Convert a number between any two bases from 2 to 36 – binary, ternary, octal, decimal, hex, base 32, base 36 and everything in between – exactly, with no size limit.
Show calculation steps
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Between any two bases, exactly
Base conversion does not privilege 2, 10 and 16 β the positional principle works identically in base 7 or base 33. This converter accepts both endpoints as parameters: 1,190 ordered base pairs from binary to base 36, each conversion exact at any length.
The digit alphabet extends past 9 with letters, a=10 through z=35, case-insensitive. Base 36 is thus the largest base writable with digits and one case of letters β the reason compact record keys and some URL schemes stop exactly there.
Worked example
Input: zz (base 36) β base 10 z = 35 zz = 35Γ36 + 35 = 1260 + 35 = 1295 Check the reverse: 1295 Γ· 36 = 35 r 35 β zz β
The two-stage method
Every conversion crosses an exact integer bridge: source digits fold into a big integer via place values, and repeated division by the target base unfolds it into new digits. The calculation-steps panel shows both stages for your own number β the same procedure you would use on paper, minus the arithmetic slips.
Applications beyond the usual suspects
Ternary appears in balanced-number-system research, base 12 and base 60 in historical metrology (and your clock), base 20 in Maya numerals, base 26 in spreadsheet column names (with a twist β no zero digit), and bases 32/36 in human-typable identifiers. Whenever one of those systems needs decoding, an arbitrary-base converter is the tool.
Limits, honestly stated
Integers only β fractional values belong to the Fractional Base Converter, which adds repeat detection. Base 1 is excluded because tally notation is not positional; base 64 is excluded because Base64 is a data encoding, not a number base (its alphabet even differs by implementation). Everything runs locally in your browser β nothing you type is sent anywhere.
How to use the Any Base Converter
- Enter the number, then set "From base" to the base it is currently written in.
- Set "To base" to the base you want.
- Click "Convert base" – the steps panel shows the decimal bridge value and the repeated division that produced the output digits.
- For bases above 10, digits use letters: a=10, b=11 … z=35 (case-insensitive here).
Frequently asked questions
Which bases can this convert between?
Any pair from base 2 to base 36 in either direction – 1,190 possible pairs. Base 36 is the ceiling because it exhausts 0-9 plus the 26 letters; for the case-sensitive alphabet that reaches base 62, use the Base 2 to 62 Converter.
How does the conversion actually work?
In two exact stages: the input digits are folded into an arbitrary-precision integer (each digit multiplied by its place value), and that integer is then rewritten in the target base by repeated division. The steps panel shows both stages for your number.
Why do letters appear in my result?
Any base above 10 needs more than ten digit symbols, so letters continue where digits end: in base 16, a-f stand for 10-15; in base 36, z stands for 35. Your input may use upper or lower case – they mean the same here.
Is base 1 or base 64 possible?
Not in positional notation as implemented here. Base 1 (tally marks) has no positional meaning, and base 64 in computing is a data ENCODING with its own alphabet including + and /, not a number base – the Base64 Encoder handles that, and it is a different operation entirely.
Can it handle huge numbers?
Yes – conversion is BigInt-exact at any length. A 60-digit base-7 number converts to base 29 without losing a digit, which is precisely the case where double-precision converters fail silently.
What happens to fractional input like 12.5?
This tool is integers-only, and it will tell you rather than round silently. The Fractional Base Converter performs exact radix-point conversions, including detection of digits that repeat forever.
What are unusual bases actually used for?
Base 3 appears in balanced-ternary research and some puzzles, base 12 in historical measure systems, base 20 in Maya numerals, base 32 in Crockford-style human-readable IDs, and base 36 in compact record keys – it is the densest base that stays case-insensitive.
