Number Base Converter - Convert Between Any Bases from 2 to 36
Number Base Converter
Binary, octal, decimal, hex and any base up to 36, exactly
Any Base 2 to 36
Convert from and to any base, with the common ones (2, 8, 10, 16, 36) always shown.
No Size Limit
Big integers are exact: no rounding at 2^53 like ordinary JavaScript numbers.
Exact Fractions
Repeating digits are detected and shown in brackets, e.g. 0.1 = 0.0(0011) in binary.
Private
Everything runs in your browser; nothing you paste is uploaded.
How Base Conversion Works
In base b, each digit is worth b times the one to its right: 2F in hexadecimal is 2 × 16 + 15 = 47. Bases above 10 use letters for the extra digits (A = 10 up to Z = 35). Prefixes 0b, 0o and 0x are accepted for binary, octal and hex, and spaces or underscores used to group digits are ignored. Every whole number has an exact representation in every base.
Fractions are different: a fraction terminates in a base only if its denominator's prime factors divide the base. That is why 0.1 in decimal repeats forever in binary, 0.0(0011), which is the root of the classic 0.1 + 0.2 ≠ 0.3 floating-point surprise. This converter works with exact rational arithmetic and marks the repeating block in brackets, or shows … if it is longer than the digit limit.
Key Takeaways
- Prefixes welcome: 0x, 0b and 0o are understood.
- Exact, any size: Integers use BigInt arithmetic.
- Repeating digits: Brackets mark the block that repeats forever.