Hexadecimal to Octal Converter

Enter a hexadecimal number to convert it to octal.

By

Joe Sexton

Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications.

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How to Convert Hex to Octal

The first step to converting hex to octal is to convert hex to decimal. Then, you can convert from decimal to octal.

Step One: Convert Hex to Decimal

To convert a number from hex to decimal, multiply each digit in the hex number from the rightmost number to the left by 16 to the power of n, where n is the distance from the right.

When reading the hex number from right to left, the digit furthest to the right is equal to the digit times 16⁰. The digit one position in from the right is equal to the digit times 16¹.

decimal number₁₀ = (d₀ × 16⁰) + (d₁ × 16¹) + … + (d_{n – 1} × 16^{n – 1})

In the formula above, d₀ is the hex digit furthest to the right, d₁ is the digit one position from the right, and d_{n – 1} is the digit furthest to the left.

Step Two: Convert Decimal to Octal

To convert from decimal to octal, divide the decimal number by 8 using long division. There should be a remainder of 0 through 7; write that to the side of the division problem.

Take the result of the first division problem and divide that by 8 again. Like before, there should be a remainder, which you should write to the side of the problem.

Continue this process until the result is 0.

The remainders that you wrote to the side of the division problems are the resulting octal number. The number should be read from the bottom to the top since the least significant digit will be at the top, and the most significant digit will be at the bottom.

Hex to Octal Conversion Table