A numeral base, or radix, defines how many unique digits a positional number system uses before it rolls over into the next place value. This arbitrary base converter translates a whole number from any base between 2 and 36 into any other, using the digit set 0-9 followed by A-Z. It is handy for programming, digital electronics, cryptography puzzles and understanding how the same quantity looks in different notations.
How it works
In any base b, a number is the sum of each digit multiplied by b raised to the power of its position, counting from zero on the right. The tool reads your input left to right, repeatedly multiplying the running total by the source base and adding each digit’s value — this yields the exact integer. It then re-encodes that integer in the target base by repeated division: divide by the base, record the remainder as the next digit (from right to left), and continue until the quotient reaches zero.
Because the maths is done with exact big integers rather than floating-point numbers, conversions stay precise no matter how many digits you enter. For example, FF in base 16 parses as 15 × 16 + 15 = 255, which in base 2 becomes 11111111.
Example
Convert 7G3 from base 17 to base 10. The digit G equals 16, so the value is 7 × 17² + 16 × 17 + 3 = 7 × 289 + 272 + 3 = 2023 + 275 = 2298. The decimal cross-check line confirms this independently.
Tips and notes
You can include spaces or underscores as visual grouping separators in your input — they are ignored. If you enter a digit that is too large for the chosen source base (for example the digit 8 in base 8), the tool flags exactly which character is invalid. Everything is computed locally; nothing you type is sent to a server.