Roll Pitch Yaw From Accelerometer Calculator

Sensor Input Form

Ax acceleration

Ay acceleration

Az acceleration

Acceleration unit

Decimal places

Magnetic declination, degrees

Optional yaw helpers

Yaw cannot be solved from an accelerometer alone. Add magnetometer axes or gyro data when available.

Mx magnetometer

My magnetometer

Mz magnetometer

Previous yaw, degrees

Gyro Z rate, degrees per second

Sample interval, seconds

Formula Used

The calculator converts all acceleration inputs to g units first. It assumes a common right handed sensor frame.

Roll = atan2(Ay, Az)
Pitch = atan2(-Ax, sqrt(Ay² + Az²))
Magnitude = sqrt(Ax² + Ay² + Az²)
Yaw from acceleration alone is not observable.
Optional heading uses Xh = Mx cos(Pitch) + Mz sin(Pitch).
Optional heading uses Yh = Mx sin(Roll) sin(Pitch) + My cos(Roll) - Mz sin(Roll) cos(Pitch).
Yaw heading = atan2(-Yh, Xh) + declination.

How To Use This Calculator

Enter Ax, Ay, and Az from your accelerometer.
Select g or m/s² as the input unit.
Enter optional magnetometer values for tilt-compensated yaw.
Enter optional gyro data when only a yaw estimate is needed.
Press the calculate button and review the result above the form.
Use CSV or PDF export for documentation.

Example Data Table

Device position	Ax	Ay	Az	Expected roll	Expected pitch	Yaw note
Flat, face up	0	0	1	0°	0°	Unavailable without helper sensor
Right side raised	0	0.707	0.707	45°	0°	Needs magnetic or gyro input
Nose up 30 degrees	-0.500	0	0.866	0°	30°	Needs magnetic or gyro input
Moving sample	0.30	0.40	1.20	18.43°	-13.26°	Low confidence if magnitude is high

Understanding Accelerometer Orientation

An accelerometer senses acceleration along three body axes. When a device is still, the strongest acceleration is gravity. The gravity vector lets the calculator estimate roll and pitch. Roll describes side tilt around the X axis. Pitch describes nose up or nose down tilt around the Y axis. These values are useful for drones, robots, phones, vehicles, and small lab fixtures.

Yaw Needs More Than Gravity

Yaw is rotation around the vertical axis. Gravity looks the same after a flat device spins on a table. Because of that, an accelerometer alone cannot solve true yaw. This tool reports that limit clearly. It can also calculate a tilt compensated heading when optional magnetometer readings are supplied. A gyro based yaw estimate can be shown when a previous yaw, rate, and time step are entered.

Useful Checks For Clean Results

The acceleration magnitude should be near one g for static tilt. If it is much higher or lower, the device may be moving, vibrating, or scaled incorrectly. The confidence score is based on how close the vector magnitude is to gravity. It does not prove perfect calibration, but it quickly shows whether the input is reasonable. The normalized vector is also shown, so users can inspect axis direction.

Practical Notes

Axis mapping matters. Some boards label axes differently. A sign change can flip roll or pitch. Mounting direction can also change the formula convention. Use a known flat position first. Then rotate the device slowly and compare the output with expected movement. If the result moves opposite to the real motion, swap a sign or choose the matching axis convention in your project code.

Export And Review

The page includes CSV and PDF buttons for quick reports. The example table gives common test cases. Use them to compare flat, side tilted, and nose tilted positions. For production work, combine accelerometer data with gyroscope and magnetometer data. A complementary filter or Kalman filter can smooth noise, reduce drift, and provide stable roll, pitch, and yaw over time.

The formulas use radians internally, then present degrees for readability. Rounded output can hide small sensor errors, so choose more decimal places during calibration and fewer decimals for simple field notes and logs.

FAQs

Can an accelerometer calculate yaw by itself?

No. Yaw is rotation around gravity. A flat device can spin without changing the gravity vector, so acceleration readings cannot reveal true yaw alone.

Why are roll and pitch possible?

Roll and pitch change how gravity projects onto Ax, Ay, and Az. When the device is mostly still, those projections define the tilt angles.

What unit should I use for acceleration?

Use the unit from your sensor output. Select g if readings are already scaled to gravity. Select m/s² for raw physical acceleration values.

Why is my confidence score low?

The total acceleration is probably far from one g. Motion, vibration, impact, poor scaling, or sensor bias can reduce static tilt accuracy.

How do I get a real yaw angle?

Add magnetometer readings for heading, or combine gyro and magnetometer data. Sensor fusion gives a more stable yaw than either helper alone.

What does magnetic declination mean?

Declination corrects magnetic north to true north. Enter your local declination in degrees when using magnetometer axes for heading output.

Why are my signs reversed?

Your board may use a different axis direction. Try a known flat test, then flip the sign or remap axes in your project.

Can this work while the device moves?

It can calculate values, but motion adds acceleration beyond gravity. For moving devices, use filtering and combine accelerometer, gyro, and magnetometer data.