Taking on the challenge of running up and downhill has increased health benefits for you. If you run uphill you are working against gravity and that taxes your muscles, making them work harder than they do when on flat ground, which helps strengthen your quads, hamstrings, glutes, and calves, helping you able to run faster and longer.
This is also helpful with injury prevention and to strengthen the upper body, since your leg muscles tire more easily on uphill climbs you will naturally pump the arms more to take some of the workload from the lower body, which will also burn more calories.
Since running up steep hills is naturally more challenging than running on flat surfaces, both building lower-body muscles and increasing your lung function will enable you to run longer with ease.
Meanwhile when you run downhill, you increase speed since the pull of gravity makes your quads and hamstrings work much harder to slow down your pace to prevent your feet from pounding the ground with each step, and as mentioned above, having stronger thigh muscles is one way to build speed and power.
Since gravity also targets your shins, it is also very important to engage your core to brace knees against the added impact a downhill run can have on the body and after running up the hill provides a welcome rest, it feels easier, which can give the muscles a break during a run that allows conserving energy.
