About this calculator
Free binary converter to convert between binary, decimal, hexadecimal, and octal number systems. Instant conversion with live updates as you type.
How to use
Pick the number system your value is currently in, then type it into the field above — results for decimal, binary, hexadecimal, and octal update instantly as you type. You can also click Calculate to refresh the results, or press Enter. Click Clear to reset the fields.
Frequently Asked Questions
How do I convert decimal to binary by hand?
Divide the decimal number by 2 repeatedly, writing down each remainder, until the quotient reaches 0. Reading the remainders from bottom to top gives the binary value. For example, 42 divided by 2 repeatedly gives remainders 0, 1, 0, 1, 0, 1 (bottom to top), which is 101010 in binary — the same answer this calculator gives instantly.
What is the difference between binary, hexadecimal, and octal?
They are all ways of writing the same number using a different base, or radix. Binary (base 2) uses only 0 and 1 and is how computers store data at the hardware level. Octal (base 8) and hexadecimal (base 16) are shorthand for binary: each octal digit represents exactly 3 binary digits, and each hexadecimal digit represents exactly 4, which is why programmers use hex to write long binary values more compactly.
Why does hexadecimal use the letters A-F?
Hexadecimal is base 16, so it needs 16 distinct digits. After 0-9 run out, the letters A through F stand in for the values 10 through 15 (A=10, B=11, C=12, D=13, E=14, F=15). So the hex value 2A equals 2 x 16 + 10 = 42 in decimal.
Is there a limit to how large a number this tool can convert?
Yes. This calculator runs entirely in your browser using standard JavaScript numbers, which can represent whole numbers exactly only up to 9,007,199,254,740,991 (2^53 - 1). Enter a larger value and the calculator will tell you it is out of range rather than show an inaccurate result. It also only handles non-negative whole numbers, not fractions or negative values.