# Calculating Roll & Pitch Angles with Accelerometer Data

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In summary: However, when either roll or pitch reaches ~±90 degrees, the other angle experiences unusual behavior. This can be solved by incorporating the x-axis into the calculation to compensate for the transition from x to z during roll. This can be done using the equations roll = asin(x-axis) * 180/Pi and pitch = asin(y-axis) * 180/Pi. These equations have been used successfully with the LIS302DL accelerometer.
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Hi, I'm new to the forum.

I have a 3 axis accelerometer that I am trying to obtain roll and pitch from. Besides the accelerometer itself, I was provided the raw data values of what each axis will report when it has 0g being applied to it and when it has 1g being applied to it. Using this I am able to find and normalize how many gravity forces are currently being applied to each axis.

In the rest of this post assume x, y, and z are normalized; so if x=1 then 1g is applied to the x-axis in the positive direction.

I'm using the following equations:

$$roll = atan(\frac{z}{x})$$
$$pitch = atan(\frac{z}{y})$$

If the accelerometer is lying flat, with the z-axis facing up, and I rotate it over the y-axis (roll), then I can use the above equation to obtain the roll from 0 to 360 degrees. Same with pitch.

However I run into two problems:
1. When either roll or pitch reach ~$$\pm$$90 degrees then the other angle experiences unusual behavior. For instance, if I roll it over to 90 degrees the pitch may suddenly become 45, 92, 120, etc (it's unstable).
2. It also appears that if I both roll and pitch the device at the same time the values are not correct.

Is there a special way to calculate angles based on this type of data, or am I just going about this wrong? It's been a while since I've done any 3d geometric math and I don't remember a whole lot.

Thanks.

How is the accelerometer constructed?

The chip itself is an http://www.analog.com/en/prod/0%2C2877%2CADXL330%2C00.html" .

I think the problem may be that when I roll the chip 90 degrees, the z-axis becomes perpendicular to gravity. The z-axis is used in the calculation for pitch when roll is near 0.

The solution to this is probably somehow incorporating the x-axis into the calculation in order to compensate for the transition from x to z moving towards gravity during roll, however I'm unsure of how to go about doing that. Does that make any sense?

Last edited by a moderator:
Roll= Asin(X-axis) in radian * 180/Pi in degree
Pitch= Asin (Y/axis) in radian * 180/Pi in degree

Try these equations may be this will work for you.

I am Using LIS302DL, both equation are working fine for me.. in order to find the pitch and roll angle from raw acceleration data

Hello and welcome to the forum! Calculating roll and pitch angles with accelerometer data can be a bit tricky, but it is definitely possible. It seems like you have a good understanding of the basics and are on the right track with your equations. However, there are a few things you should keep in mind when working with accelerometer data.

First, it is important to note that accelerometers measure acceleration, not orientation. This means that the values you are getting from your accelerometer are affected by both gravity and any other accelerations (such as movement or rotation). In order to accurately calculate roll and pitch angles, you will need to separate the gravity component from the other accelerations.

One way to do this is to use a complementary filter, which combines data from both the accelerometer and a gyroscope to determine orientation. This can help to eliminate the instability you are experiencing when one angle reaches ~±90 degrees. Another option is to use a Kalman filter, which is a more complex algorithm but can also provide more accurate results.

Additionally, when both roll and pitch are being changed at the same time, it can be difficult to accurately calculate the individual angles. This is because the accelerometer is measuring the combined effect of both rotations. In this case, it may be helpful to use a sensor fusion algorithm that combines data from multiple sensors (such as an accelerometer, gyroscope, and magnetometer) to determine orientation.

I hope this helps guide you in the right direction for calculating roll and pitch angles with your accelerometer data. Good luck with your project!

## 1. How do you calculate roll and pitch angles with accelerometer data?

To calculate roll and pitch angles with accelerometer data, you will need to use trigonometry and the accelerometer's readings for the x, y, and z axes. The roll angle can be calculated using the arctangent function of the ratio of the y and z axis readings, while the pitch angle can be calculated using the arctangent function of the ratio of the x and z axis readings.

## 2. What is the formula for calculating roll and pitch angles with accelerometer data?

The formula for calculating roll angle (𝜃) is arctan(y/z), and the formula for calculating pitch angle (φ) is arctan(x/z). These angles are typically measured in radians.

## 3. Can you explain the concept of roll and pitch angles in relation to an accelerometer?

Roll and pitch angles represent the rotation of an object in three-dimensional space. In the context of an accelerometer, the roll angle represents the rotation around the x-axis, while the pitch angle represents the rotation around the y-axis. These angles can be calculated using the accelerometer's readings for the x, y, and z axes.

## 4. Are there any limitations to calculating roll and pitch angles with accelerometer data?

Yes, there are certain limitations to calculating roll and pitch angles with accelerometer data. These include potential errors due to noise or drift in the accelerometer readings, as well as inaccuracies caused by the orientation and placement of the accelerometer in relation to the object being measured.

## 5. How can calculating roll and pitch angles with accelerometer data be used in practical applications?

Calculating roll and pitch angles with accelerometer data can be used in various applications, such as navigation systems, motion tracking, and robotics. These angles can provide important information about the orientation and movement of objects, which can be useful in designing and controlling systems and devices.

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