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A 3/8-inch puncture ruined a rear tire. After replacing it, I started wondering is having two different rolling diameters a bad thing. The difference in tread depth is noticeable but the remaining original has a fair number of useful miles.
Just as a rule of thumb for high-performance cars:
If the remaining tire on that axle has greater than 50% of its tread depth remaining, keep it. If it has less than 50% of the tread remaining, replace it along with the damaged tire.
Regular cars that aren't driven fast or hard and have high-mileage (40,000 mile) tires can get by with a 25% tread depth remaining rule.