A partial home sale tax exclusion is ordinarily limited to the percentage of the two years up to the date of the sale that you owned and occupied the home as your principal residence. So your proposed calculation should be acceptable to the IRS.
When you calculate your capital gain, you are allowed to include in your cost basis the cost of capital improvements you made to the house, but you cannot include the cost of items (such as appliances) that are not part of the house. Examples of capital improvements would be a new roof, a room addition, a new central HVAC system, etc.
An old rule of thumb is that, if you can carry it away from the house, it's not a capital improvement.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
