How to Convert Decimal to Octal: Step-by-Step Guide with Examples

The Repeated Division-by-8 Method, Step by Step

The idea behind the method is simple. Every time you divide a number by 8, the remainder tells you exactly one digit of the octal answer — specifically, the next digit from the right. Repeat the division on the quotient, and you peel off the octal digits one at a time until nothing is left. Here is the full procedure:

1. Write down the decimal number you want to convert.
2. Divide it by 8. Write down the quotient (the whole-number result) and the remainder. The remainder is always between 0 and 7, which is exactly the range of a single octal digit.
3. Divide the quotient by 8 again and record the new remainder.
4. Keep repeating — always dividing the previous quotient — until the quotient becomes 0.
5. Read the remainders from bottom to top (the last remainder you found is the first digit of the answer). That sequence of digits is the octal number.

That is genuinely all there is to it. The only two things to remember are: always divide by 8 (the base of the target system), and always read the remainders in reverse order. Everything else is ordinary short division.

Worked Example: Converting 365₁₀ to Octal

Let's apply the method to 365. We divide by 8 repeatedly and track each quotient and remainder:

Check the arithmetic at each step: 8 × 45 = 360, and 365 − 360 = 5, so the first remainder is 5. Next, 8 × 5 = 40, and 45 − 40 = 5, so the second remainder is 5. Finally, 5 is smaller than 8, so 5 ÷ 8 gives a quotient of 0 with a remainder of 5 — and reaching a quotient of 0 tells us to stop.

Now read the remainders from bottom to top: 5, 5, 5. So 365₁₀ = 555₈. Notice why the reading direction matters: the first remainder (the rightmost 5) is the least significant digit, and the last remainder is the most significant digit.

Second Example: Converting 144₁₀ to Octal

Now try 144, which produces a remainder of 0 along the way:

1. 144 ÷ 8 = 18, remainder 0 (because 8 × 18 = 144 exactly).
2. 18 ÷ 8 = 2, remainder 2 (8 × 2 = 16, and 18 − 16 = 2).
3. 2 ÷ 8 = 0, remainder 2. The quotient is now 0, so we stop.

Reading the remainders bottom-up — 2, 2, 0 — gives 144₁₀ = 220₈. A remainder of 0 is perfectly normal; zero is a valid octal digit and must be written down like any other. Dropping it would give 22₈, which is a completely different value (18 in decimal).

How to Verify Your Answer by Converting Back

Every octal-to-decimal check uses place values that are powers of 8: from the right, the positions are worth 1 (8⁰), 8 (8¹), 64 (8²), 512 (8³), and so on. To verify 555₈, multiply each digit by its place value and add:

5 × 64 + 5 × 8 + 5 × 1 = 320 + 40 + 5 = 365 ✓

The total matches the number we started with, so the conversion is correct. The same check confirms our second example: 220₈ = 2 × 64 + 2 × 8 + 0 × 1 = 128 + 16 + 0 = 144 ✓. This ten-second check catches almost every hand-conversion error, so it is worth doing every time — especially in exams, where no calculator is watching your work.

Quick Table: Decimal 0–15 in Octal

Small values come up constantly, so it helps to recognize them on sight. Notice the pattern: octal counts 0–7 exactly like decimal, then "rolls over" — 8 in decimal is written 10 in octal, just as 10 in decimal follows 9.

Common Mistakes to Avoid

Reading the remainders top-down

This is the single most common error. The remainders are produced from the least significant digit to the most significant, so they must be read in reverse — bottom to top. In our first example all three remainders happened to be 5, which hides the issue, but with 144 the remainders are produced in the order 0, 2, 2. Reading them top-down would give 022 (which is just 22₈ = 18₁₀), while the correct reading, bottom-up, gives 220₈ = 144₁₀. If your answer ever looks suspiciously small, you probably read the remainders in the wrong direction.

Forgetting the final step where the quotient becomes 0

Many people stop as soon as the quotient is smaller than 8 — for 365, that means stopping after 45 ÷ 8 with a quotient of 5. But that leftover quotient is itself a remainder waiting to happen: you must still divide it by 8 (5 ÷ 8 = 0, remainder 5) and include that final remainder as the leading digit. Stopping early silently drops the most significant digit of your answer.

Writing a digit of 8 or 9 in the result

Octal digits only run from 0 to 7. If an 8 or 9 appears anywhere in your answer, something went wrong — most likely a remainder was copied incorrectly, since a remainder from division by 8 can never be 8 or more.

Try It Yourself

Want to check your practice answers instantly, or convert a number too large for quick hand work? Use our free Decimal to Octal Converter — it shows the division steps as well as the result, so you can compare its method with yours. And when you are ready to see how octal compares with the other big base used in computing, read our companion guide: Octal vs Hexadecimal: Key Differences, Uses and Conversion Tips.

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