How does the Calvin Cycle in photosynthesis work?

If you recall the basic chemical equation for photosynthesis: CO2 + H2O --> O2 + Carbohydrate (with 6-Carbons)
​This is precisely what occurs during the calvin cycle. Carbon dioxide is fixated and at the end, the whole purpose of the cycle is to produce a carbohydrate integral to the plant, like Sucrose.

The process of the calvin cycle (light-independent stage) occurs in the Stroma of the chloroplast. It uses the products of the light-dependent stage (ATP and NADPH) in order to carry out the cycle.

Firstly, CO2 is fixed by a special enzyme called RuBisCo. The carbon atom from the CO2 molecule is added to the 5C molecule (Ribulose-1,5-bisphosphate) to form an unstable 6C molecule which then splits in half to form two 3C molecules (this 3C molecule is called 3-phosphoglycerate). Then, ATP is introduced (remember: the ATP came from the previous light-dependent reactions). The ATP loses a phosphate group to the 3C molecule - ADP is formed as a result and the 3C molecules become 1,3-bisphosphoglycerate. The 1,3-bisphosphoglycerate is then reduced by NADPH (NADPH is itself oxidised during the process) to form GALP, also known as Glyceraldehyde-3-phosphate. One Carbon atom from GALP is removed in every cycle - this carbon will contribute to the creation of the desired 6C carbohydrate (therefore, 6 cycles of the calvin cycle are needed to form the carbohydrate). We have 5 carbons remaining - the Ribulose-5-phosphate is then regenerated. Lastly, ATP will donate a phosphate group to the 5C Ribulose which will then form Ribulose-1,5-bisphosphate, which brings us back to square one. The cycle then repeats.