Decimal to Octal Converter to Convert Base 10 to Base 8

Decimal to Octal Converter Sign

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

Tapping any number within the generated conversion chart will display an explanation of how the calculator arrived at the number located within the tapped cell.

Be sure to check out my other decimal conversion calculators for converting:

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Decimal to Octal Converter

Convert decimal to octal and create the conversion chart.

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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
Decimal:Decimal:Decimal number (base 10):Decimal number (base 10):

Decimal number (base 10):

Enter the decimal (base 10) number you would like to convert into an octal number. Note that the entered number must be positive and may only consist of digits 0-9, a single decimal point, and the leading number must not be a zero. For numbers containing a decimal point, the converter will only convert out to the last digit entered.

Octal:Octal:Equivalent octal (base 8):Equivalent octal (base 8):

Octal (base 8) equivalent:

This is the octal equivalent to the entered decimal number. Note that after clicking the Convert Decimal to Octal button the converter will display a result summary and an interactive conversion chart 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.

Help and Tools

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 what an octal number is is to compare it to something you already know -- a decimal number.

As you know, a decimal number uses the base 10 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.

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

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

Place Values of Decimal Vs. Octal Systems

← swipe left and right →← swipe left and right →
Power of 10:103102101100.10-110-210-3
Base 10 Place value:1000100101.1/101/1001/1000
Power of 8:83828180.8-18-28-3
Base 8 Place value:5126481.1/81/641/512

As you can see, since each place value in a base 10 number is different than the corresponding place value in a base 8 system, we need a method for converting 0-9 base 10 place values into 0-7 base 8 place values.

How to Convert Decimal to Octal

To convert a base 10 number into a base 8 number, the first step is to find the first base 8 place value that is greater than or equal to the decimal number you are converting -- starting at the 80 place and working your way to the left.

For example, suppose you want to convert the decimal number 125 into an octal number. In that case, you would find the first base 8 place value that is greater than or equal to 125, which would be 512.

Step# 1: First Base 8 Value Greater than 12510

Power of 8:83828180
Place value :5126481

Once you have located your base 8 place value starting point, the next step is to create a conversion chart like the one shown below.

Step #2: Create Decimal to Octal Conversion Chart

← swipe left and right →
APower of 8:83828180
BRemainder of Division:125   
CPlace value (A result):5126481
DOctal digit  (B ÷ C):    

Notice that the decimal you want to convert is placed in the left-most cell of Row B, just above the base 8 place value row (C).

Step #3: Complete Conversion Chart for Converting 12510 to Octal

Next, attempt to divide the amount in row B into the amount in row C. If the amount in row C is greater than the amount in row B, enter a "0" in row D and move the amount in row B one cell to the right. Otherwise, if the amount in row C is less than the amount in row B, enter the number of times row C goes into row B in row D and enter the remainder in the next open cell in row B. Then simply repeat this process for each subsequent column. Here is how the completed conversion chart would look:

← swipe left and right →← swipe left and right →
APower of 8:83828180
BRemainder of Division:125125615
CPlace value (A result):5126481
DOctal digit  (B ÷ C):0175

Step #4: Combine Numbers In Last Row of Chart

Combining the numbers in the last row of the chart we can see that the base 10 number 125 converts to the base 8 number 175 (1*64 + 7*8 + 5*1 = 125). Note that the leading zeros are dropped since they represent no value (just like the base 10 system).

As you can see, converting a decimal number to an octal number is a simple process of identifying the first base 8 place value greater than or equal to the base 10 number you are converting, and then dividing each place value into the remainder of previous division.

Adjust Calculator Width:

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".

Show/Hide Popup Keypads:

Select Show or Hide to show or hide the popup keypad icons located next to numeric entry fields. These are generally only needed for mobile devices that don't have decimal points in their numeric keypads. So if you are on a desktop, you may find the calculator to be more user-friendly and less cluttered without them.

Stick/Unstick Tools:

Select Stick or Unstick to stick or unstick the help and tools panel. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically. If you find that annoying, select "Unstick" to keep the panel in a stationary position.

If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel.