A number base, or radix, is simply how many distinct digits a counting system uses, ten for the everyday decimal system, two for binary, sixteen for hexadecimal. This tool converts a number from one base to another, covering binary, octal, decimal, hex, and any base from two to thirty-six. It also shows the decimal value and the digital root, tying the conversion back to numerology.
What a Base Means
In base ten we use the digits zero to nine and each place is worth ten times the one to its right. Binary uses only zero and one, octal eight digits, and hexadecimal sixteen, borrowing the letters A to F for the values ten to fifteen. Higher bases up to thirty-six use the whole alphabet, which is why the converter can handle such a wide range.
How the Conversion Works
To convert, the tool first reads your number from its source base into a plain decimal value, then expresses that value in the target base. Doing it through decimal keeps the process reliable across any pair of bases. The result is the same quantity written in a different system of digits.
Why Convert Bases
Base conversion is everyday work in computing, where binary and hexadecimal are the natural languages of machines, and it appears in maths, puzzles, and coding. Programmers read colours and memory in hex, while binary underlies all digital data. Being able to switch quickly between bases is a genuinely useful skill, and the tool makes it instant.
The Numerology Touch
Alongside the conversion, the tool gives the decimal value's digital root, the single digit you reach by adding its digits repeatedly. This is the bridge to numerology, where the digital root carries meaning, so you can convert a number and immediately see its root, useful if you are exploring the numbers behind codes, dates, or identifiers.
How to Use It
Enter your number, choose its source base and the base you want, and calculate. The tool returns the converted number, its decimal value, and its digital root.
Bases in Everyday Computing
You meet number bases more often than you might think. Web colours are written in hexadecimal, like the familiar six-character codes for shades of red and blue. File permissions on many systems use octal. And underneath everything, computers work in binary, the on-off language of circuits. Being comfortable moving between these systems demystifies a lot of technical detail, and a converter that handles any base from two to thirty-six covers every case you are likely to run into, from a coding lesson to a stubborn puzzle.
Frequently Asked Questions
What is the highest base supported?
Base thirty-six, which uses the ten digits plus all twenty-six letters of the alphabet to represent values up to thirty-five in a single place.
Why convert through decimal?
Reading any number into decimal first and then writing it in the target base keeps the conversion reliable for any pair of bases, rather than converting directly.
What is the digital root for?
It is the single digit you reach by repeatedly adding a number's digits. The tool shows it as a bridge to numerology, where the root carries meaning.
What base is hexadecimal?
Base sixteen. It uses the digits zero to nine plus the letters A to F for the values ten to fifteen, and is widely used in computing for colours and memory addresses.
Can it convert between two non-decimal bases?
Yes. You can convert directly from, say, binary to hexadecimal. The tool reads your number into decimal internally and then writes it in whatever base you choose.
What does base 2 mean?
Base two is binary, which uses only the digits zero and one. Each place is worth twice the one to its right, and it is the system computers use internally.
Related tools
Take it a step further with these number calculators: Roman Numeral Converter, Hijri Gregorian Converter, Julian Day Number Calculator and Unicode Code Point Sum. Looking at a couple of them together rounds out the picture and adds useful context. Find the full set under number calculators, or open all the calculators in one place.