Octal to Decimal Converter

Going the other way? Convert decimal back to octal →

How do you convert octal to decimal?

Octal to decimal conversion gives each digit the weight of its position, multiplies the digit by that weight, and adds the products together.

1. Number the positions from the right, starting at 0.
2. Give each position the weight 8ⁿ, so the rightmost digit is worth 1.
3. Multiply every digit by its weight and add the products.
4. The total is the decimal value: 234 = 156.

Octal to Decimal Conversion Table

One hexadecimal digit equals exactly 4 bits (16 = 2⁴); one octal digit equals exactly 3 bits (8 = 2³). Hex and octal are therefore converted by grouping bits, and hex ↔ octal passes through binary. That is the whole method, so the table below is the only thing you need: every group of 3 bits has exactly one octal digit, and the mapping never changes. Binary writes values on the digit set 0, 1 with each place worth 2ⁿ, and a value marked 0b is binary; octal values are marked 0o.

Each base is defined by three things: which digits it uses, how a value is marked, and what each position is worth.

Worked Example: 234 to Decimal

One value, converted the long way so the working is visible. This is the same grid the converter shows when you turn on "show steps".

Number the positions from the right, starting at 0. Each position is worth 8 raised to that number, so the rightmost digit is worth 1, the next 8, the next 64, and so on up the value.

That turns 234 into 2 x 8^2 + 3 x 8^1 + 4 x 8^0, which adds up to 156. Digits that are 0 contribute nothing and can be skipped, but the position still counts — dropping a zero shifts every digit to its left and changes the value. This is the same expansion decimal itself uses; only the base in the weights differs.

Check it in reverse

The value returns unchanged. Convert 156 back and you get 234, because a base change rewrites the digits without touching the quantity they stand for. That is the whole test: if the round trip differs, a digit was misread. To check it by hand, convert the octal result back to decimal and compare it with the number you started from.

Worked examples: octal to decimal

Each example gives the value first, then the working. Click a value to load it in the converter.

Every example above reverses exactly — divide the same value down to octal digits.

What About Padding, Fractions and Width?

Leading zeros and width

A number carries no leading zeros unless a width is fixed. 156 and 0156 are the same value, so the converter writes the short form. Fixed widths belong to bytes and registers, not to arithmetic. the two universal conversion methods covers where width does matter.

Fractions and the point

Digits after a point convert by the same rule with negative powers, so the first place after the point is worth 1/10. Many fractions that end neatly in decimal repeat forever in binary, which is where rounding creeps in.

Negative values

A minus sign is kept in front of the digits. Fixed-width binary encodes sign differently, using two's complement, and that is a separate rule from the base change itself.

How large a value can be

The method has no ceiling; each extra octal digit multiplies the range by 8. Practical limits come from the width a machine stores the value in, not from the conversion.

Octal to Decimal in Code

The same rule in one line. Both read the digits and return the decimal total.

Python: int('234', 8)

JavaScript: parseInt('234', 8)

Common Mistakes

• Reading the remainders top to bottom. They come out in reverse, so the digits land backwards.
• Using a digit the base does not have — an 8 in octal, or a 2 in binary. The value cannot be read at all.
• Grouping bits from the left. Groups are counted from the right, and the leftmost group is the one that gets padded.
• Treating the result as a character code. 101 is a number here, not the letter A.

Frequently Asked Questions

Related Conversions

• Octal also converts to binary by the same route — convert octal to binary.
• Octal also converts to hex by the same route — change an octal number into hex.
• Octal also converts to text by the same route — look up the character for an octal ASCII code.
• If your input is hex rather than octal, work out the decimal value of a hex number instead.
• If your input is binary rather than octal, convert binary to decimal instead.
• If your input is decimal rather than octal, decimal to hex by dividing by 16 instead.

The rest of the family sits on all the number and text converters in one place.