This calculator rewrites a nonnegative decimal integer in octal, or base 8. Octal uses only the digits 0 through 7. The quantity remains the same while its place-value notation changes.
Octal has a close relationship with binary because one octal digit represents three bits. It appears in subjects such as Unix file permissions, older computer documentation and compact binary grouping.
The result has no leading prefix. Some programming languages or documents mark octal values specially, but this page returns the digits alone. It also removes unnecessary leading zeros.
An octal numeral dₙ…d₁d₀ has decimal value:
value = Σ(dᵢ × 8ⁱ)
For a manual conversion, repeatedly divide the decimal integer by 8. Each remainder is an octal digit from 0 through 7. Read the remainders from last to first. The place values from right to left are 1, 8, 64, 512 and 4096.
Because every remainder is less than eight, the digits 8 and 9 can never appear in a valid octal result.
| Term | Meaning | Example |
|---|---|---|
| Decimal input | A nonnegative base-10 integer | 83 |
| Base | The target system’s number of digit values | 8 |
| Remainder | A digit from 0 through 7 found by division | 3 |
| Octal output | The same integer expressed in base 8 | 123 |
Convert decimal 83. First, 83 ÷ 8 = 10 remainder 3. Next, 10 ÷ 8 = 1 remainder 2. Finally, 1 ÷ 8 = 0 remainder 1. Reading the remainders from last to first gives 123.
Check by expanding: 1×8² + 2×8¹ + 3×8⁰ = 64 + 16 + 3 = 83. At a base boundary, decimal 7 is octal 7, decimal 8 is octal 10, and decimal 64 is octal 100.
The returned numeral must be read with base 8 place values. Octal 123 is not decimal one hundred twenty-three; it is decimal eighty-three. Label the base when the audience could misunderstand it.
Leading zeros do not change the mathematical value, but they may be meaningful formatting in a system that expects a fixed width. The calculator supplies a minimal representation.
In Unix permission notation, a three-digit value is commonly interpreted digit by digit as owner, group and other permission bits. This converter only changes the number base; it does not explain whether a permission setting is secure or appropriate.
Replace each octal digit with three bits to verify a conversion. Octal 123 becomes 001 010 011. Ignoring the leading zeros gives binary 1010011, whose decimal place values total 64+16+2+1=83. The reverse also works: group a binary numeral into sets of three from the right, padding the left group with zeros if needed, then replace each group with one octal digit.
Different languages mark octal literals differently. A leading zero has historically served as a marker in some languages, while others use forms such as 0o123. Copying bare digits into code without checking that language’s notation can change how they are interpreted. This calculator deliberately returns only the numeral. Add a prefix or fixed width only when the destination format requires it.
Octal also needs enough digits for the value. Three octal digits cover values through 777, which is decimal 511. A larger decimal input can validly produce four or more octal digits.
For a manual check, label the positions 1, 8, 64, 512 and so on from right to left. Multiply each digit by its position and add. This both recovers the decimal input and reveals any invalid digit. Keep the base label when copying the result because a string such as 100 has different values in bases 8 and 10.
Octal 10 has one group of eight and zero ones. It plays the same positional role that decimal 10 plays after decimal 9.
No. Base 8 has eight digit values, 0 through 7. Reaching eight carries one into the next place.
No. This page accepts nonnegative integers. Signed machine encodings require a word size and representation that the form does not ask for.
Each octal digit corresponds to three bits: 0 is 000 and 7 is 111. Grouping binary digits in threes provides a quick binary-to-octal conversion.
They do not change the numerical value. They can matter as formatting or as a notation marker in a particular programming context.
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