Math
Base Converter
Enter a number, the base it is written in, and the base you want, from 2 to 36.
The converter expands the digits by place value to reach decimal, then divides repeatedly by the target base, showing every remainder. Fractions convert by repeated multiplication, and repeating expansions are marked.
Use digits valid in the source base: 0-9 then A-Z (A = 10 … Z = 35). A radix point and a minus sign are allowed.
Any base from 2 (binary) to 36 (digits 0-9 and A-Z).
Any base from 2 to 36.
Try an example
Result
Converted value
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- Decimal
- —
- Binary
- —
- Hexadecimal
- —
- Octal
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Study path
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What the base converter solves
Any whole number can be written in any base: base 10 uses ten digits, base 2 uses two, and base 36 uses 0-9 plus A-Z. Converting between two arbitrary bases is a two-step trip through decimal: expand the source digits by place value, then divide by the target base and collect remainders. This converter shows both legs and handles fractional parts.
Digits above 9
| Digit | A | B | C | D | E | F | G | … | Z |
|---|---|---|---|---|---|---|---|---|---|
| Value | 10 | 11 | 12 | 13 | 14 | 15 | 16 | … | 35 |
How to use it
- Set From base to the base of your number and To base to the one you want (2-36).
- Type the number using only valid digits for the From base; letters can be upper or lower case.
- Read the place-value table for the trip to decimal and the division table (bottom to top) for the trip to the target base.
- If your number has a radix point, follow the multiplication table for the fractional digits.
How to read the answer
The converted value uses uppercase letters for digits above 9. The decimal value is always shown so you can sanity-check the size of the number. A repeating block in parentheses means the fraction never terminates in the target base, which happens whenever the The bottom number of a fraction; it says how many equal parts make one whole. shares no factors with the base.
Common mistakes and edge cases
- Using a digit that is too big for the base: 8 is not a base-8 digit, and 2 is not a binary digit. The converter names the character.
- Reading remainders top to bottom. The first remainder is the last digit.
- Assuming a terminating fraction stays terminating: 0.1 (decimal) repeats in binary and in base 3.
- Base 1 does not exist as a positional system and bases above 36 run out of letters; the range is 2-36.
- Converting from base 10 to base 10 simply echoes the number.
Worked examples
Decimal to base 7
2024 → base 7
Converted value
5621
Base 36 to decimal
ZZ → decimal
Converted value
1,295
Base 5 to base 3
1234 (base 5) → base 3
Converted value
21012
Fraction that repeats
0.1 → base 3
Converted value
0.(0022)
Negative
−255 → base 16
Converted value
-FF
Zero
0 → base 2
Converted value
0
Invalid digit for base
129 in base 8
Converted value
—
Frequently asked questions
How do you convert between two bases that are not 10?+
Convert to decimal first by place values, then convert that decimal to the target base by repeated division. The calculator shows both stages.
What are the digits in base 36?+
0-9 then A-Z, where A = 10 and Z = 35. Base 36 is used for short URL codes and license keys because it packs a lot into few characters.
Why does 0.1 repeat in base 3?+
0.1 = 1/10, and 10 shares no factor with 3, so the base-3 expansion never terminates: 0.002200220022… The repeating block is shown in parentheses.
Can I convert a number with a fractional part?+
Yes. The whole part uses repeated division and the fraction uses repeated multiplication by the target base. Both tables are shown.
What bases are supported?+
Any base from 2 to 36. Base 1 is not a positional system, and beyond 36 there are no standard digit symbols.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026