Octal to Decimal Converter Online

What is the octal to decimal converter?

An octal to decimal converter is a tool that turns a base 8 number into its base 10 equivalent. The octal numbering system uses 8 symbols, 0 to 7, to represent numbers, while the decimal system uses 10 symbols, 0 to 9. The converter reads each octal digit and returns the matching decimal value instantly.

It operates by converting each octal digit to its decimal equivalent based on its place value. The converter multiplies every digit by the matching power of 8, then sums the products to create the final decimal number. Because decimal numbers are more widely used and simpler for people to read than octal numbers, this conversion comes up constantly in programming and electronics.

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.

How to use the octal to decimal converter?

Converting an octal number takes a single click and nothing is installed or uploaded. Follow these steps:

• Enter the octal number: Type or paste a base 8 value, using only the digits 0 to 7, into the Octal field.
• Click Convert to Decimal: The converter multiplies each digit by its place value power of 8 and adds the results, entirely in your browser.
• Copy the result: The equivalent decimal number appears in the Decimal field, ready to use anywhere base 10 is expected.

How to convert octal to decimal manually?

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.

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

• Arrange the powers of 8: Since an octal number only uses digits from 0 to 7, label each digit with a power of 8, starting from 8⁰ at the rightmost digit.
• Evaluate each power: Work out all the power of 8 values and write them under each digit of the octal number.
• Multiply each digit: Once the place values are known, multiply every octal digit by its power of 8.
• Add the products: The final step is to add the product of all the numbers to obtain the decimal number.

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.

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.

Convert 127.2 fractional octal to decimal

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.

• 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.