🔁 Octal to Hex Converter with Steps

What is the Octal to Hex Converter?

Octal is a base 8 number system that uses only the digits 0 to 7, and hexadecimal is a base 16 system that uses the digits 0 to 9 followed by the letters A to F for the values 10 to 15. Both are shorthand ways of writing binary. One octal digit maps to exactly 3 bits and one hex digit maps to exactly 4 bits, which is why programmers reach for these bases when reading file permissions, memory dumps, or color values. Because octal and hex do not share a common digit width, you cannot line them up directly the way you can octal and binary, so the reliable path from octal to hex passes through the underlying value.

The cleanest method is to convert the octal number to its plain value first, then express that value in hex. To get the value, multiply each octal digit by its place value (a power of 8) and add the results, counting places from 0 at the rightmost digit. For octal 377 the places from the left are 64, 8 and 1, so the value is 3x64 + 7x8 + 7x1, which equals 192 + 56 + 7 = 255. That same value written in base 16 is FF, because 255 = 15x16 + 15, and 15 is the hex digit F. So octal 377 converts to hex FF.

A faster shortcut works through binary, since both octal and hex are powers of 2. Replace each octal digit with its 3 bit binary group, join the bits into one string, then split that string into groups of 4 bits from the right and turn each 4 bit group into one hex digit. Octal 377 becomes 011 111 111, which joins to 011111111; grouped into nibbles from the right that is 1111 1111 (dropping the leading zeros), and each 1111 is the hex digit F, giving FF. Both routes always agree, so pick whichever you find easier to check.

On the computing side, standard JavaScript number math is only exact up to 53 bits, so a naive conversion can drift on long octal strings. This tool parses the octal input with BigInt, which keeps the hexadecimal, decimal and binary results exact no matter how many digits you paste in. Whether you are checking a 3 digit permission code like 755, decoding a 16 bit value such as 177777, or converting a long register dump, the octal to hex result you see is the true value, not a rounded approximation.

When to use it

• Converting Unix or Linux file permission codes such as 755 or 644 from octal into a hexadecimal or binary form.
• Translating an octal value from older documentation, assembly listings, or a device manual into modern hexadecimal notation.
• Cross checking an octal number against its hex and decimal equivalents while debugging low level code.
• Teaching or learning how the base 8 and base 16 number systems relate through their shared binary representation.

How to use the Octal to Hex Converter

1. Type or paste an octal number (only the digits 0 to 7) into the input box, or tap one of the example buttons.
2. Read the hexadecimal value at the top; it updates instantly as you type.
3. Check the decimal and binary equivalents and the step by step breakdown below the main result.
4. Use the copy buttons to grab the hex, decimal, or binary result for use elsewhere.

Formula & method

Worked examples

Octal digit to binary and hex reference (single digit values)

Common octal values with their decimal, hex, and binary equivalents

Common mistakes to avoid

• Using an 8 or 9 in an octal number. Octal only has the digits 0 to 7, so an 8 or a 9 is never a valid octal digit. If your source value contains one, it is not octal, and the converter will flag it rather than guess.
• Trying to map octal digits straight to hex digits. One octal digit is 3 bits and one hex digit is 4 bits, so they do not line up one to one. Always go through the value or through binary; you cannot swap digit for digit.
• Grouping bits from the left instead of the right. When using the binary shortcut, split the joined bits into groups of four starting from the rightmost bit. Grouping from the left misplaces the boundaries and produces the wrong hex digits.
• Reading the hex letters as decimal. In hex the letters A to F stand for 10 to 15, not for text. FF is 255, not two Fs, so treat each letter as its numeric value when you check the result.

Glossary

Octal

A base 8 number system that uses only the digits 0 to 7, where each position is worth eight times the position to its right.

Hexadecimal

A base 16 number system that uses the digits 0 to 9 and the letters A to F, where A to F represent the values 10 to 15.

Decimal

The everyday base 10 number system using digits 0 to 9, used here as the common value that links octal and hex.

Nibble

A group of 4 bits. One nibble maps to exactly one hexadecimal digit, from 0 to F.

Place value

The amount a digit is worth because of its position. In octal the place values are the powers of 8: 1, 8, 64, 512 and so on.

Radix

Another word for the base of a number system, such as 8 for octal or 16 for hexadecimal.

Frequently asked questions