Base Converter

How to convert between number bases

1. Write down the number and number each digit's position from right to left, starting at 0.
2. Convert each digit to its value (0–9 stay 0–9; A–Z mean 10–35) and multiply by the base raised to its position.
3. Add all the results — that's the decimal value. To reach another base, repeatedly divide by the target base and read the remainders from bottom to top.

Example: FF₁₆ = (15 × 16¹) + (15 × 16⁰) = 240 + 15 = 255₁₀.

Background reading: radix and positional notation on Wikipedia.

Digit values (bases up to 36)

int("ff", 16)          # → 255  (any base 2–36)

def to_base(n, b):
    digits = "0123456789abcdefghijklmnopqrstuvwxyz"
    if n == 0:
        return "0"
    out = ""
    while n > 0:
        out = digits[n % b] + out
        n //= b
    return out

to_base(255, 16)       # → 'ff'

parseInt("ff", 16);   // → 255  (any base 2–36)
(255).toString(16);   // → "ff" (any base 2–36)

#include <stdio.h>
#include <stdlib.h>

int main(void) {
    printf("%ld\n", strtol("ff", NULL, 16));  /* → 255 */
    return 0;
}

Real-world applications

• Reading hex color codes (#FF5733), memory addresses and error codes in programming.
• Understanding file permissions (octal, e.g. chmod 755) and Unix modes.
• Shortening IDs and URLs with base 36 or base 62 encodings.
• Learning how positional number systems work — the foundation of computer arithmetic.

Common mistakes

• Using a digit the base doesn't allow — e.g. "2" is invalid in binary, "G" is invalid in hex.
• Forgetting that A–Z count as 10–35, not as letters with their alphabet position.
• Reading remainders top-down instead of bottom-up when dividing into the new base.

Frequently asked questions

Need a specific pair? Try our hex to decimal or binary to decimal converters.