how to compute income on a year when you sell an asset with some capital gain while you have a rolling over capital loss from passed years

say you are a 100K/year salary guy. You sell a home ( an investment home, not your primary residence ) for 1M with 500K capital gain. Is your income for that year, 100K + 500K? or because you got a 1M in the sale, your income would be 1.1M?

Your income would be $600k ($100k salary + $500k capital gain). The proceeds of the sale are never relevant, only the gain.

If this is correct, what about a capital loss. Let's say you got a capital loss of 300K rolling over from the previous years from say some stock market loss.

Would you then factor that in and say, the real capital gain on the home sale would be 500K-300K and therefore your income for that year would be computed as 200K + 100K = 300K?

Capital gains net with capital losses before being added to your income, so yes, it would be a capital gain of $200k ($500k gain - $300k loss), plus your $100k salary for a total income of $300k. Also worth mentioning that if there were no capital gain, capital losses are limited to offsetting $3k of regular income per year, so in that case your income would be $97k.