Capital Gains on Inherited Stocks.

Long story short, my grandfather worked for an oil company from the 70s-80s, took part of his paycheck in stock options, the stock split a few times, and when he died, a chunk of that was passed onto me. If I were to sell that stock, would my capital gains be based on the difference in value from when he received the stock in the 70s until now, or just based on my income? Forgive if this is an ignorant question, I just don't know how that would work considering the stock has grown so much in value from when he first got it. Thanks!