Accelerometer Angle Calculation Arduino

Calculator

Example Data Table

Formula Used

The calculator first converts each input axis into g units.

• For raw counts: Ax = ((X - Ox) / sensitivity) × Sx
• For g input: Ax = (X - Ox) × Sx
• For m/s² input: Ax = ((X - Ox) / 9.80665) × Sx
• Magnitude = √(Ax² + Ay² + Az²)
• Pitch = atan2(-Ax, √(Ay² + Az²)) × 180 / π
• Roll = atan2(Ay, Az) × 180 / π
• Total tilt = acos(Az / magnitude) × 180 / π
• Filtered angle = α × previous angle + (1 - α) × current angle

Arduino Formula Example

float ax = (rawX - offsetX) / sensitivity;
float ay = (rawY - offsetY) / sensitivity;
float az = (rawZ - offsetZ) / sensitivity;

float pitch = atan2(-ax, sqrt(ay * ay + az * az)) * 180.0 / PI;
float roll  = atan2(ay, az) * 180.0 / PI;

How to Use This Calculator

1. Enter X, Y, and Z accelerometer readings.
2. Select raw counts, g values, or m/s² values.
3. Enter sensitivity if using raw Arduino sensor counts.
4. Add calibration offsets from your sensor test.
5. Adjust scale factors if the axes need gain correction.
6. Add mounting offsets when the board is installed at an angle.
7. Set filter alpha if you want a smoothed reading.
8. Press calculate and review the result above the form.
9. Download CSV or PDF for reports and project records.

Accelerometer Angle Calculation Guide

What This Calculator Does

This calculator converts accelerometer readings into Arduino tilt angles. It accepts raw counts, g values, or meters per second squared. It then corrects offsets, applies scale factors, and finds pitch, roll, total tilt, XY heading, and gravity magnitude. The goal is simple. It helps you test sensor math before loading code on a board.

Why Angle Math Matters

An accelerometer senses gravity when the board is still. Gravity points down, while the sensor axes measure its projection. Those projections form a right triangle. Trigonometry turns that triangle into angles. Pitch shows forward or backward tilt. Roll shows left or right tilt. Total tilt shows how far the Z axis moved away from vertical. These values are useful in robots, leveling tools, drones, displays, and lab projects.

Calibration And Filtering

Raw modules often have small bias errors. A flat board may not return zero on X and Y. The Z axis may not equal exactly one g. The offset fields remove bias. The scale fields adjust gain. The sensitivity field converts raw counts into g units. For example, an MPU6050 at ±2g usually uses 16384 counts per g. The optional filter blends a new angle with a previous angle. It can reduce jumpy readings. It does not replace a gyro for fast motion.

Best Practices

Keep the sensor still during a reading. Avoid vibration and sudden movement. Compare magnitude with one g. If magnitude is far from one, linear acceleration is present. That can distort angles. Use several samples on Arduino and average them. Mount the board consistently. Record the mounting offset after installation. Use radians in code only when needed. Convert to degrees for display.

Arduino Use

Copy the formulas into your sketch. Read X, Y, and Z from the sensor library. Subtract offsets first. Convert raw values to g. Then calculate pitch and roll with atan2. The atan2 function handles signs and quadrants better than atan alone. Test known positions, such as flat, nose up, and side tilt. Save the final offsets for repeatable measurements.

Output Checks

Use the CSV file to compare trials. Use the PDF report for class notes, repair logs, or build records. Recheck calibration whenever the sensor position or range changes.

FAQs

What does this calculator measure?

It calculates pitch, roll, total tilt, XY angle, and acceleration magnitude from three accelerometer axes. It is designed for Arduino sensor projects and classroom math checks.

Can I use raw MPU6050 readings?

Yes. Select raw counts and use 16384 counts per g for the common MPU6050 ±2g range. Change sensitivity if your sensor range is different.

Why is my angle unstable?

Vibration, noise, loose wiring, and fast movement can make readings unstable. Average several samples and use the filter alpha option for smoother output.

What is pitch?

Pitch is forward or backward tilt. It uses the X axis against the combined Y and Z axes. The sign depends on sensor direction.

What is roll?

Roll is left or right tilt. It compares the Y axis with the Z axis. It is useful for leveling and balance projects.

Why check magnitude?

A still sensor should read close to one g. If magnitude is far from one g, motion or calibration error may distort the angle result.

Do I need offsets?

Offsets improve accuracy. Measure the sensor while flat and still. Then subtract the small bias values from each axis before calculating angles.

Is this enough for fast motion?

No. Accelerometer-only angle math works best when still or moving slowly. For fast motion, combine accelerometer and gyroscope data with a complementary or Kalman filter.