I want to create buffers around points, where the area of the buffer is equal to an area value specified in the attribute table of the point dataset. Generally in ArcMap a buffer distance is specified in the buffer tool, which is essentially the radius of the buffer circle. I don't have this distance but have the area which I want the total buffer area to be. I have tried creating a new field for a buffer distance, and used field calculator to work out the radius of a circle with the area values, however this equation includes the pi sign which I am unsure how to include in the field calculator.

You'll just have to answer the question: "To what level of precision am I happy to live with?"

I'd use 3.14159, but you can go out as far as you want....

What is the exact value of pi? - Quora has a post that gives the value of pi out 100 digits: 100,000 Digits of Pi provides it to 100,000 Digits. Some folks just have way too much time on their hands....