Octal Calculator

Octal Calculator: solve octal problems step-by-step. Clear formula, worked example, and FAQs included.

For nearby base-specific checks, compare the binary-to-decimal calculator and hexadecimal calculator while keeping the source and target bases visible.

Octal is base 8 and uses the digits 0 through 7. It is a compact bridge between binary and human-readable notation because each octal digit corresponds to three binary bits. Although hexadecimal is more common in many modern codebases, octal remains especially visible in Unix and Linux permission notation.

This page starts with an octal source and decimal target, then lets you choose any base from 2 through 36. The strict input rule is important for octal: 8 and 9 are not alternative spellings; they are invalid digits for base 8. Octal is useful for understanding file permissions such as 755, older computer architectures, bit-grouping exercises, and systems documentation that preserves a three-bit grouping.

Strict validation: A permissive parser might read 18 as just 1 and silently discard the invalid 8. This calculator rejects the entire input so the result cannot be mistaken for a valid conversion.

Enter a whole number using the symbols allowed by the selected source base. Spaces are ignored, but prefixes such as 0b and 0x are not part of the input.
Choose the source base from 2 through 36. The source base controls how every character is interpreted.
Choose the target base. The result updates immediately and uses 0–9 followed by uppercase A–Z for values from 10 onward.
Open the place-value expansion when converting from a non-decimal base and check each digit contribution.
Use “Swap bases and convert reverse” to send the result back through the opposite direction and confirm the original value.
If an error appears, correct the complete input rather than relying on a partial parse. A rejected digit means the numeral is not valid in the selected source base.

Octal Calculator formula and method

For a numeral with digits d and source base b, each position contributes d×bⁿ, where n starts at zero on the right. Add the contributions to obtain the quantity in decimal. The calculator uses exact integer arithmetic for this part, so long values are not first rounded to a JavaScript floating-point number.

The octal numeral 144 expands as 1×8² + 4×8¹ + 4×8⁰ = 64 + 32 + 4 = 100 decimal. The same value is 1100100 in binary and 64 in hexadecimal.

To convert a decimal integer into another base, divide by the target base and keep each remainder. Continue with the quotient until it reaches zero, then read the remainders from the last one back to the first. The quotient-and-remainder method is the reverse of positional expansion.

To reverse 100 decimal into octal, divide by 8: 100 gives remainder 4, then 12 gives remainder 4, then 1 gives remainder 1. Reading those remainders from the last division upward produces 144.

Binary, octal, and hexadecimal have convenient shortcuts: one hex digit corresponds to four binary bits, and one octal digit corresponds to three. Those shortcuts are checks on the same place-value mathematics, not different definitions of the number.

Reading your octal calculator result

The base is part of the answer

A result without its base is incomplete. For example, “10” means two in binary, eight in octal, ten in decimal, and sixteen in hexadecimal. Always copy the target base with the displayed digits when moving the value into code, a worksheet, a shell command, or technical documentation.

This page starts with an octal source and decimal target, then lets you choose any base from 2 through 36. The strict input rule is important for octal: 8 and 9 are not alternative spellings; they are invalid digits for base 8. The octal numeral 144 expands as 1×8² + 4×8¹ + 4×8⁰ = 64 + 32 + 4 = 100 decimal. The same value is 1100100 in binary and 64 in hexadecimal. The decimal value is shown as a reference, while the selected target-base result is the answer to the conversion you requested.

To reverse 100 decimal into octal, divide by 8: 100 gives remainder 4, then 12 gives remainder 4, then 1 gives remainder 1. Reading those remainders from the last division upward produces 144. If the reverse result differs, check the source and target selectors, the direction of the copied value, and whether a leading zero is meaningful for the format you are using.

Math tips and best practices

Read the rightmost octal digit as 8⁰, or 1.
Group binary digits in threes when checking an octal result.
For permissions, remember that 4 is read, 2 is write, and 1 is execute.
Preserve leading zeroes when a value is being used as a fixed-width permission or identifier.
Use the expansion to verify a manual result before applying a permission value to a real system.

Each octal digit covers three binary bits.
Octal 10 equals decimal 8, while hexadecimal 10 equals decimal 16.
Permission digit 7 combines 4 + 2 + 1, representing all three common permission bits.
Octal 377 equals decimal 255, the largest unsigned byte.

Common mistakes to avoid

Entering 8 or 9 and assuming the parser will correct it.
Confusing octal 10 with decimal 10.
Reading 755 as a decimal number instead of three permission groups.
Changing a leading zero that is part of a system’s notation.

Number-base conversion is educational mathematical information, not a security guarantee or a substitute for testing the syntax required by a particular programming language, operating system, protocol, or file format. Integer conversions on this page are exact when the input is valid. Check the receiving system's documentation for signed interpretation, fixed-width padding, prefixes, overflow rules, and permission semantics before using a result in a consequential technical setting.