Understanding mineral growth mechanism is a key to understanding biomineralisation, fossilisation and diagenesis. The presence of trace compounds affect the growth and dissolution rates and the form of the crystals produced. Organisms use ions and organic molecules to control the growth of hard parts by inhibition and enhancement. Calcite growth in the presence of Mg2+ is a good example. Its inhibiting role in biomineralisation is well known, but the controlling mechanisms are still debated. Here, we use a microkinetic model for a series of inorganic and organic inhibitors of calcite growth. With one, single, nonempirical parameter per inhibitor, i.e. its adsorption energy, we can quantitatively reproduce the experimental data and unambiguously establish the inhibition mechanism(s) for each inhibitor. Our results provide molecular scale insight into the processes of crystal growth and biomineralisation, and open the door for logical design of mineral growth inhibitors through computational methods.