How long does it take for tartar to develop?

Dental plaque takes several days to weeks to form following poor oral hygiene, and calcification can occur soon after. Calculus needs to be professionally removed by your dentist or hygienist. More info here: ref: https://en.wikipedia.org/wiki/Dental_pellicle ref: https://en.wikipedia.org/wiki/Dental_plaque

Tarter is the normal calcification of the plaque accumulated on teeth, that is not removed by good oral hygiene. This can occur within 10 days if the plaque is not removed. This condition causes gum disease and loss of bone which leads to loss of teeth. A dentist or hygienist needs to remove these hard deposits.