Enter any decimal number (base 10) into the Decimal to Octal Converter and get its octal equivalent (base 8) immediately. The tool shows you the octal result along with the step-by-step division process used to reach it — perfect for students, programmers, and anyone working with number systems.
Octal Result
--
Binary Equivalent
--
Hexadecimal Equivalent
--
Conversion Steps
--
A decimal to octal converter is a tool that transforms a number from base 10 (the standard number system using digits 0–9) into base 8 (octal, using digits 0–7). It automates the repeated division-by-8 process, saving you time and reducing errors.
To convert decimal to octal, repeatedly divide the decimal number by 8 and record the remainder at each step. Once the quotient reaches 0, read the remainders from bottom to top — that sequence is your octal number. For example, 255 ÷ 8 = 31 R 7, 31 ÷ 8 = 3 R 7, 3 ÷ 8 = 0 R 3, giving octal 377.
The octal number system is a base-8 positional numeral system that uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. Each digit position represents a power of 8. It is commonly used in computing because one octal digit neatly represents exactly three binary bits.
Octal is used in computing primarily because one octal digit corresponds to exactly three binary bits. This makes it a compact and readable shorthand for binary values, especially useful in older systems and file permission notation (e.g., Unix/Linux chmod values like 755).
This converter can handle very large non-negative integers — up to 999,999,999,999 in decimal. For typical computing tasks, values up to 9,223,372,036,854,775,807 (the maximum 64-bit signed integer) are generally supported by JavaScript's number handling.
This converter focuses on non-negative integers. Fractional decimal numbers require a separate process — multiply the fractional part by 8 repeatedly and record the integer parts — which is a more advanced conversion. For most computing use cases, integer conversion is what you need.
The decimal number 8 is represented as 10 in octal. This is because 8 equals 1×8¹ + 0×8⁰, so the octal representation is '10'. Similarly, decimal 64 equals 100 in octal.
Octal (base 8) uses digits 0–7 and each digit represents three binary bits. Hexadecimal (base 16) uses digits 0–9 and letters A–F, with each digit representing four binary bits. Hexadecimal is more common in modern computing, while octal was popular in older systems and is still used for Unix file permissions.