As the name implies, an accelerometer measures acceleration. Acceleration happens when the velocity of something changes, like a Circuit Playground at rest which is suddenly moved. A Circuit Playground sitting still on your desk is obviously not accelerating. So why does the accelerometer still read 9.8 m/s²? The answer is gravity.

Gravity is what makes apples fall from trees and holds us to the Earth. If you looked at the planet from far away, you could think of gravity looking something like the figure below. All the arrows point in towards the planet. That's how you can stand at the South Pole and not fall off.

If we zoomed way in to just the local area where you might be, say standing outside with a Circuit Playground, it would look more like the figure below. The Earth is so big that close up it looks flat. Now all the lines are straight and point down.

Just like gravity happens in a direction (down), acceleration also happens in a direction. In order to determine the direction, the Circuit Playground uses an XYZ coordinate system. For reference, there's a little diagram printed on the silk screen next to the accelerometer chip. A larger version is shown in the figure below. Z points out.

So let's say you held the Circuit Playground at a little tilt angle as shown by the coordinate system below. Gravity, as shown by the blue arrow, will still point down. In this case, the accelerometer will sense some of it in the X direction and some of it in the Y direction. However, from the point of view of the Circuit Playground, it feels like it's accelerating in the direction of the green arrow. You can test this yourself by placing the Circuit Playground flat on your desk. The Z axis will be pointing up and gravity will be pointing down. However, the value returned from motionZ()is positive. The Circuit Playground feels like it's accelerating up off your desk!

OK, now for the math. Sorry, but this is important. It's how we can use the accelerometer to measure angles and turn the Circuit Playground into an inclinometer. Also, rockets are built using math like this.

The same tilted axis and green arrow from above are shown again below. The red arrow represent the amount that the X axis will sense and returned by motionX(). Similarly, the blue arrow represents the amount the Y axis will sense and returned by motionY(). All together they form a special kind of triangle called a "right triangle", where one of the angles is a "right angle", which means it equals 90 degrees.

The tilt angle is shown in two places. The one on the left is what we are really interested in. However, it turns out it is the same as the one on the right, inside our right triangle. That's cool, since it let's us use motionX() and motionY() to compute the tilt angle.

Now let's focus on that right triangle. It is shown below with the other stuff removed and rotated to make it easier to look at. Also, the equation needed to compute the tilt angle is shown.

The function atan is called the arctangent, or inverse tangent. It does the opposite of what the tangent function does. They are both part of a whole discipline of math called trigonometry. We will use the tangent function later when we go outside to measure the height of things. However, we will let either the Circuit Playground or a calculator do the math for us.