Octal to Decimal Converter Online

An Octal to Decimal Converter is a tool to convert octal numbers into decimal representations. The octal numbering system uses 8 symbols, ranging from 0 to 7, to represent the numbers. In contrast, the decimal numbering system uses 10 symbols, from 0 to 9, to represent numbers. Because decimal numbers are more widely used and simpler for people to understand than octal numbers, the conversion from octal to decimal is crucial.

The first step in using octal to decimal converter is entering the octal number that needs to be converted into decimal format. The outcome will be presented in decimal form. It operates by converting each octal digit to its decimal equivalent. The final decimal representation of the octal number is then created by combining the decimal equivalents. Each octal digit is converted to its decimal equivalent using a lookup table. The converter then sums the decimal equivalents to create the final decimal number.

Working with other number systems? You can also try the Decimal to Octal, Octal to Binary, Binary to Decimal, and Hex to Decimal converters from TestMu AI.

Octal to Decimal Formula

To convert an octal (base 8) number to decimal (base 10), write it in expanded form: multiply each digit by 8 raised to the power of its position, counting from 0 at the rightmost digit, and add the results. The general formula is:

Here d₀ is the rightmost digit and d_n is the leftmost digit. Since 8⁰ = 1, 8¹ = 8, and 8² = 64, each place value is a rising power of 8. The negative powers of 8 are used only for digits written after the octal point.

What is the Octal number system?

An octal number system, also known as base 8, is a numbering system that uses 8 symbols, 0 to 7, to represent numbers. Its values are commonly converted to the base 10 decimal system, which uses the digits 0 to 9 and is easier for most people to read.

Why is it important to convert Octal to Decimal?

It is important to convert Octal to Decimal because decimal numbers are more commonly used and easier for people to understand compared to octal numbers.

How to convert an octal number to a decimal?

Here are the steps to convert a number from octal to decimal:

Step 1: Since an octal number only uses digits from 0 to 7, arrange the number with the power of 8.
Step 2: Evaluate all the power of 8 values and write each value of an octal number.
Step 3: Once the value is obtained, we multiply each number.
Step 4: Final step is to add the product of all the numbers to obtain the decimal number.

How do I convert octal to decimal by hand?

To convert an octal number to decimal by hand, multiply each octal digit by 8 raised to the power of its position, counting from 0 at the rightmost digit, and then add the results together. For example, to convert the octal number 157, calculate (1 x 8^2) + (5 x 8^1) + (7 x 8^0), which equals 64 + 40 + 7, giving a decimal value of 111.

Is it safe to convert octal numbers using this online tool?

Yes. This octal to decimal converter runs entirely in your browser, so the octal number you enter is processed on your own device and is never sent to or stored on any TestMu AI server. Because your data never leaves your machine, you can convert sensitive or internal values with confidence.

What is the difference between the octal and decimal number systems?

The octal number system is base-8 and uses only the digits 0 to 7, while the decimal number system is base-10 and uses the digits 0 to 9. In octal, each place value is a power of 8, whereas in decimal, each place value is a power of 10, so the same sequence of digits represents different quantities in each system.

Octal to Decimal Conversion Table

Use this quick-reference table to look up common octal to decimal values without any calculation.

Step-by-Step Octal to Decimal Conversion Examples

Each example below is worked out in expanded form, multiplying every digit by a power of 8 and adding the results.

Convert 345 octal to decimal

(3 × 8²) + (4 × 8¹) + (5 × 8⁰) = 192 + 32 + 5 = 229. So 345 in octal equals 229 in decimal.

Convert 275 octal to decimal

(2 × 8²) + (7 × 8¹) + (5 × 8⁰) = 128 + 56 + 5 = 189. So 275 in octal equals 189 in decimal.

Convert 120 octal to decimal

(1 × 8²) + (2 × 8¹) + (0 × 8⁰) = 64 + 16 + 0 = 80. So 120 in octal equals 80 in decimal.

How to Convert Fractional Octal Numbers (with a Decimal Point)

An octal number can also have a fractional part - the digits written to the right of the octal point. To convert them, multiply each fractional digit by a negative power of 8 (8^-1, 8^-2, and so on) and add the results to the whole-number part.

Example - convert 127.2 octal to decimal:

• Whole part: (1 × 8²) + (2 × 8¹) + (7 × 8⁰) = 64 + 16 + 7 = 87.
• Fractional part: 2 × 8^-1 = 2 ÷ 8 = 0.25.
• Add them together: 87 + 0.25 = 87.25.

So 127.2 in octal equals 87.25 in decimal. The converter above is designed for whole octal numbers, so values with an octal point are best worked out using this expanded-form method.