A Cessna 172 general aviation pilot reported an engine malfunction during cruise. The engine performance decreased and the pilot diverted and landed safely.

Narrative

Flight planned from ZZZ to ZZZ1. The plane was rented to me by my flight school. I was the pilot; and brought my father as a passenger to attend a family reunion in the vicinity of ZZZ1. I am a current IFR pilot and judged that the weather conditions were acceptable to make the flight safely. Icing levels were at 8000 feet; and I knew that I would likely need to climb to 7000 feet for assured obstacle clearance. A full weight and balance was performed and was well within envelope (2 passengers 290 pounds; 30 pounds baggage). Cumulus clouds; light rain; and light/moderate turbulence were encountered. After 2.5 hours of flight en-route at 5000 feet; I noticed that the single piston engine seemed to be decreasing in performance; and that the RPM gauge indicated that I was not achieving full engine power. I expected that if I could not resolve this issue; the airplane would not safely be able to climb to and maintain 7000 feet MSL. I indicated to ZZZ approach that I seemed to be having reduced engine performance; and that I wanted to divert to ZZZ2 airport in order to access the safety of the airplane and call my flight school. During this time; I performed checklists to attempt to resolve the issue by maintaining carb heat; leaning the fuel/air mixture; and checking all systems. No problems were identified; and all temperature gauges indicated safe temperatures. While performing these checks; the RPM gauge faltered and then stopped working completely; which I have been assured by mechanics is consistent with the measuring system becoming disconnected from the instrument. With the plane now un-airworthy; I confirmed with ATC the need to divert. ATC asked if I wished to [request priority handling]; and I said that an emergency did not need to be declared at that time. After a few minutes of diversion; ATC asked if I had been able to regain full engine power. I replied that I had not; and ATC then [requested priority] on my behalf. I made a safe VFR landing at ZZZ2; maintaining engine power and airspeed until I was sure that I would be able to safely land on the runway in the event of full engine loss.