General aviation pilot reported a rough running engine and loss of power in cruise. Pilot executed an off-airport landing.

Narrative

During a pleasure flight counterclockwise thru ZZZ area beginning and ending at ZZZ1 (intended) at approximately 3;000 ft MSL; my engine suddenly experienced unexpected vibration and rough running. I applied full-rich mixture; turned on electric fuel pump; and switched fuel tanks. I attempted to vary power setting to see if had any positive effects on the vibration: It did not. Since vibration lead me to believe that there was physical damage to the engine (like a broken piston) I reduced power somewhat.Anticipating an off-field landing; I verified that my airspeed was acceptable and immediately began to scan for a suitable place to land. I observed a sufficient field directly to my left. I continued to scan but determined that no other area was acceptable.Already tuned into ZZZ2 CTAF I made a call indicating I was experiencing engine malfunction and intended to fly direct for a straight-in approach. Student Aircraft at the field indicated they would clear area for my arrival. I began my turn towards ZZZ2 and evaluated the area between myself and the field. I observed only trees and houses - No fields of any type. I looked at my EFB and observed that the safe-glide area; identified by a green circle; fell far short of the airfield. Realizing that should I lose power completely that I had no acceptable area to land; and that the ONLY safe option was an immediate off-field landing; I aborted my intent for a landing at ZZZ2. I turned and started my downwind into the field that I had previously selected; continued my decent and turned 180 degrees to align with the longest portion of the field. I set the aircraft down using a soft-field technique and bled off speed while rolling. As I approached the end of the field I applied full braking power and the aircraft came to a stop within 30-40 feet on the grass. I shut down the aircraft; exited and with assistance from the local Instructor (who was now circling overhead) and the nearby residents; contacted Emergency Services.I evaluated the aircraft and observed no external damage. The plane was resting normally on its landing gear and I experienced no injuries or unexpected motion within the cockpit.All things being considered; other than the need to set down off-field; it was an uneventful landing.