PA-28 general aviation pilot reported an engine failure during climb. The pilot did not have enough altitude to reach an airport and landed in an empty field.

Narrative

I took off from ZZZ1 airport around XA:00 for ZZZ. The planned in route altitude for this leg was 4500ft. The weather conditions were VFR. This leg went smoothly as planned and didn't encounter anything unusual. I entered the left downwind for runway XX and landed on XX on ZZZ. I made a full stop and did a taxi back to the run up area. I did the run up test and took off from runway XX. After I took off I was climbing and turning for left crosswind everything seemed normal at this point. I was departing for North East to head back to ZZZ1. My in route altitude was supposed to be 5500ft for this leg. So I was climbing to reach that altitude but around 5 miles east from the airfield I started noticing all of a sudden I was losing RPM and the plane wouldn't climb anymore. The aircraft was losing altitude slowly so I looked back to the left and I could see the airfield but I realized I could barely glide over there since I didn't gained much of an altitude till this point. There was couple of houses in front of me but I could see empty fields behind me so I did a 180 turn and then started gliding towards the empty field. I tired to bleed the airspeed as much as I can before it touched the ground. And made a stop on the field.