You *do not* need carbon.
The main reason carbon is sold is to make a profit for carbon manufacturers. Here's a run through of what it's meant to do...
Remove organic materials. As others have said, water changes do this. In fact, they do it better. A 25-50% water change removes more than a bit of organic material (specifically "gelbstoff") but also nitrate and phosphate that carbon does nothing with. In addition, carbon removes medications, so each time you treat the tank, you need to remove the carbon.
Supports biological filtrations. Yes, it does this. But in doing so, it loses the ability to remove organic materials. Furthermore, it isn't as good as, say, quality ceramic media. Ceramic media can be cleaned easily and remain stable for years, decades even. Cleaning them is easy and effective. Carbon cannot really be cleaned properly because it disintegrates after a while. As it decays into small particules it impedes the flow of water. The surface area of the biological media is only one factor to consider when choosing media for your filter; water flow is another. Anything that decreases the flow of water limits the rate at which the water is cleaned. Ceramic media maintain very good water flow for weeks, months, even years.
Carbon, like "tonic salt", is something that should have been dumped years ago. It is to freshwater fishkeeping what gas lighting is to houses: archaic and inefficient. In the old days of the hobby people avoided water changes for months at a time, because they thought old water was best, and as a result the water turned yellow. Carbon removed the yellowness. In a modern tank, where we do water changes every week, there's nothing for carbon to remove, so it is entirely redundant.
Cheers, Neale