Number Base Converter

Written byOleh Soloninupdated 5 October 2026

Value

From Base

To Base

Result

Converted ValueFF

Base 2 to base 36, both directions

Convert between binary, octal, decimal and hexadecimal, plus any base from 2 to 36. Handy for permissions, colour codes and debugging.

Bases show up whenever you get close to the machine: file permissions in octal, colours in hex, bit masks in binary. Converting them by hand is slow and easy to fumble.

Enter the value, say which base it is written in, and pick the base you want it in. The tool rejects digits that cannot exist in the source base instead of quietly producing nonsense.

How to use

Enter a whole number; spaces between digit groups are fine — '1111 0000'.
Choose the base you are converting from: binary, octal, decimal or hexadecimal.
Choose the base to convert to. If the input has a digit that the source base does not have, the calculator names it.

One number in several bases

Each hex digit is exactly four binary digits and each octal digit three. That is why FF is 1111 1111, and why 255 is the largest number one byte can hold.

Every row comes from the calculator on this page.
Decimal	Binary	Hexadecimal
10	1010	A
100	1100100	64
255	11111111	FF
1,000	1111101000	3E8
4,096	1000000000000	1000
65,535	1111111111111111	FFFF

Unix file permissions

File permissions are written as octal digits, one each for owner, group and others. Each digit is three bits: read (4), write (2), execute (1).

The binary form comes from the calculator on this page.
Octal	Binary	Meaning
755	111101101	owner everything, others read and execute
644	110100100	owner read and write, others read

What this calculator shows

The number in binary, octal, decimal or hexadecimal
An exact answer even for very long numbers — nothing is lost to rounding
A clear error when the input has an invalid digit or a fractional part

What to keep in mind

Works with whole numbers, negatives included; fractions are not supported.
Digits above 9 are letters: A–F in hexadecimal, in either case.

FAQs

What is 255 in hexadecimal?

FF. It is the largest value a single byte holds, which is why pure white in RGB is #FFFFFF and colour channels stop at 255.

How do I convert binary to decimal?

Add up the powers of two where the ones are: 1010 is 8 + 2 = 10. The calculator does the same for any length.

Why does hex use letters?

Base 16 needs sixteen distinct digits and we only have ten numerals, so A through F stand in for 10 through 15.

Why is 2 not a valid binary digit?

Binary only has 0 and 1. Anything else means the number was not really binary, so the calculator says which digit is wrong rather than guessing.

Can it convert fractions?

No, it works with whole numbers. A fraction such as 3.5 is not silently cut down — the calculator says fractions are not supported.

What does chmod 755 mean?

Three octal permission digits: 7 is read, write and execute for the owner, 5 is read and execute for group and others. In binary that is 111 101 101.

Worked example

A file permission

Input: 755 in octal → binary

Output: 111101101

Note: Read in threes: 111 is read-write-execute for the owner, 101 is read-execute for group and others. That is what chmod 755 actually sets.

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