Binary / Hex / Decimal Converter
Convert a number between binary, octal, decimal and hexadecimal, with a breakdown table.
Results update as you type.
About this calculator
A binary, hex and decimal converter shows the same whole number across number bases. Computers ultimately work in binary (base 2), but programmers routinely switch between bases to make values readable: decimal (base 10) for everyday quantities, hexadecimal (base 16) for byte values and memory addresses, and octal (base 8) for things like Unix file permissions. This converter takes a whole number in any of those four bases and shows it in all four at once, along with its bit length. The digits allowed in each base go up to one less than the base — binary uses 0–1, octal 0–7, decimal 0–9 and hex 0–9 then A–F for 10–15 — and the tool rejects digits that are out of range for the base you pick.
As a worked example, the decimal value 255 is FF in hexadecimal, 377 in octal and 11111111 in binary — eight bits all set, i.e. exactly one byte at its maximum. To convert decimal to hex by hand you repeatedly divide by 16 and read the remainders from last to first; the calculator does it instantly and also accepts input prefixed with 0x (hex), 0b (binary) or 0o (octal) and handles negative numbers.
The reason hexadecimal is so common in computing is that each hex digit maps to exactly four binary bits (a nibble), so two hex digits describe one byte with no ambiguity — which is why colour codes like #FF8800, MAC addresses and memory dumps are written in hex. This tool is handy for bit masks, colour values, debugging register contents and any low-level work where you need to see the same number across bases.
Frequently asked questions
How do I convert decimal to hexadecimal?
Repeatedly divide by 16 and read the remainders from last to first, using A–F for 10–15. Decimal 255 is FF in hex and 11111111 in binary.
Why is hexadecimal used in computing?
Each hex digit maps to exactly four binary bits, so hex is a compact, readable way to write byte values and memory addresses — 0xFF is one byte of all ones.
Can I enter numbers with 0x, 0b or 0o prefixes?
Yes. A leading 0x (hex), 0b (binary) or 0o (octal) prefix is stripped automatically, so you can paste values straight from code. Just make sure the input base you select matches the digits you enter.
What does the bit length tell me?
It is how many binary digits the value needs. Decimal 255 is 8 bits (one byte); 256 needs 9 bits. Bit length is useful for choosing data types and checking whether a value fits in a byte, 16-bit word or 32-bit register.
What is octal used for?
Octal groups bits in threes and shows up mainly in Unix file permissions (like 755 or 644) and some legacy systems. Each octal digit maps to exactly three binary bits, the way each hex digit maps to four.
Why did I get "invalid number for this base"?
A digit you entered is not allowed in the selected base — for example the letter F or the digit 8 in a binary number, which only permits 0 and 1. Switch the input base to match your value, or correct the out-of-range digit.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/binary-hex/curl
curl "https://calculator.free/api/v1/binary-hex/?value=255&base=10"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/binary-hex/?" + new URLSearchParams({
"value": "255",
"base": "10"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.