How do I convert Decimal to Octal on this page?

Enter a Decimal value in the converter input and the Octal result is generated automatically with matching pair rules.

Are fractional values supported here?

Yes for numeric bases. You can enter one radix point and fractional digits when the selected format is numeric.

Can I move to other base-pair converters quickly?

Yes. Related pair links are listed below the converter for fast switching.

Decimal to Octal Converter

developer · number system

Convert Decimal to Octal 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

Input (Decimal)

From: Decimal

Result (Octal)

To: Octal

Formulas

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

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.

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.

How to convert decimal to octal

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

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

Dev note

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

Step 2 — Repeated Division by 8

Repeated division by 8: same idea as binary, but divide by 8 each time. Remainders are octal digits (0–7), read bottom-up.

Fractional decimal values: convert the whole part with repeated division, then multiply the fractional part by the target base over and over; each integer you get is the next digit after the radix point (same idea the calculator shows in Formulas).

Step 3 — Worked examples

Two practice values in Decimal, converted to Octal 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

"26" (Decimal) → Octal.

From decimal

N₁₀ = 26

Whole part — repeated division:
26 ÷ 8 = 3  R 2
3 ÷ 8 = 0  R 3

Read remainders bottom → top → 32

→ tool: 032

Verify: "26" → 032

Example 2

"100" (Decimal) → Octal.

From decimal

N₁₀ = 100

Whole part — repeated division:
100 ÷ 8 = 12  R 4
12 ÷ 8 = 1  R 4
1 ÷ 8 = 0  R 1

Read remainders bottom → top → 144

→ tool: 0144

Verify: "100" → 0144

Example 3

"10.625" (Decimal) → Octal.

From decimal

N₁₀ = 10.625

Whole part — repeated division:
10 ÷ 8 = 1  R 2
1 ÷ 8 = 0  R 1

Read remainders bottom → top → 12

Fractional part — multiply by 8, integer of each product = next digit after .
  0.625×8 = 5  →  5
Digits after . (in order): .5

→ tool: 012.5

Verify: "10.625" → 012.5

Summary

To convert Decimal to Octal, the tool first parses your input strictly as decimal, 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 octal 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

Decimal, Octal, 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

Decimal (input)	Octal (output)
0	0
1	01
2	02
3	03
4	04
5	05
6	06
7	07
8	010
9	011
10	012
15	017
16	020

Decimal (input)	Octal (output)
11	013
32	040
64	0100
128	0200
256	0400
512	01000
1024	02000
2048	04000
4096	010000
8192	020000
16384	040000
32768	0100000
65535	0177777

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.

← Number System Converter (all formats)Developer Tools home