Convert octal numbers to decimal and decimal numbers to octal instantly. The tool validates your input, supports very large integers, and shows the conversion steps.
Choose the conversion direction, enter a whole number, and copy the result. Decimal uses digits 0–9. Octal uses only digits 0–7.
2181
The explanation updates as you type. For very large numbers, the tool keeps the result exact and summarizes the method instead of displaying an overly long step list.
BigInt for integer conversion, so large whole numbers are handled exactly instead of being rounded like regular floating-point numbers.
The decimal system is the everyday base-10 number system. It uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
The octal system is base-8. It uses only eight digits: 0, 1, 2, 3, 4, 5, 6, 7. Digits 8 and 9 are not valid in octal numbers.
Octal is useful when working with binary-related systems because one octal digit represents exactly three binary bits. For example, octal 7 equals binary 111.
To convert octal to decimal, multiply each digit by a power of 8. The rightmost digit uses 80, the next digit uses 81, then 82, and so on.
4205₈ = 4×8³ + 2×8² + 0×8¹ + 5×8⁰ = 2181₁₀
This means octal 4205 is equal to decimal 2181.
To convert decimal to octal, repeatedly divide the decimal number by 8 and record each remainder. The octal result is the remainders read from bottom to top.
2181 ÷ 8 = 272 remainder 5
272 ÷ 8 = 34 remainder 0
34 ÷ 8 = 4 remainder 2
4 ÷ 8 = 0 remainder 4
Result: 4205₈
So decimal 2181 converts to octal 4205.
Octal is less common than decimal or hexadecimal, but it still appears in technical contexts. One familiar example is Unix and Linux file permissions.
For example, permission value 755 is commonly used for executable files and directories. In decimal, octal 755 equals 493, but in permission notation it is read as three separate octal digits.