You are correct in your calculations. As a single taxpayer, the sale of a primary home qualifies you for a $250,000 exclusion on the gain on the sale of your primary home.
You can deduct from the sale price any expenses paid at the sale of your home. Refer to your closing statement to find the expenses for you, the Seller of the property. Also, the basis of the home may be increased by any improvements you have made to the home during your ownership/residence. Improvements do not include regular upkeep of the home, such as painting, repairs, etc. Improvements would be anything that adds to the value of the home, such as adding a room, upgrading a kitchen or bath, replacing a heating/ac system, etc.
Once you have considered the above, any gain above the $250,000 exclusion would be taxable. Purchasing another property would not affect that.
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