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If social security and Medicare taxable wages are calculated the same, why are the amounts in boxes 3 and 5 on my W-2 different?

The amount in W-2 box 3 represents "Social Security Wages." The amount in box 5 is "Medicare Wages." There is no maximum amount for Medicare Wages. However, there is a calendar year maximum for an employee's "Social Security Wages." Once that maximum is reached, social security taxes no longer apply for that calendar year. The yearly maximum for social security typically changes each year: 

2017 - $127,200
2018 - $128,400
2019 - $132,900
2020 - $137,700
2021 - $142,800
2022 - $147,000

In addition, some employees are exempt from social security but not Medicare, and that would therefore result in social security and Medicare amounts not being equal.