Number Base Converter
Convert a number between any two bases from 2 to 36, fractions included, with digits the source base does not have named and cut-off fractions flagged.
Result
Converted: FF
Whole numbers are exact at any length; fractions are shown to the chosen number of digits.
- In decimal
- 255
- In binary
- 11111111
- In octal
- 377
- In hexadecimal
- FF
https://calcgallery.com/algebra-numbers/number-base-converter-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Number Base Converter
- Type the number. Bases above 10 use letters for the extra digits, A for 10 up to Z for 35, in either case. Use a point for a fraction.
- Enter the base it is written in and the base you want, each from 2 to 36.
- Read the converted number, with decimal, binary, octal and hex alongside. A fraction that never ends is cut off and flagged.
How conversion works
A number in base b has digits worth 1, b, b², b³ and so on from the right, and b⁻¹, b⁻², … after the point. The page reads the whole number exactly, then writes it out in the new base by repeated division. For the fraction it multiplies by the new base and takes the whole part as the next digit, repeating until the fraction is used up or the digit limit is reached.
0.625 × 2 = 1.25 → 10.25 × 2 = 0.5 → 00.5 × 2 = 1.0 → 1 so 0.625 is 0.101 in binaryWith your numbers
- Each digit is worth the base times the digit to its right: 777 in base 8 = 7 × 64 + 7 × 8 + 7 = 511.
Quick reference
Whole numbers are exact at any length; fractions are shown to the chosen number of digits.
| Example | Converted |
|---|---|
| 255 to base 16 | FF |
| 255 to base 2 | 11111111 |
| 777 in base 8 to 10 | 511 |
| ZZ in base 36 to 10 | 1295 |
| 1010 in base 2 to 16 | A |
| 0.5 to base 2 | 0.1 |
| 0.1 to base 2 | 0.000110011001 |
| 789 in base 8 |
Common questions about the Number Base Converter
- How do I convert a number to another base?
- Divide by the new base again and again, keeping the remainders: they are the digits, read from the last to the first. 255 ÷ 16 is 15 remainder 15, and 15 ÷ 16 is 0 remainder 15, so 255 is FF in base 16. To go the other way, multiply each digit by its place value and add.
- Why does 0.1 never end in binary?
- A fraction ends in a base only when its denominator, in lowest terms, is built from the prime factors of that base. One tenth has a factor of 5 in its denominator, and 2 has no 5, so in binary 0.1 repeats 0011 forever: 0.000110011001… The page stops at the number of digits you choose and says it has cut the answer off, rather than rounding it silently.
- Why was my number rejected?
- A base only has as many digits as its number: base 8 uses 0 to 7, so 789 cannot be an octal number. The page names the first digit that does not belong rather than guessing what you meant.
- What is base 36 used for?
- It is the largest base that can be written with the ten digits and 26 letters, which makes it a compact way to write large whole numbers as short codes, such as in some URL shorteners and reference numbers.