In general, you share an average of 50% less DNA with an ancestor with each additional generation. To find how much DNA you likely share with a cousin, consider that they have also inherited 50% less DNA with each generation. A modified version of the genealogical relationship chart shows this.
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For example, you and your relative share a common ancestor, Emmet Wiscured. Emmet is your 4th great-grandfather. He is your cousin’s 3rd great-grandfather. To use the chart, start with you. Look across the headings at the top to find 4th great-grandparent. Then look down the left column for your cousin’s relationship of 3rd great-grandparent. Find the point on the chart where the 4th great-grandparent column and 3rd great-grandparent row meet. You and your relative should share .098% of your common ancestors’ DNA.
This is an average. The amount of each grandparent’s DNA passed on to you is random. Thus, the amount of DNA that you share with a particular cousin will be much more or much less.