Number Base Converter
Convert between binary, octal, decimal, hexadecimal and any base from 2 to 36 — all four common bases update at once.
How to use it
- Type in whichever box matches what you have — the rest convert live.
- Use the custom base row for anything from base 2 to base 36.
- Invalid digits for the chosen base are flagged instead of silently ignored.
Examples
| 255 (decimal) | FF (hex) · 11111111 (binary) |
| 1010 (binary) | 10 (decimal) · A (hex) |
Number bases are different ways of writing the same value. Decimal (base 10) is what everyone uses day to day; binary (base 2) is what computer hardware operates in; hexadecimal (base 16) is how programmers write binary data compactly; octal (base 8) shows up in older Unix file permissions. Type into any one field and the other three update at once, plus a custom-base row for anything from base 2 to base 36.
Where each base actually gets used
| Base | Digits used | Typical use |
|---|---|---|
| Binary (2) | 0–1 | How data is physically stored and processed in hardware |
| Octal (8) | 0–7 | Unix/Linux file permissions (e.g. chmod 755) |
| Decimal (10) | 0–9 | Everyday numbers |
| Hexadecimal (16) | 0–9, A–F | Colour codes, memory addresses, byte values |
Converting by hand
Binary to decimal: multiply each digit by 2 raised to its position, counting from 0 on the right, and sum. 1010 = 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10. Hex to decimal works the same way with powers of 16: hex FF = 15×16 + 15 = 255, which is also why FF is the maximum value of a single byte.
Custom bases
Any base from 2 to 36 is supported using 0–9 then A–Z for digits beyond 9 — base 36 is the practical ceiling since it exhausts every alphanumeric character. This is occasionally used for compact ID encoding, where a large decimal number is shortened by expressing it in a higher base.
Questions people ask
How do I convert binary to decimal by hand?
Multiply each digit by 2 raised to its position index counting from the right, then add them up. 1010 = 1×8 + 0×4 + 1×2 + 0×1 = 10.
Last updated 17 August 2026