Base Converter
Convert integers between any two bases from 2 to 36 with step-by-step working.
About Base Converter
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
Worked example
With the default values below, Base Converter returns Converted Value of FF. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Number
- 255
- From Baseaccepts 2–36
- 10
- To Baseaccepts 2–36
- 16
Results
- Converted Value
- FF
- Decimal Equivalent
- 255
Step by step
- 1Parse base-10
- 2Convert to base 16
- 3Result= FF (base 16)
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.