Octal to Decimal Converter

To use octal to decimal converter, type any octal value e.g. "176" and click on the Convert button and you will get the decimal value of "126" on right side. The detailed explanation of how to convert the octal number to decimal is given below.

Octal to Decimal Conversion:

• Octal Numeral System
• Decimal Numeral System
• How to Convert Octal to Decimal
• How to Convert Fractional Octal to Decimal
• Octal to Decimal Examples
• FAQs (Octal to Decimal Conversion)
• Octal to Decimal Table

Octal Numeral System

The octal number system is a type of positional numeral system that works on base 8, meaning it uses eight distinct digits to represent numbers.

The valid digits in the octal system are:

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

Unlike the decimal system, the digits 8 and 9 do not exist in the octal format. Each position in an octal number carries a value that is calculated using powers of 8. For example, the rightmost position represents 8⁰, the next one to the left represents 8¹, and so on.

This makes the octal system especially useful in computer science, digital electronics, and low-level programming, where data is often grouped in multiples of 3 binary bits.

Example:

Octal number "7654.73" expressed as powers of 8:

(7654.73)₈ = (7 × 8³) + (6 × 8²) + (5 × 8¹) + (4 × 8⁰) + (7 × 8^-1) + (3 × 8^-2) = 3584 + 384 + 40 + 4 + 0.875 + 0.046875 = (4012.921875)₁₀

Decimal Numeral System

The decimal number system is a positional numeral system with a base of 10.

It uses ten unique digits:

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

When these digits are combined, they form any number. The value of each digit depends on its position in the number, and every position is represented as a power of 10.

Example:

Decimal number "8975.987" can be broken down as power of 10:

Total = (8 × 10³) + (9 × 10²) + (7 × 10¹) + (5 × 10⁰) + (9 × 10^-1) + (8 × 10^-2) + (7 × 10^-3) = 8000 + 900 + 70 + 5 + 0.9 + 0.08 + 0.007 = 8975.987

How to Convert Octal to Decimal

Octal numbers are the base-8 numbers and every octal digit can be represented as powers to the base-8. For example, every digit of the octal number "237" represent the power to the base-8.

• Octal digit"7" is in 8⁰ position.

• Octal digit"3" is in 8¹ position.

• Octal digit"2" is in 8² position.

Considering the above scenario any octal value can be converted to decimal by using three steps below. Octal digits (0 to 7) represents the same decimal values from (0 to 7).

• Step-1: Separate the octal digits.

• Step-2: Multiply every octal digit to the corresponding power to the base-8.

• Step-3: Sum all the multipliers to get the final decimal value of octal number.

How to Convert Fractional Octal to Decimal

We can convert the fractional octal value using the following steps:

• Step-1: Get the fractional value of octal.

• Step-2: The fractional digits are multiplied with the negative powers of 8.

• Step-3: Sum all the products to get the final fractional value.

Octal to Decimal Examples

Example 1: Convert octal value "741" to decimal.

Example 2: Convert octal value "7757" to decimal.

Example 3: Convert octal value "6735" to decimal.

Example 4: Convert octal value "2775.77" to decimal.

Example 5: Convert octal value "3673.56" to decimal.

Frequently Ask Questions: Octal to Decimal Conversion

Q1: Assume that embedded controller register address is signed octal value 601, what is the decimal equivalent?

As each octal digit can be interpreted with 3 bits, 6 = 110, 0 = 000, 1 = 001, in binary (110000001)₂

In sign-magnitude, the MSB is a sign-bit (leftmost most). MSB = 1 which means the number is negative, now convert the remaining bits to decimal:

(10000001)₂ = (129)₁₀. As it is signed value, so decimal value = -129

For the signed values, always check the MSB for sign, and take the magnitude value from the remaining bits.

Q2: Convert (7635.47)₈ to a decimal value?

Powers of 8 are:

• 8³ = 512

• 8² = 64

• 8¹ = 8

• 8⁰ = 1

• 8^-1 = 1/8 = 0.125

• 8^-2 = 1/8² = 0.015625

Multiply all the octal digits with their position and add all the products to get the final decimal value:

Decimal value: (7 × 8³) + (6 × 8²) + (3 × 8¹) + (5 × 8⁰) + (4 × 8^-1) + (7 × 8^-2) = (7 × 512) + (6 × 64) + (3 × 8) + (5 × 1) + (4 × 0.125) + (7 × 0.015625) = 3584 + 384 + 24 + 5 + 0.5 + 0.109375 = (3997.609375)₁₀

Q3: Convert (1.1)₈ to a decimal value?

(1.1)₈ = (1 × 8⁰) + (1 × 8^-1) = 1 + 0.125 = (1.125)₁₀ (in decimal)

Q4: A 9-bit signed octal value is given as (377)₈, how to convert it to decimal?

Let's check the MSB to check whether the number is positive or negative, 3 = 011, 7 = 111, 7 = 111, binary is (011111111)₂

As MSB is 0 so the value is positive, Magnitude of the value is (11111111)₂ = (255)₈, you can also check Binary to Decimal Converter for in depth understanding.

Decimal value is: 255

Q5: Conside that Unix file permission value is octal 755, convert it to decimal?

Unix permission 755 represents read/write/execute per owner/group/other, let's convert it to decimal:

(755)₈ = (7 × 8²) + (5 × 8¹) + (5 × 8⁰) = (7 × 64) + (5 × 8) + (5 × 1) = 448 + 40 + 5 = 493 in decimal.

Q6: Can octal numbers be negative and how to convert them to decimal?

Yes, octal numbers can have a negative sign and you can simply apply the negative sign after converting it to decimal:

(-127)₈ = -(1 × 8²) + (2 × 8¹) + (7 × 8⁰) = -(64 + 16 + 7) = -87 in decimal.

Octal to Decimal Conversion Table

by Wasim Khan and it was last modified on August 27, 2025

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