Base Converter
Convert integers between any two bases from 2 to 36 with step-by-step working.
Inputs
The number to convert. Use digits 0-9 and letters A-Z for bases > 10.
Source base (2–36).
Target base (2–36).
Converted Value
FF
Decimal Equivalent
255
Step by step
Parse base-10
255 (base 10) = 255 (decimal)
Convert to base 16
255 ÷ 16 = 15 remainder F; 15 ÷ 16 = 0 remainder F
Result
= FF (base 16)
How it works
Any positive integer can be represented in any base (radix) from 2 to 36. The conversion proceeds in two stages: first parse the input from its source base into a decimal (base-10) value by expanding the positional notation, then repeatedly divide by the target base and collect remainders to build the output digits from least-significant to most-significant.
Formulas
Positional expansion
decimal = Σ(digit_i × base^i) for i from 0 to n-1
- digit_i
- Value of the ith digit
- base
- Source radix
- i
- Position (0 = rightmost)
Repeated division
Divide decimal by target base; collect remainders bottom-to-top
- decimal
- Intermediate base-10 value
- target_base
- Destination radix
Frequently Asked Questions
What bases are supported?
Any integer base from 2 (binary) to 36. Bases above 10 use letters A-Z as digit symbols, so base 16 uses 0-9 and A-F, and base 36 uses the full set 0-9, A-Z.
How do I convert a large number by hand?
First convert to decimal by multiplying each digit by its positional weight and summing. Then repeatedly divide by the target base and read the remainders in reverse order to get the digits in the new base.