thickness of carpet runner on stairs

We moved into our current home about 2 years ago. It has wooden stairs with a carpet runner on them that's pretty worn. We're looking to replace it. The current runner is about 1/2" thick. The first person we had come give us a quote recommended something that was notably thicker. I'm concerned about somewhat of a safety hazard with the difference between the wood and the carpet being too great. If someone stepped halfway on the carpet and halfway on the wood it could easily throw them off balance. We have parents in their 70s and 80s visit us. The width of the stairs between the railing spindles is 43" and the width of the current carpet is 27". What would the typical height of a carpet runner on stairs be, including the pad?