Decimal to Octal Converter

How to Use Decimal to Octal Converter

1. Enter Your Number: Type or paste your decimal number (like 10 or -8) into the “Enter Decimal Number” box.
2. Or, Upload a File: Got a whole list of numbers? No problem. You can also upload a .txt file containing one number per line.
3. Click “Convert to Octal”: Hit the button, and… that’s it!
4. Get Your Result: Your octal (base-8) equivalent will instantly appear in the “Octal Output” box.
5. Save Your Work: You can then “Copy to Clipboard” or “Download .txt” to save your converted number. Need to start over? Just hit “Clear Text.”

Understanding Decimal and Octal

It sounds complex, but it’s just two different ways of counting. Let’s break it down.

What is the Decimal (Base-10) System?

This is the number system we all know and love. It’s called “base-10” because it uses ten digits:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Every position in a number is a power of 10. For example, the number 157 really means:

• (1 × 100) + (5 × 10) + (7 × 1)

What is the Octal (Base-8) System?

The octal system, as you might guess, is “base-8.” This means it only uses eight digits:

0, 1, 2, 3, 4, 5, 6, 7

That’s right—you’ll never see an 8 or 9 in an octal number!

In this system, each position is a power of 8. For example, the octal number 235 means:

• (2 × 64) + (3 × 8) + (5 × 1) = 128 + 24 + 5 = 157 in decimal.

Why Would Anyone Use Octal?

It seems a bit strange, right? Octal’s main advantage is that it’s a fantastic shorthand for binary (base-2), which is the language computers actually speak.

• Binary is Long: The decimal number 157 is 10011101 in binary. That’s hard to read!
• Octal is Short: The same number is just 235 in octal.

Because 8 is a power of 2 ($2^3$), converting between binary and octal is super easy for computers. Octal is often used in file permissions on Linux and macOS (you may have seen commands like chmod 755) and in some older computer systems.

How to Convert Decimal to Octal (The Manual Way)

Want to know what our tool is doing behind the scenes? It’s using a simple “division and remainder” method.

Let’s try an example.

Example 1: Convert Decimal 42 to Octal

1. Take your decimal number, 42.
2. Divide it by 8: 42 / 8 = 5 with a remainder of 2.
3. Take the quotient (5) and divide it by 8: 5 / 8 = 0 with a remainder of 5.
4. Stop, because your quotient is now 0.
5. Now, read the remainders from the bottom up: 5, then 2.

So, Decimal 42 = Octal 52.

Example 2: Convert Decimal 160 to Octal

1. 160 / 8 = 20 with a remainder of 0.
2. 20 / 8 = 2 with a remainder of 4.
3. 2 / 8 = 0 with a remainder of 2.
4. Read the remainders from the bottom up: 2, 4, 0.

So, Decimal 160 = Octal 240.

Or… you could just use our tool and get the answer in a fraction of a second! 😉

Decimal to Octal Conversion Table

For quick reference, here are the first 16 decimal numbers and their octal equivalents.

Decimal (Base-10)	Octal (Base-8)
0	0
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	10
9	11
10	12
11	13
12	14
13	15
14	16
15	17
16	20

Frequently Asked Questions (FAQs)

Q: Is octal the same as hexadecimal?

A: No! They’re both used in computing, but they’re different. Octal is base-8 (using digits 0-7), while Hexadecimal is base-16 (using digits 0-9 and letters A-F).

Q: How do you write the octal number 8?

A: That’s a trick question! The digit “8” doesn’t exist in octal. The decimal number 8 is written as “10” in octal, which means (1 × 8) + (0 × 1).

Q: Can this tool convert octal back to decimal?

A: This tool is specifically designed for Decimal to Octal conversion. (If you have a separate tool for the other way, you can link it here!)

Q: Can this converter handle negative numbers?

A: Yes! As you can see from the example placeholder (e.g. 10 or -8), our tool correctly converts negative decimal numbers into their corresponding negative octal representation.