Written by Alex Chen · Reviewed by Sarah Mitchell · July 21, 2026
Convert numbers between any two bases (2–36) and view the result in every common numeral system.
A base is the set of digits a number system uses before it carries over to the next column. Decimal counts with ten digits, binary with two, and hexadecimal with sixteen. This converter takes a value written in one base and rewrites it in another, covering every base from 2 up to 36 so you can move between the systems that actually show up in computing, electronics, and mathematics.
Pick the base your input is currently written in, type the number, and choose the base you want the answer in. The result appears instantly, and the page also fills in the same value in binary, octal, decimal, and hexadecimal below it, so you can see how the quantity looks across the common bases at once.
Input is accepted in upper or lower case for bases above 10, where letters stand in for digits. In base 16 the letter A represents ten, B represents eleven, and so on through F for fifteen. Bases above 16 continue the same pattern up to Z for thirty-five, which is why the tool stops at base 36.
Every positional system works the same way: each column carries a weight, and the weight is the base raised to a power. In decimal, the rightmost column is the ones place, the next is tens, then hundreds, each ten times the last. In binary the columns double instead: ones, twos, fours, eights, and so on. In hexadecimal they multiply by sixteen.
That is why 255 is special in binary. The eight columns of an eight-bit number hold 128, 64, 32, 16, 8, 4, 2, and 1, and adding every column together gives exactly 255, the largest value eight binary digits can express. The same quantity in hexadecimal fills two columns with fifteen each, written as FF. Understanding the columns makes the conversion results feel less like magic and more like arithmetic.
Enter 255 with base 10 selected, then set the target base to 16. The converter answers FF: 255 divided by 16 leaves a remainder of 15, and 15 is written as the single digit F in hexadecimal.
Switch the target to base 2 and the same input becomes 11111111. Dividing 255 repeatedly by 2 gives eight remainders of 1, so all eight binary positions are filled. Watch the common-bases table: it shows 11111111 in binary, 377 in octal, 255 in decimal, and FF in hexadecimal, four spellings of one quantity.
The math behind the tool is a simple loop. Divide the value by the target base, note the remainder as the next digit, and repeat with the quotient until nothing is left, then read the remainders in reverse order. For 255 in base 16: 255 divided by 16 is 15 with remainder 15, then 15 divided by 16 is 0 with remainder 15, giving F and F. The page runs this loop instantly for any pair of bases, but knowing the procedure helps you sanity-check an unusual result.
Most conversions run through ordinary integer arithmetic, which stays exact for everyday values. When the input grows beyond fourteen digits, the tool switches to a wider integer type that can represent much larger values without losing precision, so a twenty-digit decimal converts to its binary form exactly rather than being rounded.
Any base from 2 to 36, chosen from the dropdown lists on each side. Below 2 there is only one digit and above 36 the Latin alphabet runs out, so those limits define the practical range.
Each base accepts only its own digits. If you enter 9 while base 8 is selected, the tool flags the digit instead of guessing what it means, because an out-of-place digit has no defined value in that system.
The calculation switches to a larger integer type so the value stays exact. You will not notice any difference in the answer, but very long inputs no longer risk rounding at the boundary of ordinary arithmetic.
Yes. The copy button places just the converted value, without the label, onto your clipboard so you can paste it into code, a document, or another field.
Those four bases cover nearly every practical use, from memory addresses to file permissions. Showing them side by side lets you compare the same quantity across systems without running four separate conversions.
Binary sits underneath every program because processors work with two states. Hexadecimal keeps long binary strings short: four bits collapse into one hex digit, which is why color codes and memory dumps are written that way. Octal survives in Unix file permissions, where three bits per digit map to read, write, and execute flags. Each system trades digit count against readability, and this page converts freely between all of them.