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Binary to Octal Converter

Enter a binary number to convert it to octal and decimal.

How it is calculated

Enter a string of 0s and 1s. The tool strips spaces, drops leading zeros, reads the bits as a base-2 integer and writes it in base 8 and base 10. The decimal value is d = Σ bi · 2i, where bi is the bit at position i counted from the right (the last digit is position 0). The octal digits come from grouping the bits in threes from the right, since 8 = 23: each 3-bit group is one digit from 0 to 7. Only the characters 0 and 1 are accepted, so a prefix like 0b, a minus sign or a binary point gives no result. The input may hold up to 63 significant bits (leading zeros do not count), which keeps the decimal value exact; 64 significant bits is rejected.

Worked example

Convert 111101101. Group from the right in threes: 111 | 101 | 101. Each group is a digit: 111 = 7, 101 = 5, 101 = 5, so the octal result is 755. For the decimal value add the powers of two for the 1 bits: 256 + 128 + 64 + 32 + 8 + 4 + 1 = 493. Check from the octal side: 7 × 64 + 5 × 8 + 5 = 448 + 40 + 5 = 493. The tool shows octal 755 and decimal 493.

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Common mistakes

  • Grouping from the left instead of the right. Always start at the least significant bit; only the leftmost group may be short and is padded with zeros.
  • Typing a prefix such as 0b or digits other than 0 and 1 (for example 1012); the tool returns nothing for these, so enter the bare bits.
  • Entering a binary fraction like 101.1 and expecting a fractional octal. The tool handles whole numbers only.
  • Reading the output as a decimal number when it is octal (755 octal is 493 decimal, not 755), or assuming leading zeros change the value; they do not.
  • Pasting more than 63 significant bits and expecting an answer; such long strings are rejected.

About this calculator

Because 8 is a power of 2 (2³), converting binary to octal doesn't require going through decimal — it's a direct grouping trick: starting from the right, split the binary digits into groups of three, padding the leftmost group with zeros if needed, then convert each group independently to its single octal digit (000–111 maps to 0–7).

This calculator performs that grouping and also shows the decimal equivalent. Octal was historically popular in computing (e.g., Unix file permissions like 755) because it compresses long binary strings into a shorter, still bit-aligned form that's easier for humans to read than raw binary.

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Comments (1)

  • Editorial team

    Octal is still worth knowing for Unix file permissions, where each digit is one group of three bits for owner, group and others. Enter 111101101 and the tool returns 755, with decimal 493. Group your bits in threes from the right to check any answer by eye. Input must be plain 0s and 1s of up to 63 significant bits, with no prefix. Where do you run into octal?

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