Number & Base Conversion Tools

Why a number gets written in another base

A base is a notation, not a different number. Thirty-one is 11111 in binary, 37 in octal and 1F in hex, and none of those is more true than the others. Bases exist because some of them line up with hardware. One hexadecimal digit is exactly four bits, so a byte is always two hex digits and a colour is always six, which is why hex shows up in memory dumps, colour codes and byte offsets. One octal digit is three bits, which is why Unix file permissions are written 755. Binary is where the bits are visible individually, and where an 0b-prefixed literal in source code usually means someone is working with flags.

• The number base converter handles any base from 2 to 36 in either direction, including the ones without names.
• For the common pairs there are direct tools: binary to decimal, hex to decimal and octal to decimal.
• Conversion uses big integers, so a value far past the point where a spreadsheet or a JavaScript number starts rounding still converts digit for digit.

Numbers written as language

Number to words and words to number convert in both directions, which is what cheques, contracts and read-aloud interfaces need. Ordinal numbers handles the suffix rule and its exception: 1, 2 and 3 take st, nd and rd, but 11, 12 and 13 take th regardless, and that exception comes back every hundred. Roman numerals follow the subtractive convention, where IV is four rather than IIII. There is no roman numeral for zero and no single symbol above M, so the ordinary range stops at 3,999.

Decimals, fractions and magnitude

Fraction to decimal works in both directions, finding the closest simplified fraction for a decimal you paste in. A fraction terminates only when its reduced denominator has no prime factor other than 2 or 5, which is why an eighth resolves cleanly and a third never will. Scientific notation moves between 0.00000000662 and 6.62e-9, and also gives the engineering form where the exponent is always a multiple of three. Percentage conversion shows the same quantity as a percentage, a decimal, a simplified fraction, a ratio and basis points at once, which is what financial documents mix.