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Octal to Decimal Converter

developer · number system

Convert Octal to Decimal with a fixed input and output format, step-by-step formulas under the result, and reference tables. Parsing matches the main hub (0b, 0x, leading 0 for octal; one optional . for fractional digits on numeric bases; single character for character mode).

Calculator

From: Octal

To: Decimal

Formulas

Enter a value → place-value expansion + division chain.

About Octal

Octal (base 8) uses digits 0–7. A leading 0 denotes octal in this converter (e.g. 0777). One radix point is allowed; fractional places use 8⁻¹, 8⁻², …. Grouping binary digits in threes maps cleanly to octal, which is why Unix file permissions often use it.

About Decimal

Decimal (base 10) uses digits 0–9; no prefix is required. A single . may separate the fractional part (10⁻¹, 10⁻², …). Values are parsed to a number and re-encoded into the target format; very long fractions are limited by floating-point precision.

How to convert octal to decimal

Three steps: symbols → the right math move for this pair → worked examples you can copy on paper. Numeric bases (binary, octal, decimal, hex) also support one radix point and digits after it; character mode stays a single code unit.

Step 1 — Identify the symbols

Input (Octal): Each digit is 0–7 (eight possibilities per position).

Output (Decimal): Ordinary digits 0–9; each position is a power of ten.

Dev note
  • A leading 0 is often used to mark octal (e.g. 012).

Step 2 — Octal Place Weights

Number positions from the right, starting at 0. At each position, multiply that digit by 8 raised to the position index, then add every term. The total is your decimal number.

Digits after the dot: use negative powers of 8 (8−1, 8−2, …). Each place is still (digit × weight); add the fractional side to the whole side.

Step 3 — Worked examples

Two practice values in Octal, converted to Decimal using the same rules as Step 2. Example 3 uses a fractional part (digits after the radix point); the hub and pair calculators accept a single . on binary, octal, decimal, and hex inputs.

Example 1

"12" (Octal) → Decimal.

Toward decimal

Octal "12"
= 1×8¹ + 2×8⁰
= 8 + 2
= 10  (decimal)

Verify: "12" → 10

Example 2

"377" (Octal) → Decimal.

Toward decimal

Octal "377"
= 3×8² + 7×8¹ + 7×8⁰
= 192 + 56 + 7
= 255  (decimal)

Verify: "377" → 255

Example 3

"12.4" (Octal) → Decimal.

Toward decimal

Octal "12.4"
Left of . : 1×8¹ + 2×8⁰ = 10
Right of .: 4×8^-1 = 0.5
= 10.5  (decimal)

Verify: "12.4" → 10.5

Summary

To convert Octal to Decimal, the tool first parses your input strictly as octal, producing a decimal value. For binary, octal, decimal, and hex, you may include one radix point and fractional digits; character input remains a single code unit with no dot. That value is formatted as decimal using the same rules as the main Number System Converter (prefixes 0b, 0, 0x where applicable; character output uses symbolic names for common controls and requires a whole-number code point). Long fractional expansions are truncated to a fixed digit cap; ordinary floating-point rounding may appear in extreme cases.

Relationship context

Octal, Decimal, and the other numeric bases on this site all describe the same numeric value; only the radix changes (including optional fractional digits after one dot). Moving between them is equivalent to changing how the value is written, not to scaling or unit conversion. Binary, octal, and hex align with bit boundaries (powers of two), while decimal is optimized for human arithmetic.

Conversion tables

Octal (input)Decimal (output)
00
011
022
033
044
055
066
077
0108
0119
01210
01715
02016
Octal (input)Decimal (output)
01311
04032
010064
0200128
0400256
01000512
020001024
040002048
0100004096
0200008192
04000016384
010000032768
017777765535

More number system pairs

Other fixed input/output converters use the same parsing rules as the hub. Open any pair for the same calculator layout and reference tables.

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