Arbitrary Base Converter

How it is calculated

Enter an integer, the base it is written in (2 to 36) and the base you want (2 to 36). Digits above 9 are the letters a to z, where a = 10, b = 11 and z = 35, and upper or lower case is accepted. The tool reads the value digit by digit in the source base:

decimal = decimal × from + digit

and then divides that decimal number repeatedly by the target base, collecting the remainders as digits from the last to the first. Both steps use exact string arithmetic, so very long numbers are not rounded. A leading minus or plus sign is allowed. The result is shown in lower case together with its decimal value (without sign) and a label naming the bases. Any digit that is not valid in the source base, a fraction point, spaces inside the number, a prefix such as 0x or a base outside 2 to 36 gives no result.

Common mistakes

• Entering a digit that does not exist in the source base. A 2 in base 2 or a g in base 16 is invalid, and the tool returns nothing rather than guessing.
• Typing a prefix like 0x1a7 or a suffix such as 1a7h. Only the plain digits are accepted, so remove the prefix and put the base in the From field.
• Entering a number with a fraction point, like 10.5. The converter handles whole numbers only.
• Confusing the From and To fields. Swapping them reads your number in the wrong base, and 1a7 as a base 2 number is invalid.
• Treating the decimal line as signed. For a negative input the converted value keeps the minus sign, but the decimal line shows the size alone, so read the sign from the main result.