Number Converters · Browser · Free

Binary to Octal Converter

Type a binary number and read off its octal form, with the same value also shown in decimal and hexadecimal. The answer appears in a card below the button as soon as you press Convert.

What this tool does

It converts binary numbers, which are base 2, into octal numbers, which are base 8. There is one text field. A sign and a fractional point are both accepted, and if you type several numbers separated by spaces, each number is converted on its own. Next to the octal answer you also get the decimal and hexadecimal forms, and any letters in them print uppercase.

The form computes only when you press Convert, and the result shows up in a card below the button. Copy writes the result and its unit to the clipboard, and Clear resets the form so you can start over.

How the places in a number work

Binary is base 2 and octal is base 8. In either base a digit is worth whatever position it sits in: the digit on the right counts plain units, and every step to the left is worth twice as much in binary and eight times as much in octal. The amount a whole number stands for is the sum of the places that are switched on.

The table shows that reading. Binary 1111 fills four places and comes out as octal 17, which is one group of eight together with seven units. Add one more binary place and 11111 comes out as octal 37, three eights and seven units. Binary 10000 has a single 1 in the fifth place and prints as octal 20, that is two eights.

Longer values read the same way. Binary 10000000000 prints as octal 2000, and binary 11111111 prints as octal 377, where the repeated 7 is the largest digit base 8 has room for.

Binary to octal formula

One rule sits behind every row: take what each binary place is worth, then restate that same amount using octal places, where each place going left counts eight times the place before it. The table works this out for the sample values.

Two short rows show it end to end. Binary 1010 uses two places and its octal form is 12, one eight and two units. Binary 1100100 comes out as octal 144, and binary 11111111 comes out as octal 377.

Groups of three binary digits per octal digit explain the tidy rows near the foot of the table. Binary 100000 is octal 40, binary 1000000 is octal 100, and binary 100000000 is octal 400. Each of those starts as a single 1 followed by zeros, and each lands as one digit followed by zeros in octal.