Number Base Converter
Convert integers between any bases from 2 to 36 — binary, octal, decimal, hexadecimal and beyond — exactly, at any size.
Your inputs
Results
Base 2
11111111
- Decimal (base 10)
- 255
- Binary (base 2)
- 11111111
- Octal (base 8)
- 377
- Hexadecimal (base 16)
- FF
✓Exact calculation — rounded only for display
What this calculator does
Number bases are different ways of writing the same quantity. Programmers use binary, octal and hex; base 36 uses all letters.
Formula and method
Value = Σ digit × base^position; converted with arbitrary-precision integers.
Worked example
Calculated by this tool with its default inputs:
Inputs
- Value: FF
- From base: 16
- To base: 2
Results
- Base 2: 11111111
- Decimal (base 10): 255
- Binary (base 2): 11111111
- Octal (base 8): 377
- Hexadecimal (base 16): FF
How to read the results
The value is unchanged; only its written form differs.
Assumptions and limitations
- Integers only; digits above 9 use letters A–Z.
Questions
What is base 36 used for?
Compact identifiers and short URLs, since it uses digits and letters.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 6 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy