Number Base Converter
Convert numbers between binary, octal, decimal and hexadecimal.
Results update as you type.
About this calculator
A number base converter rewrites an integer from one positional base to another — binary (base 2), octal (base 8), decimal (base 10) and hexadecimal (base 16). It reads your value in the source base, works out its plain decimal value, and re-expresses that value in the target base.
Each base uses a fixed set of digits: 0–1 for binary, 0–7 for octal, 0–9 for decimal and 0–9 then A–F for hexadecimal, where A–F stand for 10–15. Because 16 is 2⁴, each hex digit maps to exactly four binary digits, which is why programmers use hex as shorthand for raw bytes.
Worked example: the decimal number 255 is 11111111 in binary and FF in hexadecimal, since 255 = 15×16 + 15. The converter also reports the intermediate decimal value so you can check the working. A results table shows the same number in all four bases at once, and an invalid digit for the chosen source base is flagged rather than silently miscounted.
Frequently asked questions
How do I convert decimal to binary?
Repeatedly divide by 2 and read the remainders from bottom to top. For example 10 in decimal is 1010 in binary, and 255 is 11111111.
What is hexadecimal used for?
Hexadecimal (base 16) packs four binary bits into one digit (0–9 then A–F), so it is a compact way to write bytes. The decimal number 255 is FF in hex.
Why does my number show a dash?
The digits must be valid for the source base — for example only 0 and 1 in binary, or 0–9 and A–F in hex. An invalid digit makes the result undefined.
What do the letters A to F mean in hexadecimal?
They are single digits for the values 10 through 15: A is 10, B is 11, up to F which is 15. This lets base 16 fit numbers up to 15 into one place before it has to carry.
Why does each hex digit equal four binary digits?
Because 16 equals 2 to the fourth power, every hexadecimal digit covers exactly four bits. So the byte 11111111 groups into 1111 1111, which is FF — this number base converter does that grouping for you.
Can this converter handle very large numbers?
It works on whole numbers and is accurate up to the range integers are stored exactly (about 9 quadrillion, or 2⁵³). Beyond that, extremely long binary or hexadecimal strings may lose precision in their last digits.
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/number-base/curl
curl "https://calculator.free/api/v1/number-base/?amount=255&from=10&to=2"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/number-base/?" + new URLSearchParams({
"amount": "255",
"from": "10",
"to": "2"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.