This is a very important question. If we look at an aquatic (water) food web, we see that the phytoplankton are essential. They take energy from the sun and matter from water and carbon dioxide to make sugar and oxygen. They can use the energy to make the other parts of their bodies too.

To the consumers on the next level of the food web, the phytoplankton are just food. When zooplankton eat the phytoplankton, there may be parts of the phytoplankton that they can’t digest, so the zooplankton don’t get the energy locked in those chemical bonds. The zooplankton had to spend energy to catch and digest the phytoplankton, so that has to be subtracted from the energy “profit.”

Where does this energy go? Some wastes might be broken down by decomposers, but they only get a portion of the energy too. The rest is lost as heat. It doesn’t disappear, but it spreads out and is not useful to the other species in the food web.

A general rule of thumb is that only about 10% of the energy that the phytoplankton originally took in will make it to the next level in the food web.

How many kilograms of phytoplankton will it take to produce 1 kg of fish that eat zooplankton that eat phytoplankton?

Aquatic ecologists study questions like this. You may want to pursue a career in that.

This is kind of a cool question to show unit conversions. There are about 0.003 Calories per milligram dry weight of phytoplankton. For every 100g wet plankton, there are 20g when dried. So:

0.003Cal/mg dry *1000mg dry/1g dry * 20g dry/100g wet = 0.6 Calories/gram.

Calories is actually a measure of energy.

I think that you are asking how many nutritional calories an animal would consume when eating a certain amount of phytoplankton. According to a paper from 1973 from the Fisheries Research Board of Canada, the observed calorie content of phytoplankton ranges from ~3-9 nutritional calories per gram of dry plankton. Recently, phytoplankton has started to become popular as a specialty health food for people. This may lead to increased research into the nutritional content of these marine protozoa.

When an organism is eaten, roughly 10% of the energy goes up to the next level in the food chain. The other 90% is lost as heat. For warm-blooded animals, it's more like 98% is lost as heat. This is true regardless of what the organism being eaten is, assuming that the organism is digested (we do not digest much of the plants that we eat, for example, because we cannot digest cellulose).