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Engines

Nerdulator recognises 22 kinds of input and works out everything that follows from each. Give it a number, a date, a colour, an IP address, a tyre size or a chord, and you get the same answer every time, because every one is calculated rather than looked up.

This page lists all 468 things it can work out, so you can see what it knows before you ask. There are also 100 calculators for questions that need more than one number. Those are listed separately.

IP & networking

ip

IPv4 and IPv6 address analysis, CIDR subnet and prefix calculations.

23 transformations
  • IPv4 address analysis
  • 32-bit integer form
  • Binary and octal forms
  • Reverse DNS name
  • IPv4-mapped IPv6
  • Special-use range classification
  • Legacy class
  • CIDR calculations
  • Subnet mask
  • Wildcard mask
  • Network address
  • Broadcast address
  • Usable host range
  • Number of hosts
  • RFC 3021 point-to-point handling
  • Related prefixes
  • IPv6 address parsing
  • RFC 5952 compression
  • Full expansion
  • IPv6 prefix arithmetic
  • IPv6 range classification
  • IPv6 reverse DNS
  • Embedded IPv4 in IPv6

Web

web

URL and email address structure, parts and encodings. Syntax only, never a network lookup.

17 transformations
  • URL structure
  • Scheme, host and port
  • Path segments
  • Query parameters
  • Internationalised domain names (punycode)
  • Fragment
  • Domain labels and TLD
  • Percent encoding
  • Email address parts
  • RFC length validation
  • mailto links
  • HTTP status codes
  • Status class and cacheability
  • Well-known port numbers
  • IANA port ranges
  • MIME media types
  • File extension to media type

Developer identifiers

dev

Cron expressions, UUIDs, semantic versions and checksummed identifiers, decomposed.

35 transformations
  • Cron field expansion
  • Cron in plain English
  • Next scheduled runs
  • Day-of-month/day-of-week OR rule
  • UUID version and variant
  • UUID embedded timestamps (v1, v6, v7)
  • Semantic version components
  • Semver precedence rules
  • Caret and tilde range expansion
  • ISBN-10 and ISBN-13 check digits
  • ISBN-10 to ISBN-13 conversion
  • EAN-13 and UPC-A check digits
  • Luhn validation
  • IBAN mod-97 validation
  • GTIN-8, GTIN-12 and GTIN-14 check digits
  • ISSN check digit
  • ISMN validation
  • VIN check digit
  • VIN decomposition
  • VIN model year code
  • DOI structure
  • Regular expression decomposition
  • Regex quantifier and anchor explanation
  • Regex character class expansion
  • Regex capture and named group counting
  • Regex flag meanings
  • MAC address decomposition
  • MAC unicast/multicast and local/universal bits
  • Modified EUI-64 and IPv6 link-local derivation
  • JWT header and claim decoding
  • JWT registered claim meanings
  • JWT algorithm notes
  • BCP 47 language tag decomposition
  • BCP 47 canonical casing
  • Binary to text decoding

Reference tables

reference

Polyhedra, paper sizes, screen resolutions, solar-system bodies and musical pitches.

23 transformations
  • Platonic and Archimedean solids
  • Faces, edges, vertices and Euler characteristic
  • Polyhedron volume, area and dihedral angle
  • Dual polyhedra
  • ISO 216 and North American paper sizes
  • Paper size in mm, inches, points and pixels
  • Screen resolution aspect ratios
  • Megapixels and pixel density
  • Solar-system body mass and radius
  • Surface gravity and escape velocity
  • Weight on another world
  • Musical pitch to frequency
  • MIDI note numbers
  • Enharmonic equivalents
  • Wavelength of a pitch in air
  • Gas mark to Celsius and Fahrenheit
  • Resistor colour band decoding
  • Resistance tolerance and E-series
  • Unicode code point analysis
  • UTF-8, UTF-16 and UTF-32 encodings
  • HTML, CSS and JavaScript escapes
  • Unicode block and plane
  • General category

Colour

colour141 named colours, 16.7 million addressable

HEX, RGB, HSL, HSV and CMYK conversion with contrast, harmonies and named-colour matching.

23 transformations
  • HEX
  • RGB
  • HSL
  • HSV and HSB
  • Approximate CMYK
  • 24-bit integer
  • Relative luminance
  • Perceived brightness
  • Greyscale
  • Inverted
  • Complementary colour
  • Analogous colours
  • Triadic colours
  • Split complementary
  • Tetradic
  • Lighter variants
  • Darker variants
  • Saturation variants
  • WCAG contrast ratios
  • Black or white text recommendation
  • Nearest named colour by CIELAB
  • Similar named colours
  • Channel breakdown

Date

date

Calendar position, formats, Unix time and navigation for any date from year 1 to 9999.

45 transformations
  • Day of the week
  • Day of the year
  • ISO week number
  • Month
  • Quarter
  • Year
  • Leap year status
  • Days in the month
  • Days remaining in the year
  • Days elapsed in the year
  • Previous and next day
  • Previous and next week
  • Previous and next month
  • Previous and next year
  • ISO 8601 date
  • British and American formats
  • RFC 2822
  • Unix timestamp
  • Unix timestamp in milliseconds
  • Unix epoch relationship
  • Julian Day Number
  • Hebrew calendar conversion
  • Islamic (tabular) calendar conversion
  • Persian (arithmetic) calendar conversion
  • Rata Die fixed day number
  • Time of day
  • Seconds since midnight
  • Decimal hours
  • Clock hand angles
  • Frame counts and timecode
  • Zodiac sign
  • Chinese zodiac
  • Season
  • Days, months and years from today
  • Easter Sunday
  • Weekday occurrence in the month
  • Julian calendar equivalent before 1582
  • Whole-year pages
  • Whole-decade pages
  • Leap years in a decade
  • Where a decade starts
  • Month calendar grid
  • Working days in a month
  • Weekday counts in a month
  • ISO weeks spanned by a month

Units

unit202 units across 20 categories

Conversion across 20 categories and 202 units, all defined as data.

24 transformations
  • Length and distance
  • Mass and weight
  • Temperature
  • Area
  • Volume
  • Speed
  • Time
  • Energy
  • Power
  • Pressure
  • Data and storage
  • Data rate
  • Frequency
  • Angle
  • Force
  • Density
  • Fuel economy
  • Absorbed dose
  • Equivalent dose
  • Radioactivity
  • Focused conversions (X in Y)
  • Exact conversion factors
  • Reverse conversion
  • The formula used

Computing

computing

Base literals, bit widths, Unix timestamps and Base64.

16 transformations
  • Decimal to binary
  • Decimal to hexadecimal
  • Decimal to octal
  • Binary to hexadecimal
  • Base 32 and base 36
  • ASCII characters
  • Unicode code points
  • Base64 decoding
  • Unix timestamps
  • Bit length and byte length
  • Population count
  • Two’s complement
  • Bitwise NOT
  • Shifts
  • Byte-order swap
  • Interpretation as a colour, an IPv4 address or a duration

Maths

maths

Fractions, percentages, ratios, money arithmetic, statistics and expression evaluation.

32 transformations
  • Percentages
  • Percentage change
  • Percentage increase and decrease
  • Fractions
  • Fraction simplification
  • Mixed numbers
  • Equivalent fractions
  • Ratios
  • GCD
  • LCM
  • Powers
  • Roots
  • Logarithms
  • Factorials
  • Permutations
  • Combinations
  • Probability
  • Mean
  • Median
  • Mode
  • Range
  • Variance
  • Standard deviation
  • Quartiles and IQR
  • Outlier detection
  • Basic algebra (quadratics)
  • Money arithmetic and VAT
  • Safe expression evaluation
  • Magic squares
  • Magic constant
  • Magic square construction
  • Magic square of squares

Geometry

geometry

Areas, perimeters, volumes and angles for the common 2D and 3D shapes.

20 transformations
  • Circle area and circumference
  • Rectangle area and perimeter
  • Square
  • Triangle area and perimeter
  • Triangle side and angle calculations
  • Hypotenuse
  • Pythagorean triples
  • Sphere volume and surface area
  • Cube volume and surface area
  • Cylinder volume and surface area
  • Cone volume and slant height
  • Rectangular prism volume
  • Angle calculations
  • Inradius and circumradius
  • Regular polygon interior and exterior angles
  • Regular polygon area and apothem
  • Polygon diagonal count
  • Polygon symmetry group
  • Compass and straightedge constructibility
  • SVG diagrams

Science

science29 constants, 118 elements

Physical constants, chemical elements, molar masses and physics calculators.

24 transformations
  • Physical constants
  • Exact versus measured values
  • Chemical elements
  • Atomic weights
  • Electron configuration
  • Noble gas shorthand
  • Unpaired electrons
  • Isotope notation
  • Protons, neutrons and nucleons
  • Molar mass of a formula
  • Percentage composition
  • Compound names
  • Speed, distance and time
  • Kinetic energy
  • Potential energy
  • Ohm's law
  • Electrical power
  • Density
  • Pressure
  • Frequency and wavelength
  • Photon energy
  • Ideal gas calculations
  • Basic pH calculations
  • Half-life and decay

Geography

geography196 countries

Country reference data, coordinates, great-circle distance and bearing.

17 transformations
  • Country
  • Capital
  • Continent
  • ISO 3166 codes
  • Internet TLD
  • Calling code
  • Currency
  • Population (versioned)
  • Neighbouring countries
  • Coordinates
  • Time zone
  • Daylight saving
  • Area
  • Distance between coordinates
  • Bearing and compass point
  • Antipode
  • Coordinate formats (decimal, DMS, radians)

Algebra

algebra

Solves, expands and factorises single-variable equations exactly, in rational arithmetic.

11 transformations
  • Linear equation solving
  • Quadratic equation solving
  • Quadratic formula
  • Discriminant
  • Factorising over the rationals
  • Completing the square
  • Parabola vertex and axis of symmetry
  • Expanding brackets
  • Collecting like terms
  • Exact rational coefficients
  • Identity and contradiction detection

Dimensions, uncertainty and sequences

analysis

What a quantity is, how well it is known, and every rule that fits a sequence. Three questions whose honest answer is not a single number.

15 transformations
  • Dimensional analysis of an expression
  • SI base-unit reduction
  • Named quantity identification
  • Dimension mismatch detection
  • Torque-versus-energy dimensional ambiguity
  • Uncertainty propagation in quadrature
  • Worst-case tolerance stack-up
  • Relative and absolute uncertainty
  • Significant figures justified by an uncertainty
  • Sequence rule finding
  • Arithmetic, geometric and affine rules
  • Polynomial fitting by finite differences
  • Linear recurrence solving
  • Named integer sequence matching
  • Multiple competing continuations

Matrices and coordinate geometry

linear

Determinants, inverses and eigenvalues in exact rational arithmetic, and what a set of points determines. Singular means exactly singular, not close to it.

17 transformations
  • Matrix determinant, exactly
  • Matrix inverse in rational arithmetic
  • Rank and nullity
  • Reduced row echelon form
  • Null space basis
  • Eigenvalues of a 2×2 matrix
  • Symmetric and orthogonal tests
  • Transpose and matrix product
  • Distance and midpoint between points
  • Line through two points
  • Gradient and intercepts
  • Triangle area by the shoelace formula
  • Exact right-angle test on squared sides
  • Centroid, incentre and inradius
  • Circumcircle through three points
  • Collinearity by determinant
  • Lattice point counting by Pick's theorem

Chemical equations

chemistry

Equation balancing solved as a null space, so "cannot be balanced" is a proof rather than a failure to find an answer: and "infinitely many balancings" is a real answer too.

6 transformations
  • Equation balancing by null space
  • Formula parsing with nested brackets
  • Hydrate notation (CuSO4·5H2O)
  • Detection of unbalanceable equations
  • Detection of underdetermined equations
  • Mass conservation check

Electronics

electronics

Ohm's law, the power law and RC time constants. One line of algebra each, so the answers are fixed: but never a verdict on whether a part is safe.

6 transformations
  • Ohm's law from any two quantities
  • Power dissipation
  • Series and parallel resistance
  • RC time constant and settling time
  • RC filter cutoff frequency
  • LED series resistor

Cards, the chessboard and entropy

counting

Exact counting: poker hands as ratios of binomial coefficients, knight distances by exhaustive search, and the two different things people call entropy.

15 transformations
  • Poker hand identification
  • Exact five-card hand counts
  • Why the poker ranking is ordered as it is
  • Hypergeometric draw probabilities
  • The wheel (ace-low straight)
  • Chessboard square colour
  • Squares attacked by each piece
  • Knight's shortest distance by search
  • Knight colour parity
  • Squares and rectangles on a grid
  • Eight queens solution count
  • Shannon entropy of a string
  • Generation entropy of a password
  • Diceware passphrase entropy
  • Time to exhaust a keyspace

Games

games

Dice notation and dart checkouts, both by exact enumeration over a fixed rule set.

9 transformations
  • Dice notation parsing (NdM+K)
  • Dice sum distribution
  • Dice mean and variance
  • Dice outcome counting
  • Probability of rolling at least a total
  • Dart checkout routes
  • Shortest dart finish
  • Bogey numbers
  • One-dart finishes

Music

music

Scales, chords and key signatures in twelve-tone equal temperament, spelled correctly.

12 transformations
  • Scale notes and intervals
  • Modes of the major scale
  • Pentatonic and blues scales
  • Chord notes and intervals
  • Chord symbol parsing
  • Chord inversions
  • Key signatures
  • Relative and parallel keys
  • Scale degree names
  • Enharmonic spelling
  • Equal-tempered frequencies
  • Interval names

Number

number

Integer and decimal properties: primality, factors, bases, words, powers.

46 transformations
  • Previous and next number
  • Even or odd
  • Prime or composite
  • Absolute value
  • Square
  • Cube
  • Square root
  • Cube root
  • Factors
  • Prime factorisation
  • Number of divisors
  • Sum of divisors
  • Aliquot sum
  • Digital root
  • Digit sum
  • Binary
  • Octal
  • Decimal
  • Hexadecimal
  • Base 32 and 36
  • Roman numeral
  • English number name
  • Ordinal name
  • Percentage representations
  • Scientific notation
  • Engineering notation
  • Powers
  • Multiples
  • Divisibility tests
  • Nearest square above and below
  • Next and previous prime
  • Distance to nearest prime
  • Euler's totient
  • Squarefree check
  • Perfect, abundant or deficient
  • Triangular number
  • Fibonacci number
  • Happy number
  • Harshad number
  • Armstrong number
  • Palindromic check
  • Factorial
  • Reciprocal
  • IEEE 754 bit pattern
  • Best rational approximation
  • Rounding and significant figures

Text

word

Character counts, case conversions, encodings, frequency and word-game scores.

32 transformations
  • Character count
  • Letter count
  • Digit count
  • Whitespace count
  • Word count
  • Unique character count
  • Vowel count
  • Consonant count
  • First and last character
  • First and last letter
  • Uppercase
  • Lowercase
  • Title Case
  • Sentence case
  • camelCase
  • snake_case
  • kebab-case
  • Reversed text
  • Alphabet positions
  • Character frequency
  • Palindrome status
  • Anagram signature
  • Scrabble score
  • Words With Friends score
  • Unicode code points
  • UTF-8 byte length
  • Base64
  • URL encoding
  • HTML entity encoding
  • ROT13
  • Morse code
  • NATO alphabet