Simplify Your Workflow: Search MiniWebtool.
Add Extension
Home Page > Math > Number System Converters > Base-N Calculator

Base-N Calculator

Convert integers between any number bases from 2 to 36 with step-by-step calculation breakdown and digit position analysis.

Base-N Calculator
Quick Examples
255 DEC FF HEX 11111111 BIN 377 OCT ZZZZ B36

Embed Base-N Calculator Widget

About Base-N Calculator

The Base-N Calculator is a powerful number base converter that transforms integers between any numeral systems from base-2 (binary) to base-36 (alphanumeric). Whether you are a programmer working with binary and hexadecimal, a student learning number systems, or anyone needing to convert between different radixes, this calculator provides instant conversions with detailed step-by-step explanations and interactive digit breakdowns.

What is a Number Base (Radix)?

A number base, also called radix, defines how many unique digits are used to represent numbers in a positional numeral system. The base determines the place value of each digit position - each position represents a power of the base.

Place Value Formula

For any number, each digit's contribution equals: digit_value × baseposition

Where position 0 is the rightmost digit.

Common Number Bases

BaseNameDigits UsedCommon Use
2Binary0, 1Computing, digital electronics
8Octal0-7Unix file permissions, legacy computing
10Decimal0-9Everyday counting, mathematics
12Duodecimal0-9, A, BTime (12 hours), measurements (dozen)
16Hexadecimal0-9, A-FMemory addresses, color codes, programming
36Hexatrigesimal0-9, A-ZURL shorteners, compact encoding

How to Convert Between Number Bases

Converting to Decimal (Base-10)

To convert any number to decimal:

  1. Identify each digit and its position (starting from 0 on the right)
  2. Multiply each digit by baseposition
  3. Sum all the results

Example: Convert 1A3 (hexadecimal) to decimal:

Converting from Decimal to Other Bases

To convert a decimal number to another base:

  1. Divide the number by the target base
  2. Record the remainder (this becomes a digit)
  3. Repeat with the quotient until it reaches 0
  4. Read the remainders in reverse order

Why Different Number Bases Matter

Binary (Base-2) in Computing

Binary is fundamental to all digital computing. Computer processors use transistors that have two states (on/off), making binary the natural language of computers. Every piece of digital data - from text to images to videos - is ultimately stored and processed as binary digits (bits).

Hexadecimal (Base-16) in Programming

Hexadecimal is widely used in programming because it provides a compact way to represent binary data. Each hex digit represents exactly 4 binary digits, making conversions straightforward:

Octal (Base-8) in Unix/Linux

Octal is used in Unix/Linux file permissions. Each octal digit represents 3 bits, corresponding to read (4), write (2), and execute (1) permissions. For example, chmod 755 sets rwxr-xr-x permissions.

How to Use This Calculator

  1. Enter your number: Type the number you want to convert. Use digits 0-9 and letters A-Z for bases higher than 10.
  2. Select the source base: Choose the base of your input number from the dropdown, or use the quick buttons for common bases (Binary, Octal, Decimal, Hexadecimal).
  3. Click Convert: The calculator instantly converts your number to all bases from 2 to 36.
  4. Explore results: View results organized by category (Computing, Mathematical), examine the digit breakdown, and copy any result with one click.

Frequently Asked Questions

What is a number base or radix?

A number base (or radix) is the number of unique digits used to represent numbers in a positional numeral system. For example, binary (base-2) uses digits 0 and 1, decimal (base-10) uses digits 0-9, and hexadecimal (base-16) uses digits 0-9 and letters A-F. The base determines how place values increase: each position is worth base^position times its digit value.

How do I convert between number bases?

To convert from any base to decimal: multiply each digit by its place value (base^position) and sum the results. To convert from decimal to another base: repeatedly divide by the target base and collect remainders in reverse order. This calculator handles both conversions automatically and shows the step-by-step process.

What are common number bases used in computing?

Binary (base-2) is fundamental to computing as it represents the on/off states of transistors. Octal (base-8) was historically used in early computing. Hexadecimal (base-16) is widely used because it compactly represents binary data - each hex digit equals exactly 4 binary digits, making it ideal for memory addresses, color codes, and byte values.

What is the maximum base supported?

This calculator supports bases from 2 to 36. Base-36 is the maximum because it uses all 10 digits (0-9) plus all 26 letters (A-Z), giving 36 unique symbols. Base-36 is sometimes called "alphanumeric" and is used in URL shorteners and compact encodings.

Can negative numbers be converted between bases?

Yes, this calculator supports negative numbers. Simply include a minus sign (-) before your number. The conversion process works the same way - the sign is preserved and applied to the final result in each base.

Additional Resources

Reference this content, page, or tool as:

"Base-N Calculator" at https://MiniWebtool.com/base-n-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Jan 15, 2026

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

Related MiniWebtools:

Base Converter

Number System Converters:

Top & Updated:

Random PickerRandom Name PickerRelative Standard Deviation CalculatorSort NumbersFPS ConverterMAC Address GeneratorRemove SpacesFeet and Inches to Cm ConverterMAC Address LookupBitwise CalculatorLine CounterWord to Phone Number ConverterPercent Off CalculatorBatting Average CalculatorSum CalculatorFacebook User ID LookupLog Base 10 CalculatorNumber of Digits CalculatorRandom Quote GeneratorSHA256 Hash GeneratorSun, Moon & Rising Sign Calculator 🌞🌙✨Random Credit Card GeneratorSaturn Return CalculatorRandom Truth or Dare GeneratorRoman Numerals ConverterDecimal to BCD ConverterERA CalculatorAI ParaphraserBinary to Gray Code ConverterVideo to Image ExtractorOne Rep Max (1RM) CalculatorQuotient and Remainder CalculatorCm to Feet and Inches ConverterOctal CalculatorMP3 LooperSalary Conversion CalculatorPhone Number ExtractorBCD to Decimal ConverterOutlier CalculatorCompound Growth CalculatorRemove Audio from VideoSquare Root (√) CalculatorOn Base Percentage CalculatorFirst n Digits of PiNumber to Word ConverterGray Code to Binary ConverterAI Punctuation AdderDay of Year CalendarScientific Notation to Decimal ConverterMerge VideosTime Duration CalculatorText FormatterRemove AccentBinary to BCD ConverterModulo CalculatorRandom Group GeneratorCM to Inches ConverterCompare Two StringsLeap Years ListIP Address to Hex ConverterSlugging Percentage CalculatorConvolution CalculatorMedian CalculatorAudio SplitterAntilog CalculatorList of Prime NumbersMaster Number CalculatorAverage Deviation CalculatorPER CalculatorPercentage Increase CalculatorStandard Error CalculatorImage SplitterPercent Growth Rate CalculatorRandom Birthday GeneratorMaze GeneratorAdd or Replace Audio in VideoRandom Emoji GeneratorOPS CalculatorBreak Line by CharactersLove Compatibility CalculatorMAC Address AnalyzerRandomize LinesWhat is my Lucky Number?First n Digits of e📅 Date CalculatorSHA512 Hash GeneratorPVIF CalculatorProportion CalculatorSum of Positive Integers CalculatorBonus CalculatorVideo SplitterPVIFA CalculatorRemove Leading Trailing SpacesNatural Log CalculatorVideo CropperCoin FlipperSpin the WheelList RandomizerDay of the Year Calculator - What Day of the Year Is It Today?Random Tournament Bracket GeneratorEmail ExtractorURL ExtractorAdd Prefix and Suffix to TextWHIP CalculatorVideo CompressorSort Lines AlphabeticallyHex to BCD ConverterBCD to Binary ConverterLottery Number GeneratorBCD to Hex ConverterAverage CalculatorReverse VideoWAR CalculatorHypotenuse CalculatorActual Cash Value CalculatorNumber ExtractorAngel Number CalculatorLog Base 2 CalculatorRoot Mean Square CalculatorSHA3-256 Hash GeneratorAI Sentence ExpanderLbs to Kg ConverterHex to Decimal ConverterRandom String GeneratorAmortization CalculatorMarkup CalculatorName Number CalculatorDecimal to Hex ConverterList of Fibonacci NumbersRandom Number PickerBlood Donation Time CalculatorField Goal Percentage CalculatorRandom Line PickerRatio to Percentage CalculatorAPY to APR CalculatorSort Text By LengthRandom Object GeneratorName RandomizerRandom Animal GeneratorSquare Numbers ListFixed Deposit CalculatorPPM to Percent ConverterCube Numbers ListCaesar Cipher ToolMorse Code GeneratorPercent to PPM ConverterSRT to TXT Converterkg to lbs ConverterXML ValidatorArithmetic Mean CalculatorBoard Foot CalculatorSquareness Checker (3-4-5 Rule) 📐Miter Angle Calculator 📐Slope and Grade Calculator 📐Sine CalculatorCosine CalculatorHigh-Precision Tangent CalculatorArcsin CalculatorArccos (Inverse Cosine) CalculatorArctan CalculatorArctan2 CalculatorCosecant/Secant/Cotangent CalculatorHyperbolic Functions CalculatorRight Triangle CalculatorGeneral Triangle SolverLaw of Sines CalculatorLaw of Cosines CalculatorDMS to Decimal Degrees ConverterDecimal Degrees to DMS ConverterPolar to Cartesian ConverterHigh-Precision Cartesian to Polar Coordinates ConverterInteractive Unit Circle VisualizerTrigonometric Identities CalculatorTrigonometric Function GrapherAlgebraic Expression SimplifierRadical SimplifierRational Expression CalculatorPolynomial Factoring CalculatorExpand Polynomials CalculatorPolynomial Long Division CalculatorSynthetic Division CalculatorLinear Equation SolverAbsolute Value Equation SolverRadical Equation SolverSystem of Linear Equations SolverInequality SolverAbsolute Value Inequality SolverSystem of Inequalities GrapherFunction GrapherDomain and Range CalculatorInverse Function CalculatorFunction Composition CalculatorVertex and Axis of Symmetry CalculatorX and Y Intercept CalculatorHTML Entity Encoder/DecoderURL Slug GeneratorJSON String Escape/UnescapeMarkdown Table GeneratorSmart Quotes RemoverDaily Time Savings CalculatorLorem Ipsum GeneratorReadability Score CalculatorKeyword Density CheckerBionic Reading ConverterText to Speech ReaderFancy Text GeneratorZalgo Text GeneratorUpside Down Text GeneratorInvisible Text GeneratorASCII Art GeneratorList Difference CalculatorText Column ExtractorText to SQL List ConverterInvisible Character RemoverStock Average CalculatorPosition Size CalculatorMargin Call CalculatorShort Selling Profit CalculatorRisk of Ruin CalculatorBlack-Scholes Option Pricing CalculatorOption Greeks CalculatorImplied Volatility CalculatorOptions Profit CalculatorImpermanent Loss CalculatorCrypto Arbitrage CalculatorSatoshi to USD ConverterCrypto Leverage CalculatorPivot Point CalculatorFibonacci Extension CalculatorStop Loss & Take Profit CalculatorKelly Criterion CalculatorMartingale Strategy CalculatorCompound Daily Interest CalculatorPip Value CalculatorGaussian Distribution GeneratorRandom Meal GeneratorRandom Color Palette GeneratorRandom Country GeneratorRandom JSON GeneratorRandom User-Agent GeneratorRandom Coordinate GeneratorRandom Date GeneratorRandom Time GeneratorRandom IP Address GeneratorRandom Playing Card GeneratorMagic 8-BallRock Paper Scissors GeneratorDice RollerAquarium Volume & Stocking CalculatorAquarium Substrate CalculatorScale Model Conversion CalculatorPlant Spacing CalculatorDice Roll Probability CalculatorDepth of Field (DoF) CalculatorGolden Hour / Blue Hour CalculatorPrint Size & Resolution Calculator (DPI/PPI)Soap Making Lye Calculator (SAP)Candle Wax & Fragrance Oil CalculatorHomebrew ABV Calculator (Alcohol by Volume)Coffee Brew Ratio CalculatorBrine and Salinity CalculatorYarn CalculatorFabric CalculatorCross-Stitch Size CalculatorBaker's Percentage CalculatorDough Hydration CalculatorBaking Pan Size ConverterYeast Conversion CalculatorJSON to YAML ConverterJWT DecodercURL to JSON ConverterSQL Formatter