Number Base Converter
Convert a number between any bases from 2 to 36 — binary, octal, decimal, hexadecimal and beyond — with a quick reference row for the common bases.
How it works
value = Σ digit_i × from^position · read left to right into a single integer, then re-expressed digit by digit in the target base · digits above 9 use letters A–Z (10–35)
A positional number system writes a value as a sum of digits times powers of its base: 255 in base 10 is 2·100 + 5·10 + 5·1. Converting between bases means reading the input into that single underlying value, then repeatedly dividing by the target base to find its digits. Bases above 10 borrow letters — A is 10, F is 15, Z is 35 — which is why hexadecimal (base 16) runs 0–9 then A–F. This tool validates that every input digit is legal for the "from" base before converting, so a stray "9" in a binary number is caught rather than silently truncated.
Worked example
The decimal number 255 converts to base 2 as 11111111 — eight ones, since 255 is 2⁸ − 1. The same value is 377 in octal and FF in hexadecimal (F = 15, and 15·16 + 15 = 255). Enter a different "to" base to see it re-expressed in anything from binary up to base 36.
Sources: Radix — Wikipedia
Frequently asked questions
What is the highest base supported?
Base 36, which uses all ten digits 0–9 and all 26 letters A–Z as digit values 10–35. That is the practical maximum for alphanumeric digits; going higher would need symbols beyond the alphabet.
Why does hexadecimal use letters?
Because base 16 needs sixteen distinct digit symbols, but we only have ten numerals. The letters A–F stand in for the values 10–15, so FF means 15·16 + 15 = 255. The same idea extends up to base 36 with the full alphabet.
What happens if I enter an invalid digit?
Each digit must be less than the "from" base — binary allows only 0 and 1, octal 0–7, and so on. If you enter a digit too large for the base (a 2 in a binary number, say), the tool reports exactly which character is invalid instead of guessing.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.