Number Base Converter

What Is the Number Base Converter?

This tool converts an integer between any two number bases from 2 to 36 -- binary, octal, decimal, and hex are just the 4 most common special cases. Base 36 uses digits 0-9 followed by letters a-z, the maximum base representable with the standard alphanumeric character set.

How to Use This Tool

Enter a value and its source base, then choose a target base. The converted value appears instantly.

How Base Conversion Works

Worked Example

Practical Uses

• Converting between unusual number bases beyond the common binary/octal/hex set
• Understanding how positional numeral systems generalize to any base
• Cross-checking a base-36 (or other unusual base) identifier used in a URL shortener or encoding scheme

For the specific binary/octal/decimal/hex conversions with dedicated tools, see the existing Decimal ↔ Binary converter pair. For two's complement binary representation of negative numbers, see the existing Two's Complement Calculator.

Step-by-Step Usage

Type the value, set the From Base (2 to 36) and the To Base (2 to 36). The result appears in lowercase in the Base N result box. The default input is 255 from base 10 to base 16, giving ff. To reverse a conversion, swap the two base numbers and paste the answer back in as the value. Upper or lower case input is accepted, since letters are lowercased before parsing, and leading zeros are ignored.

More Worked Examples

• ff from base 16 to base 2 gives 11111111, the eight bits of a full byte.
• 777 from base 8 to base 10 gives 511. Octal values like this appear in file permissions, where each octal digit stands for three permission bits.
• zz from base 36 to base 10 gives 1295, because z is 35 and 35 x 36 + 35 = 1295.
• 1295 from base 10 to base 36 gives zz, the reverse of the previous example.
• 101 from base 3 to base 10 gives 10 (1 x 9 + 0 x 3 + 1).

Input Errors and What They Mean

The tool refuses input that contains a character not valid in the source base. For instance 128 as base 8 is rejected since 8 is not an octal digit, and 12 as base 2 is rejected because 2 is not a binary digit. A decimal point also causes an error (1.5 is rejected), since the tool handles whole numbers only, as does a leading plus sign. If both bases are outside 2 to 36, an error asks you to stay within that range.

Size Limits

The conversion uses ordinary JavaScript numbers, which are exact only up to 9,007,199,254,740,991 (about 9 quadrillion). Very long inputs beyond that lose precision, and the tool may report them as invalid even when they are correct, for example a 20-digit decimal value. For big numbers, such as 64-bit identifiers, use a converter based on arbitrary-precision integers, or check the result by converting back to the original base and comparing.

Negative Numbers

The tool is designed for non-negative integers. In practice a leading minus sign is passed through, so -ff in base 16 gives -11111111 style output with a sign, but this is simple sign-magnitude notation, not two's complement. If you need the bit pattern that a computer uses for negative values, use a two's complement calculator instead.

Where Unusual Bases Show Up

• Base 36 is common in short identifiers and URL codes because it stays compact and readable.
• Base 8 and base 16 are shorthand for groups of binary digits, so they are handy when reading permissions, memory addresses and colour values.
• Learning exercises often use bases 3, 5 or 7 to reinforce how place value works.

Frequently Asked Questions