈ 299,792,458 m/s (speed of light in vacuum)
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