Decimal to Octal Calculator
Convert a decimal number to octal.
Results update as you type.
How it works
Octal is the base-8 number system, and this calculator converts a decimal number into octal. You enter a non-negative whole number in decimal, and it returns the octal equivalent using digits 0 through 7. The conversion uses repeated division by eight: divide the number by eight, record the remainder as the next octal digit, and repeat with the quotient until it reaches zero; reading the remainders in reverse gives the octal number. Equivalently, octal uses place values that are powers of eight. For example, decimal 15 becomes 17 in octal, since fifteen is one eight plus seven. Octal was historically significant in computing because each octal digit represents exactly three binary bits, making it a compact way to write binary values on systems with word sizes divisible by three. Today its most common appearance is in Unix and Linux file permissions, where a decimal grouping of read, write, and execute bits is expressed in octal, such as 755 or 644. Converting decimal to octal is useful for computer science students, system administrators setting file permissions, and anyone working with legacy systems. This calculator handles non-negative whole numbers. Enter a decimal number to convert it to octal.
Repeatedly divide by 8, reading remainders bottom-up
A decimal number is converted to octal by repeatedly dividing by eight and recording each remainder, which is a digit from 0 to 7. Reading the remainders from the last division to the first gives the octal representation. Each digit corresponds to a place value that is a power of eight.
Source:Number systems
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Worked example
How to use this calculator
- 1
Enter your values
Enter decimal number.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Octal value updates instantly as you type — no button to press.
Frequently asked questions
How do you convert decimal to octal?
Repeatedly divide the decimal number by eight, recording each remainder, then read the remainders from bottom to top. Decimal 15 gives 17 in octal. Each remainder is a digit from 0 to 7. The calculator produces the octal result instantly from the decimal number you enter.
What is octal used for?
Octal's most common modern use is in Unix and Linux file permissions, where read, write, and execute settings are grouped into octal digits like 755 or 644. It was also historically used in computing because each octal digit maps to three binary bits, giving a compact way to represent binary data.
Why does each octal digit equal three bits?
Because eight equals two cubed, each octal digit represents exactly three binary digits, from 000 to 111. This clean grouping made octal a handy shorthand for binary in early computers, letting programmers write long binary numbers more compactly, three bits at a time, before hexadecimal became more common.
How do octal file permissions work?
In Unix-like systems, each file permission set for owner, group, and others is a sum of read (4), write (2), and execute (1). So read-write-execute is 7, read-execute is 5, and read-only is 4. Combining three such digits gives codes like 755, an octal representation of the permission bits.
Does this handle fractional numbers?
This calculator converts non-negative whole numbers to octal. Fractional decimal values would require converting the fractional part separately by repeatedly multiplying by eight, producing octal digits after a point. For whole numbers, which cover the typical uses like file permissions and integer values, this calculator gives the complete octal representation.