Number Base Converter

What is a number base?

A number base (or radix) is how many distinct digits a counting system uses. Decimal — the system we use every day — is base 10: it uses the digits 0 through 9. Binary is base 2 (digits 0 and 1), octal is base 8, and hexadecimal is base 16, which adds the letters A–F to represent the values 10 through 15. The same quantity can be written in any base; only the symbols change, not the amount. This converter changes a number from one base to another for any base from 2 to 36. If you work with very large or very small numbers, you may also find our scientific notation converter and exponent calculator useful, since every base is built on powers — binary on powers of 2, decimal on powers of 10.

How it's calculated

To convert a number to base 10, multiply each digit by its place value — the base raised to the digit's position, counting from zero on the right — and add the results. For example, the binary number 1010 is 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10 in decimal. To go from base 10 to another base, divide repeatedly by the new base and read the remainders from bottom to top. Dividing 255 by 16 gives 15 remainder 15; 15 in hexadecimal is F, so 255 becomes FF. Digits above 9 use letters: A = 10, B = 11, and so on up to Z = 35 in base 36.

Example

Enter 255 with a "from" base of 10. The converter shows it as 11111111 in binary, 377 in octal, and FF in hexadecimal. Switch the input to FF with a from-base of 16 and you get back 255 in decimal — the conversion works both ways and for any base between 2 and 36.