What is the typical climb angle (versus the ground) of a single engine piston plane?
That depends on wind speed and the aircraft's thrust-to-weight ratio.

Here are some values, all valid for sea level


GA aircraft: 4 m/s climb speed, 36 m/s airspeed. In calm air, this becomes a climb angle of 6.3°. If the wind blows with 36 m/s, the aircraft will climb vertically relative to earth if it flies straight into the wind.
Airliner: 20 m/s climb speed, 120 m/s. In calm air this becomes a climb angle of 9.5°.
Empty airliner: 30 m/s at 100 m/s. In calm air this becomes a climb angle of 16.7°. At airshows this is used to dramatic effect.


Note that the spectacular angles at airshows involve the conversion of airspeed to altitude, so these maneuvers are instationary.

If you want to know more on computing the optimum climb angle, consider reading this answer.

The main influence on climb speed is the thrust-to-weight ratio of the airplane. Since thrust depends on flight speed, ambient temperature and air density, those factors control the attainable climb speed in combination with the aircraft's weight.

For an observer, the next important influence is wind speed, since the aircraft climbs relative to the air mass it is flying through. If this air mass makes the aircraft appear to fly more slowly, a steeper climb angle can be observed.



Climb performance over airspeed and thrust-to-weight ratio for an idealized turbofan engine. The blue lines show thrust (right Y-axis) and the green lines the resulting climb speed. The two black lines show how the optimum flight speed for best climb speed and best climb angle (steepest climb) vary over thrust loadings. They are easy to find graphically: Just measure the angle of a line from the origin to the point on a green line at the desired flight speed and the right thrust loading (thrust-to-weight ratio). If the scales of the two speeds on the X- and Y-axis would be the same, you could directly take the angle from the plot.

With lots of excess thrust, the optimum is limited by the stall speed (the black line bends into a vertical trend), while with no excess thrust both optimum speeds vx and vy converge. This makes sense: If thrust is just sufficient to keep the airplane from descending at one speed, this speed will both give the best flight path angle and the best vertical speed (unfortunately, both will be 0 at this point). It also helps to reduce induced drag, so aircraft with a high aspect ratio wing will climb steepest at a higher lift coefficient (= lower speed).