# Octal to Decimal Converter to Convert Base 8 to Base 10

This calculator will convert octal numbers into decimal numbers and display an interactive conversion chart to show how it arrived at the result.

Tapping any number within the generated conversion chart will explain how the calculator arrived at the number within the tapped cell.

Plus, if the entered octal number does not contain a radix point, the converter will also show its work using the Successive Duplication Method for converting octal numbers to decimal numbers.

If you're unsure what an octal number is or how to convert one into a decimal manually, it may help to visit the Learn tab before using the calculator.

Note that if you are looking to convert a base 10 number to a base 8 number, please visit the Decimal To Octal Converter.

## Octal to Decimal Converter

Convert octal to decimal number and create the conversion chart.

Special Instructions

#### Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None
Octal number:Octal number:Octal number (base 8):Octal number (base 8):

#### Octal number (base 8):

Enter the octal number you would like to convert into a decimal number. Note that the number must only consist of digits 0-7 (octal numbers do not contain 8's or 9's). Also, if the entered octal number does not have a decimal point, the result will include a second method for converting octal numbers to decimal numbers.

 Octal number
Decimal:Decimal:Decimal (base 10):Equivalent decimal (base 10):

#### Decimal (base 10) equivalent:

This is the decimal equivalent to the entered octal number. Note that after clicking the Convert Octal to Decimal button, the octal to decimal converter will display a detailed explanation of how it arrived at the result immediately below this line.

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

## Learn

### What an octal number is and how to convert it to a decimal number.

#### What is an Octal Number?

The easiest way to understand an octal number is to compare it to something you already know -- a decimal number.

As you know, a decimal number uses the base-ten system for counting and expressing value. It's called "base 10" because it uses ten numeric characters (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to count and express values.

On the other hand, the octal number system uses the base-8 method for counting and expressing value. It's called "base 8" because it uses eight numeric characters to count and express value. The eight octal numeric characters are 0, 1, 2, 3, 4, 5, 6, and 7.

Now, since we are looking to convert a base 8 number into a base 10 number, let's compare the base 10 place values to the place values in a base 8 number system:

#### How to Convert Octal to decimal

To help you to understand how to convert octal to decimal, it may help to look at how we translate the value of a decimal number. Let's use the decimal number 1234 (123410, or one-thousand, two-hundred and thirty-four) as an example:

Translating the Value of a Decimal (base 10) Number

← swipe left and right →← swipe left and right →
 A Power of 10: 103 102 101 100 B Place value (A result): 1000 100 10 1 C Entered decimal digit: 1 2 3 4 D Product of B * C: 1000 200 30 4 E Cumulative total of D: 1000 1200 1230 1234

With the above base 10 translation in mind, here is how you would convert the base 8 number 1234 (12348) into a base 10 number:

Converting an Octal (base 8) to a Decimal (base 10)

← swipe left and right →← swipe left and right →
 A Power of 8: 83 82 81 80 B Place value (A result): 512 64 8 1 C Entered octal digit: 1 2 3 4 D Product of B * C: 512 128 24 4 E Cumulative total of D: 512 640 664 668

Adding the values of line D, we get the base 10 number of 668. In other words, the number 12348 coverts to the number 66810.

As you can see, converting an octal number to a decimal number is a simple process of identifying the place value of each digit, multiplying each digit by its place value, and then adding up all of the products.

Or, if the octal number doesn't have a radix point, there is a second method you can use to convert octal numbers to decimal numbers.

Successive Duplication Method

To convert an octal number without a decimal point to a decimal number using the successive duplication method, add "0." to the front of the number and then perform the following steps:

1. Double the value to the left side of the decimal point and place the result on the next line, right-aligned to one digit right of the decimal point.
2. Subtract the doubled value from the digits above and to the left of it and place the results on the next line, moving the decimal point 1 place to the right.
3. Drop the remaining digits to the next row unchanged.
4. Repeat steps 1-3 for as long as digits remain on the right side of the decimal point.

The display below shows how to use this method to convert the earlier example (1234) to Decimal:

 0. 1 2 3 4 - 0 1. 2 3 4 - 2 1 0. 3 4 - 2 0 8 3. 4 - 1 6 6 6 6 8.

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".