Earth’s Carrying Capacity

We are interested in estimating how many people can live on earth

Some facts for our estimate:

1) The earth receives 1000 Watts/m^2 from the sun.

2) Every person on earth needs 2200 kilocalories per day to eat.

3) There are 4184 Joules/kilocalorie.

I’m interested in seeing your (scientifically grounded) estimates, and full unit conversion.