Arbitrary Base Converter — Any Radix 2–64 with Custom Alphabet
Convert a whole number between any two bases from 2 to 64, with an optional custom digit alphabet. See the result, its decimal value and the positional-expansion working — all live in your browser using exact big-integer math.
How to Use
- Type the number you want to convert into the input box.
- Pick the FROM base (the radix your input is written in) and the TO base you want it in — any value from 2 to 64.
- The result updates instantly, along with its decimal value and the step-by-step working.
- Optionally paste a custom alphabet to define exactly which character maps to which digit value.
- Click any result (or its Copy button) to copy it.
A converter for every radix, not just the famous ones
Most base tools only know the named systems — binary, octal, decimal, hexadecimal. This is the general radix engine: it converts a whole number between any two bases from 2 to 64. That includes the oddballs the everyday converters skip — base 3, base 5, base 7, base 12, base 36, base 58, base 62 — plus the popular compact encodings used for short URLs and identifiers. Everything runs in your browser with exact big-integer arithmetic, so a number with hundreds of digits converts without a single rounding error, and nothing is ever uploaded.
A base (or radix) is simply how many distinct digit symbols a number system uses before it has to “carry” into the next column. Decimal has ten (0–9); binary has two (0–1); hexadecimal has sixteen (0–9 then A–F). The digit symbols come from a fixed alphabet: by default 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/. The first character is digit value 0, the next is 1, and so on — so base 62 uses 0–9, A–Z and a–z, while bases 63 and 64 add + and /. You can override this with your own alphabet to match RFC-4648 base32, Bitcoin base58 or any private scheme.
How the conversion works
Conversion happens in two stages with the decimal value as the bridge. Stage one — parse to a number uses Horner’s method: start from zero, and for each digit (left to right) multiply the running total by the FROM base and add the digit’s value. So FF in base 16 is ((0×16 + 15)×16 + 15) = 255. The digit’s value is looked up in the alphabet’s index map; for bases up to 36 either case is accepted, but above 36 case is significant because uppercase and lowercase letters are different digits. If any character isn’t a legal digit for the FROM base, you get an explicit error rather than a wrong answer.
Stage two — emit to the target base uses repeated divmod: divide the decimal value by the TO base, record the remainder, repeat on the quotient, and read the remainders bottom-to-top. Each remainder indexes back into the alphabet to produce the output character. Because both stages use BigInt, the only ceiling is your patience — try a 200-digit base-3 number into base 64 and it stays exact. The Show work panel writes out the positional expansion and the division ladder so you can follow (or teach) the method.
Quick reference
About the Arbitrary Base Converter — Any Radix 2–64 with Custom Alphabet
Working on everyday tasks? The Arbitrary Base Converter — Any Radix 2–64 with Custom Alphabet is a free browser tool that gives you the answer in seconds. Convert a whole number between any two bases from 2 to 64, with an optional custom digit alphabet. See the result, its decimal value and the positional-expansion working — all live in your browser using exact big-integer math.
How it works
Type a value, then pick what you want to change it into. The answer appears straight away. It all happens on your own device, so it is fast and nothing you type is sent away. Just check that you picked the right “from” and “to” so you get the answer you wanted.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
Frequently Asked Questions
How is this different from the Number Converter?
The Number Converter handles the well-known named systems (binary, octal, decimal, hex, Roman, words, scientific). This tool is the general radix engine: it converts between ANY two bases from 2 to 64, including unusual ones like base 3, base 7, base 36 or base 58, and lets you supply your own digit alphabet.
What is the default alphabet?
Digits are taken from <code>0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/</code>. So bases up to 62 use 0–9 then A–Z then a–z, and bases 63 and 64 add “+” and “/”. For bases up to 36 input is case-insensitive; above 36 case matters because uppercase and lowercase letters are distinct digits.
Can I use my own symbols?
Yes. Enter a custom alphabet whose length is at least the larger of the two bases. Each character defines the digit for its position (the first character is digit 0). This is handy for base32 RFC-4648, Bitcoin base58, or any private encoding scheme.
How big a number can it handle?
There is no practical limit — the converter uses JavaScript BigInt, so hundreds or thousands of digits convert exactly with no floating-point rounding. It works on whole, non-negative numbers.
Why do I get an “illegal digit” error?
Every character in your input must be a valid digit for the FROM base. For example the character “2” is not allowed in base 2 (whose only digits are 0 and 1), and “G” is not allowed in base 16. Fix the offending character or raise the FROM base.
Is anything uploaded?
No. The entire conversion runs locally in your browser with JavaScript — nothing is sent to any server.
How do I use the Arbitrary Base Converter — Any Radix 2–64 with Custom Alphabet?
Just type or paste your value. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
Unusual radices
Convert to and from bases the everyday tools skip — base 3, base 5, base 7, base 12, base 36 — for puzzles, coursework and ID schemes.
Compact identifiers
Pack a large decimal ID into base 62 or base 64 for short URLs and tokens, then decode it back exactly.
Custom encodings
Paste a base32 or base58 alphabet to map digits to your own symbol set for a private or domain-specific encoding.
Teaching positional notation
Show students that any base works the same way: each digit times the radix to its column power, summed.
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