How base conversion works
Every number can be written in any base by expressing it as a sum of powers of that base. The calculator first reads your value in the source base and converts it to a plain decimal number, then re-expresses that decimal in the target base.
Decimal acts as a common bridge between the two bases, which is why the decimal equivalent is always shown — it lets you verify each half of the conversion independently.
The four bases
The tool supports the four bases most common in computing and math. Each uses a fixed set of digits.
- Binary (base 2) uses only 0 and 1, the language of digital circuits.
- Octal (base 8) uses 0 to 7 and groups binary into threes.
- Decimal (base 10) is the everyday number system.
- Hexadecimal (base 16) uses 0 to 9 then A to F, and is shown in uppercase here.
Tips and common mistakes
Each base only accepts its own digits. A value like "1012" is invalid in binary because 2 is not a binary digit, and the calculator will flag it.
- Hex digits A to F can be entered in either case; the result is uppercased.
- This tool handles whole numbers only — fractions and decimal points are not supported.
- If the result looks wrong, check the decimal value first to see which side of the conversion went astray.
Formula
decimal = parseInt(value, fromBase); output = decimal in toBaseFrequently asked questions
- How do I convert binary to decimal by hand?
- Multiply each digit by two raised to its position, counting from zero on the right, then add the results. So 1011 is 8 + 0 + 2 + 1 = 11.
- What bases does this support?
- Binary (base 2), octal (base 8), decimal (base 10) and hexadecimal (base 16), in any direction. The decimal equivalent is always shown so you can sanity-check the conversion.
- Can it convert fractions or negative numbers?
- No — it handles whole, non-negative numbers only. Fractional binary and two’s-complement representations are outside its scope.