The Big Sur drive is approximately 17 miles long. However, don’t let that number fool you. There are dozens of windy turns that require you to go slow. Even if you drove without stopping, the minimum time it would take you would be 2 hours.
That’s not counting all the times you’ll want to pull off on the side of the road or get out and explore, so I recommend leaving a minimum of 5 hours of allowed time to drive one way. If you do a day trip to Big Sur, it can easily take you 10–12 hours for the day, depending on where you’re coming from.