Batch CSV and time-series analysis
Paste rows using: timestamp, ax, ay, az, gx, gy, gz, mx, my, mz. Only timestamp and acceleration columns are required.
Formula used
|a| = √(ax² + ay² + az²)
Roll
roll = atan2(ay, az)
Pitch
pitch = atan2(−ax, √(ay² + az²))
The exact signs depend on the sensor coordinate convention and mounting direction. This page applies calibration, axis mapping, and convention choices before calculating angles. Yaw requires a heading reference, magnetometer, gyroscope integration, or sensor fusion.
How to use this calculator
- Enter X, Y, and Z accelerometer readings using one consistent unit.
- Select the coordinate convention and correct any swapped or inverted axes.
- Choose a yaw source, then enter magnetometer or gyroscope data when required.
- Apply measured calibration offsets and scale factors when available.
- Review the gravity agreement warning before trusting static tilt results.
- Use batch mode to filter multiple samples, graph angles, and export results.
Understanding roll, pitch, and yaw
Roll describes rotation around the device’s forward axis. Pitch describes upward or downward rotation around its lateral axis. Yaw describes heading rotation around the gravity or vertical axis.
A stationary accelerometer mainly measures the gravity vector projected onto three axes. That vector provides enough information for roll and pitch under a known convention. It does not provide a unique heading around the same gravity vector.
Dynamic movement introduces linear acceleration in addition to gravity. Braking, vibration, impacts, and turns can therefore distort accelerometer-only tilt estimates. Filtering may reduce noise, but it cannot fully separate unknown motion from gravity.
Magnetometers provide a magnetic heading but require calibration and tilt compensation. Gyroscopes track angular motion smoothly, although integration error accumulates as drift. Sensor fusion combines complementary strengths to improve practical orientation estimates.
Calibration guidance
Offset calibration removes a constant sensor bias from each measured axis. Scale calibration corrects sensitivity differences using multiplication after offset removal. A six-position procedure usually measures each axis facing upward and downward.
Magnetometer hard-iron correction removes fixed magnetic offsets caused by nearby materials. Soft-iron scale factors compensate for directional distortion in the measured magnetic field. Professional systems may require a full calibration matrix rather than three scales.
Worked example
For a stationary reading of X = −0.5 g, Y = 0 g, and Z = 0.866025 g, the magnitude is approximately one g. The aerospace equations give roll near zero degrees and pitch near positive thirty degrees. Accelerometer-only yaw remains unavailable because no heading reference was supplied.
| Preset | X (g) | Y (g) | Z (g) | Expected roll | Expected pitch |
|---|---|---|---|---|---|
| Flat | 0 | 0 | 1 | 0° | 0° |
| Right side | 0 | 1 | 0 | 90° | 0° |
| Upside down | 0 | 0 | −1 | 180° | 0° |
| Pitch upward | −0.5 | 0 | 0.866025 | 0° | 30° |
| Roll right | 0 | 0.707107 | 0.707107 | 45° | 0° |
Frequently asked questions
Can an accelerometer calculate yaw?
No. It cannot distinguish headings that share the same gravity direction, so another heading source is required.
Why does motion change the result?
The sensor measures total specific force, which may include gravity, vehicle acceleration, vibration, and impacts.
Which coordinate convention should I select?
Choose the convention used by the device documentation, then verify axis signs with known physical orientations.
What does one g mean?
Standard gravity is approximately 9.80665 m/s², although local gravity differs slightly by location and altitude.
What is tilt compensation?
It rotates magnetometer measurements using roll and pitch before computing a horizontal compass heading.
Why does gyroscope yaw drift?
Small rate bias errors accumulate during integration, causing the estimated angle to wander over time.
What is complementary filter alpha?
A higher alpha trusts integrated gyroscope motion more, while a lower alpha trusts reference sensors more.
Can the calculator process logged sensor data?
Yes. Batch mode parses CSV rows, applies selected filtering, reports statistics, plots angles, and exports results.
What happens near ninety-degree pitch?
Euler-angle representations become sensitive near singular configurations, although quaternions remain well behaved.
Is this suitable for safety-critical navigation?
No. Certified systems require characterized sensors, validated calibration, tested fusion algorithms, redundancy, and formal verification.
Engineering disclaimer
This calculator is intended for educational, prototyping, and preliminary analysis use. Aircraft, automotive, marine, robotic, medical, or industrial safety systems require calibrated hardware, validated algorithms, environmental testing, and appropriate engineering review.