Number Base Converter

What is a number base?

A number base (or radix) is how many distinct digits a numbering system uses. Everyday counting is decimal, base 10, with digits 0 to 9. Computers use binary, base 2, with only 0 and 1. Programmers also use octal (base 8) and hexadecimal (base 16, digits 0–9 and A–F) because they map neatly onto groups of bits: one hex digit represents four bits and one octal digit represents three. This tool converts between these bases and any custom base up to 36, where letters A to Z represent the values 10 to 35.

How base conversion works

Each digit in a number is multiplied by the base raised to its position. In binary 1101 is 1×8 + 1×4 + 0×2 + 1×1 = 13. To go the other way, divide repeatedly by the target base and read the remainders from last to first: 13 ÷ 2 gives remainders 1, 0, 1, 1, which read backward give 1101. Hexadecimal FF equals 15×16 + 15 = 255, and decimal 255 is 11111111 in binary and 377 in octal. The converter performs these steps for you using arbitrary-precision integers, so very long values stay exact.

Where base conversion is useful

Developers use hex for colors, memory addresses and byte values, binary for bit masks and flags, and octal for Unix file permissions such as 755. Base 36 is handy for short IDs, and base 32 or 64 style encodings build on the same idea. You can type negative numbers with a leading minus, and spaces or underscores are ignored, so grouped values such as 1111_0000 work. Everything is computed locally in your browser, so nothing you enter is uploaded.

Tip: to check a result, convert it back to the original base and confirm you get the same number. Remember that hexadecimal letters are not case sensitive, and that a leading zero never changes a value, so 0007 and 7 are identical in every base.