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

How do I convert between any two number bases?

Convert to decimal first: multiply each digit by the base raised to its position power and sum the results. Then convert the decimal value to the target base by repeated division, reading the remainders bottom-up. The converter above does both steps instantly.

What number bases does this converter support?

Any base from 2 (binary) to 36, using digits 0–9 and letters A–Z for values 10–35.

How do I convert FF from hexadecimal to decimal?

FF in hex = 15 × 16 + 15 = 255 in decimal.

What is 100 in base 36?

100 in decimal = 2S in base 36 (2 × 36 + 28 = 100, and 28 is written S).

Can I use prefixes like 0x or 0b?

Yes — 0x, 0b and 0o prefixes are recognized for hex, binary and octal inputs, and spaces, commas, underscores and dashes are ignored.

Why does base 36 use letters?

Beyond digit 9, bases use letters A–Z for values 10–35. Base 36 uses all of them, which makes numbers short — handy for compact IDs and URL shorteners.

Can this converter handle very large numbers?

Yes — it uses arbitrary-precision arithmetic, so inputs hundreds of digits long convert with no overflow or rounding.

What is the largest digit in base 16?

F, worth 15. In any base, the largest digit is always one less than the base.

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