GarageCalc 
How to find the code
Look for lettering that starts with DOT on the sidewall, followed by plant and
size codes, ending with four digits in a shallow oval. Manufacturers are only required to
put the full code on one sidewall, so if you see DOT followed by only partial characters,
check the other side of the tire.
How it's decoded
Why age limits exist
Rubber ages chemically whether or not the tire is used: oxygen and heat break down the compounds and the adhesion between internal belts. That is why guidance is time-based, not tread-based: inspection from year 5, replacement between years 6 and 10 depending on the manufacturer, and 10 years as the widely accepted absolute limit. Buying a used car? Decode every tire including the spare: a fresh-looking tire can be a decade old.
While you are at the sidewall, the other markings matter too: the load index and speed rating tell you whether the tire is even correct for the vehicle.
Frequently asked questions
Where is the date code on a tire?
At the end of the DOT marking on the sidewall: the last four digits, often in a recessed oval. It may appear on only one side of the tire, so you might need to check the inner sidewall. The first two digits are the week, the last two the year: 3422 means week 34 of 2022.
How old is too old for tires?
Most manufacturers and safety bodies say to have tires inspected annually from 5 years and replaced at 6 to 10 years regardless of tread, because rubber hardens and cracks with age. Many vehicle manufacturers specify 6 years; virtually all agree 10 years is the hard limit, spare included.
My tire has a 3-digit date code. What does that mean?
Three-digit codes were used before the year 2000 (two digits for week, one for year). Any tire still wearing a 3-digit code is more than 25 years old and belongs in a museum, not on a vehicle.
Does tire age matter if the tread looks fine?
Yes. Oxidation degrades the rubber and the bonds between belts from the inside, invisible from outside. Age-related failures typically show up as tread separation at highway speed, which is why the age limit exists independent of tread depth. Heat, sunlight and sitting unused accelerate it.