Octal To Decimal and Decimal To Octal Converter

Powerful Octal & Decimal Converter

Quickly convert numbers between the octal (base-8) and decimal (base-10) systems. Simple, fast, and free for developers, students, and engineers.

Get Started

Octal & Decimal Converter

Enter a number, select the conversion direction, and get the result instantly.

Octal To Decimal & Decimal To Octal

Input

Output

Why Use Our Converter?

Our tool provides an intuitive and fast way to convert numbers directly in your browser.

Bi-Directional

Effortlessly convert from Octal to Decimal and from Decimal to Octal with dedicated buttons.

Instant & Accurate

Calculations are performed instantly and accurately within your browser, ensuring speed and precision.

Privacy Focused

No uploads to servers. All conversions happen locally on your device, respecting your privacy.

How It Works

Converting your numbers is simple with our straightforward three-step process.

1. Enter Number

Type or paste the number you want to convert into the 'Input' text area on the left.

2. Choose Conversion

Click the appropriate button for the conversion you need: 'Octal to Decimal' or 'Decimal to Octal'.

3. Get Result

The result appears instantly in the 'Output' box. Use the 'Copy' button to save it to your clipboard.

A Guide to Decimal & Octal Number Systems

Understand the fundamentals of base-10 and base-8, and learn how conversions work behind the scenes.

What is a Number System?

A number system is a method of representing numbers using a set of symbols or digits. The 'base' or 'radix' of a number system defines how many unique digits it uses. The two systems this tool deals with are Decimal (base-10) and Octal (base-8).

The Decimal System (Base-10)

The decimal system is the one we use in our everyday lives. It is a base-10 system because it uses ten unique digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The position of a digit in a number determines its value. Each position represents a power of 10, increasing from right to left.

For example, the number 357 can be broken down as:

• (3 × 10²) + (5 × 10¹) + (7 × 10⁰)
• (3 × 100) + (5 × 10) + (7 × 1)
• 300 + 50 + 7 = 357

The Octal System (Base-8)

The octal system is a base-8 system, meaning it uses only eight unique digits: 0, 1, 2, 3, 4, 5, 6, 7. The digits 8 and 9 do not exist in the octal system. In computing, octal is sometimes used because it's a convenient way to represent binary (base-2) numbers, as one octal digit can represent exactly three binary digits.

Like in decimal, the position of a digit in an octal number determines its value, but here each position represents a power of 8.

How to Convert Octal to Decimal Manually

To convert an octal number to its decimal equivalent, you multiply each octal digit by 8 raised to the power of its position (starting from 0 on the right) and sum the results.

Let's convert the octal number (425)₈ to decimal:

• Identify the digits and their positions (from right to left, starting at 0):
  • 5 is at position 0
  • 2 is at position 1
  • 4 is at position 2
• Perform the calculation: (4 × 8²) + (2 × 8¹) + (5 × 8⁰)
• (4 × 64) + (2 × 8) + (5 × 1)
• 256 + 16 + 5 = (277)₁₀

So, the octal number 425 is equal to the decimal number 277. Our tool automates this process instantly.

How to Convert Decimal to Octal Manually

To convert a decimal number to octal, you use the method of repeated division. You continuously divide the decimal number by 8 and record the remainder at each step. You continue until the quotient is 0. The octal number is formed by reading the remainders in reverse order (from bottom to top).

Let's convert the decimal number (180)₁₀ to octal:

• 180 ÷ 8 = 22 with a remainder of 4
• 22 ÷ 8 = 2 with a remainder of 6
• 2 ÷ 8 = 0 with a remainder of 2

Now, read the remainders from the bottom up: 2, 6, 4. Therefore, the decimal number 180 is equal to the octal number (264)₈.

Why Use Octal?

While less common today than hexadecimal (base-16), the octal system served an important role in early computing. It provided a human-friendly shorthand for long binary numbers. Because 8 is a power of 2 (8 = 2³), converting between octal and binary is very simple. Each octal digit corresponds directly to a group of three binary digits.

• For example, octal (75)₈ is (111 101)₂ because 7 = 111 and 5 = 101.

This made it easier for programmers to read and write machine-level code before more advanced programming languages became widespread. It is still used in some systems, particularly for file permissions in Unix-like operating systems (e.g., the chmod command).

Frequently Asked Questions

Find answers to common questions about our Octal & Decimal Converter.

What is the Octal number system?

The octal number system is a base-8 system that uses digits from 0 to 7. It's often used in computing as a more compact representation of binary numbers than decimal.

What does this tool do?

This tool allows you to instantly convert numbers between the Octal (base-8) and Decimal (base-10) number systems directly in your browser.

Is my data stored anywhere?

No, all calculations happen locally in your browser. Your data is not sent to or stored on any server, ensuring your complete privacy.

How do I use the converter?

Simply enter a valid octal or decimal number into the 'Input' box. Then, click either the 'Octal to Decimal' or 'Decimal to Octal' button. The converted result will instantly appear in the 'Output' box.

What is an 'Invalid octal string' error?

This error occurs if you try to convert from octal to decimal and your input contains digits other than 0, 1, 2, 3, 4, 5, 6, or 7. The octal system only uses these eight digits.

Ready to Convert Your Numbers?

Start converting your numbers now. It's fast, free, and secure!

Convert Numbers Now