Accelerometer Rotation Calculator

Calculator Input

Sample Label

Input Unit

Decimal Precision

Acceleration X

Acceleration Y

Acceleration Z

Bias X

Bias Y

Bias Z

Scale Factor X

Scale Factor Y

Scale Factor Z

Mounting Roll Offset

Mounting Pitch Offset

Mounting Yaw Note

Smoothing Current Weight

Previous Filtered X

Previous Filtered Y

Previous Filtered Z

Example Data Table

Case	Ax	Ay	Az	Expected Meaning
Flat device	0	0	1	Roll and pitch near zero.
Tilted forward	0.5	0	0.866	Pitch changes about thirty degrees.
Tilted sideways	0	0.707	0.707	Roll changes about forty-five degrees.
Dynamic motion	1.4	0.2	0.9	Magnitude is high. Results need caution.

Formula Used

The calculator first converts all readings to g units.

Acal = (Araw - Bias) × Scale

Af = α × Acal + (1 - α) × Aprevious

|A| = √(Ax² + Ay² + Az²)

Nx = Ax / |A|, Ny = Ay / |A|, Nz = Az / |A|

Roll = atan2(Ay, Az)

Pitch = atan2(-Ax, √(Ay² + Az²))

Inclination = acos(Nz)

Yaw is not calculated because gravity gives no heading reference.

How to Use This Calculator

Enter X, Y, and Z accelerometer readings.
Select whether readings are in g or m/s².
Add bias corrections from calibration, if known.
Enter scale factors for each axis, if available.
Add mounting roll and pitch offsets, if required.
Use smoothing when processing repeated samples.
Press the calculate button to view the result above.
Download the result as CSV or PDF when needed.

Understanding Accelerometer Rotation

An accelerometer senses acceleration along three device axes. When a device is still, the main measured acceleration is gravity. That gravity vector points toward the earth. Its direction inside the sensor frame reveals tilt. This calculator converts that vector into roll, pitch, inclination, and a practical rotation axis.

Why Calibration Matters

Small sensor errors can create large angle errors. Bias values remove constant offsets. Scale factors correct gain errors. Mounting corrections adjust a board that is not perfectly aligned with the case. These steps are important for robots, phones, drones, tools, lab fixtures, and training devices.

Reading the Results

Roll describes rotation around the X axis. Pitch describes rotation around the Y axis. Inclination shows how far the sensor Z axis is from the gravity direction. Resultant acceleration shows whether the reading is close to one g. A value near one g means the device is probably still. A much larger or smaller value means the device may be moving, shaking, or falling.

Limits of Accelerometer Rotation

An accelerometer alone cannot measure yaw. Yaw is rotation around gravity. Gravity looks the same after any yaw turn. A magnetometer or gyroscope is usually needed for heading. The calculator reports yaw as unavailable for this reason. This is not a fault. It is a physical limit of the sensor data.

Advanced Use Cases

Use the smoothing option when readings are noisy. A higher current weight reacts faster. A lower current weight produces steadier output. Use previous filtered values only when you process continuous samples. For a single sample, leave them blank.

Best Practice

Take samples while the device is steady. Average several samples before entering values. Use correct units. Keep axis labels consistent with the sensor datasheet. Recheck signs by placing the device flat, then tilting it slowly. Good input habits make the angles more useful and repeatable.

Practical Accuracy Checks

Place the sensor flat on a stable table. One axis should show about one g. The other axes should stay near zero. Turn the board onto each side. The active axis should change clearly. If values drift, repeat calibration. If angles jump during motion, trust only steady moments. Fast movement mixes motion acceleration with gravity for best results.

FAQs

Can an accelerometer calculate full rotation?

No. It can estimate roll and pitch from gravity. It cannot calculate yaw by itself. Yaw needs a magnetometer, gyroscope, camera, or another heading reference.

Why is yaw shown as unavailable?

Yaw rotates around the gravity vector. Gravity appears unchanged during that motion. Therefore, accelerometer readings alone do not contain enough heading information.

What does resultant acceleration mean?

It is the combined size of the X, Y, and Z readings. A still device usually measures close to one g. Large differences suggest motion or vibration.

Should I use g or m/s²?

Use the unit shown by your sensor output. Many modules report g values. Some software libraries report m/s². The calculator converts m/s² to g internally.

What are bias values?

Bias values are constant sensor offsets. They appear even when the sensor should read zero. Subtracting them improves angle accuracy and repeatability.

What are scale factors?

Scale factors correct gain errors on each axis. Use 1 when no scale calibration is known. Use measured calibration values for more accurate results.

When should smoothing be used?

Use smoothing for repeated samples from a noisy sensor. It reduces jitter. For one isolated reading, keep the current weight at 1.

Why are angles wrong during movement?

The formula assumes gravity is the main acceleration. During fast motion, the sensor also measures movement acceleration. That extra force can distort tilt estimates.