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In my attribute table I have a field with some null cells and I want to fill them with the value of the other cells. how can I do it?

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You open the attribute table, and click on the button for "Select by attributes". Then you enter the following:

"Field" IS NULL

substituting Field for your field name.

Now you should have selected all features with a null value in that field.

Right-click on the header of your field --> Field calculator. Enter whatever value you wish to replace null with, or another field if you want to copy from there, and press OK.

Additionally, in an edit session you are able to edit cells manually.

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Indeed Python is the recommended scripting language for ArcGIS including the Field Calculator which is required for the second step of your anwer. However, I would like to point out that "Selecting by attributes" in fact implies a SQL query, with the field name in quotation marks. (No option for Python there, it should be "Field", but !Field! won't work.) – lavarider Feb 2 '14 at 9:33
Of course you are right about that. I've updated my answer accordingly. – Martin Feb 3 '14 at 6:57

If you right click the field title of the null cells, and select "Field Calculator". From there just double click the field name of the cells you wish to use.

You may run into issues if the column you're using to "fill in" the data also has null cells.

EDIT: Just re-read the question, you'd need to select only the nulls first. On the open attribute table "select by attribute", double click the field that has the nulls and type "is null". Should look something like this, [FIELD] is null

Run the selection and follow the field calculator step above.

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