The previous page Did You Know? This Way Up explained how to use arccos to calculate the angle between the micro:bit’s z sensing axis and gravity. 

When the LED display is facing straight down, so is the z sensing axis.  So the angle between z and gravity is zero. 

As the angle between the z-axis and gravity increases, so does the measurement.  When the LED display (and z-axis) is facing straight up, it’s angle is 180°.  Again, rotating past 180°, the angle decreases, like the last example where it’s back down to 135° again.

Example script: z_axis_degree_of_tilt_try_this

• Enter and save z_axis_degree_of_tilt_try_this.
• Flash it into the micro:bit.

# z_axis_degree_of_tilt_try_this

from microbit import *
import math

sleep(1000)

while True:
    z = accelerometer.get_z()
    
    if z > 1024:
        z = 1024
    elif z < -1024:
        z = -1024
        
    z_angle = round( math.degrees( math.acos( z/1024) ) )

    print("z =", z, ", z_angle =", z_angle)
    print()
    
    sleep(750)

• Open the terminal and experiment with various levels of tilt and rotation.

• Fill in the table with your measured z_angle values.