Calibrate an MPU6050 motion offset

Measure a stationary MPU6050 offset, remove it without erasing gravity, and distinguish a controlled motion input from rest.

Physics Phoebe: I want you to preserve gravity as evidence while separating repeatable offset from real motion., your practice guide

Physics Phoebe: I want you to preserve gravity as evidence while separating repeatable offset from real motion.
Predict the reading, then compare it with the measurement.

Wokwi ESP32

Third party Tool

Tier 1 · Web · No account

Version tested: Compiled and booted by the Wokwi gate (ESP32 Arduino core 3.3.11); captured in the Wokwi web editor on 2026-09-09. Date: 2026-09-09.

Open the ESP32 editor, paste diagram.json, then paste sketch.ino.

Open Wokwi to paste in the files (new tab)

Get the files

Use both prepared files. This is a paste-in setup; saving a project requires a Wokwi account.

diagram.json

575 bytes · Circuit connections

Download

sketch.ino

2,436 bytes · ESP32 program

Download

#include <Wire.h>

constexpr uint8_t MPU_ADDR = 0x68;
constexpr float COUNTS_PER_G = 16384.0f;
constexpr uint8_t CALIBRATION_SAMPLES = 12;

// Visible teaching bias models sensor and mounting offset for this controlled lab.
constexpr float TEACHING_BIAS_X = 0.050f;
constexpr float TEACHING_BIAS_Y = -0.020f;
constexpr float TEACHING_BIAS_Z = 0.020f;
float offsetX = 0, offsetY = 0, offsetZ = 0;

bool readAcceleration(float &x, float &y, float &z) {
  Wire.beginTransmission(MPU_ADDR);
  Wire.write(0x3B);
  if (Wire.endTransmission(false) != 0 || Wire.requestFrom(MPU_ADDR, uint8_t(6)) != 6) return false;
  int16_t rawX = (Wire.read() << 8) | Wire.read();
  int16_t rawY = (Wire.read() << 8) | Wire.read();
  int16_t rawZ = (Wire.read() << 8) | Wire.read();
  x = rawX / COUNTS_PER_G + TEACHING_BIAS_X;
  y = rawY / COUNTS_PER_G + TEACHING_BIAS_Y;
  z = rawZ / COUNTS_PER_G + TEACHING_BIAS_Z;
  return true;
}

void setup() {
  Serial.begin(115200);
  Wire.begin(21, 22);
  Wire.beginTransmission(MPU_ADDR);
  Wire.write(0x6B);
  Wire.write(0);
  const uint8_t status = Wire.endTransmission();
  Serial.printf("IMU START ack=%u range=2g scale=16384\n", status);

float sumX = 0, sumY = 0, sumZ = 0;
  for (uint8_t i = 0; i < CALIBRATION_SAMPLES; i++) {
    float x, y, z;
    if (!readAcceleration(x, y, z)) {
      Serial.println("IMU ERROR calibration read failed");
      return;
    }
    if (i == 0) Serial.printf("RAW rest ax=%.3f ay=%.3f az=%.3f\n", x, y, z);
    sumX += x;
    sumY += y;
    sumZ += z - 1.0f;
    delay(40);
  }
  offsetX = sumX / CALIBRATION_SAMPLES;
  offsetY = sumY / CALIBRATION_SAMPLES;
  offsetZ = sumZ / CALIBRATION_SAMPLES;
  Serial.printf("CAL offset ax=%.3f ay=%.3f az=%.3f samples=%u\n",
                offsetX, offsetY, offsetZ, CALIBRATION_SAMPLES);
}

void loop() {
  float rawX, rawY, rawZ;
  if (!readAcceleration(rawX, rawY, rawZ)) {
    Serial.println("IMU ERROR sample discarded");
    delay(500);
    return;
  }
  float x = rawX - offsetX;
  float y = rawY - offsetY;
  float z = rawZ - offsetZ;
  if (fabsf(x) < 0.0005f) x = 0;
  if (fabsf(y) < 0.0005f) y = 0;
  if (fabsf(z) < 0.0005f) z = 0;
  const float magnitude = sqrtf(x * x + y * y + z * z);
  Serial.printf("IMU raw=%.3f,%.3f,%.3f corrected=%.3f,%.3f,%.3f magnitude=%.3f state=%s\n",
                rawX, rawY, rawZ, x, y, z, magnitude,
                fabsf(magnitude - 1.0f) > 0.1f ? "MOTION" : "REST");
  delay(500);
}

Use the launch button above to open the ESP32 editor in Wokwi.
Select the editor’s diagram.json tab and replace all its text with the supplied diagram.json.
Select the sketch.ino tab, replace all its text with the supplied sketch.ino, then click Start Simulation.

Steps

Screens captured against Wokwi ESP32 Compiled and booted by the Wokwi gate (ESP32 Arduino core 3.3.11); captured in the Wokwi web editor on 2026-09-09 on 2026-09-09; the tool may have moved on — the text steps are the contract.

Step 1
Do
In the Wokwi simulation panel, paste diagram.json and sketch.ino into a new Wokwi ESP32 project, then trace the I2C bus.
You will see
Input: inspect diagram.json beside the running Wokwi IMU. The MPU6050 uses GPIO 21 for SDA and GPIO 22 for SCL. Its power lead reaches 3.3 V and ground is shared. Serial Monitor shows corrected=0.000,0.000,1.000 at REST.
Why it matters
The I2C and power paths are visible in the captured tool. The REST line belongs to this wired simulated board. The corrected Z axis still preserves one g. A known bus is needed before interpreting offsets.
Step 2
Do
In the Wokwi simulation panel, inspect the counts-per-g conversion, visible teaching bias, and stationary calibration loop.
You will see
Input: inspect sketch.ino while the Wokwi simulation runs. The source sets COUNTS_PER_G=16384.0 and CALIBRATION_SAMPLES=12. Visible teaching bias is X=0.050, Y=-0.020, Z=0.020. Serial Monitor shows raw=0.050,-0.020,1.020 and corrected=0.000,0.000,1.000.
Why it matters
Twelve stationary samples form the offset estimate. The corrected Z reading preserves gravity at one g. The raw and corrected tuples are both visible in this run. Subtracting gravity itself would corrupt later motion evidence.
Step 3
Do
Start Wokwi and inspect the initialization line in Serial Monitor.
You will see
Input: boot the supplied Wokwi ESP32 and MPU6050 diagram. Observed: "IMU START ack=0 range=2g scale=16384". Expected: an acknowledged 2 g range and 16384 counts per g. The run then printed a stationary raw sample.
Why it matters
ACK=0 shows the simulated I2C setup responded. The scale states how raw counts become g units. These settings precede the calibration loop. The serial label is not a physical range test.
Step 4
Do
Keep the simulated board stationary and read the first uncorrected sample in Serial Monitor.
You will see
Input: keep the simulated board stationary. Observed: "RAW rest ax=0.050 ay=-0.020 az=1.020". Expected: the visible teaching bias shifts the rest reading. The screenshot shows the same three values.
Why it matters
X and Y are offset from zero at rest. Z is 0.020 g above the ideal one-g baseline. This raw line supplies the calibration input. The offsets are deliberate firmware teaching values.
Step 5
Do
Read the calibration summary and corrected rest sample in Serial Monitor.
You will see
Input: continue through 12 stationary calibration samples. Observed: "CAL offset ax=0.050 ay=-0.020 az=0.020 samples=12". Observed: "IMU raw=0.050,-0.020,1.020 corrected=0.000,0.000,1.000 magnitude=1.000 state=REST". Expected: correction returns the rest pose to 0, 0, 1 g.
Why it matters
The offset summary reflects the 12-sample fixture. Subtracting it removes the visible teaching bias. The corrected magnitude is one g in this run. A fixed rest calibration does not cover changing physical bias.
Step 6
Do
In the MPU6050 control panel, set X acceleration to 0.5 g.
You will see
Input: set X acceleration to 0.5 g in the MPU6050 panel. Observed: "IMU raw=0.550,-0.020,1.020 corrected=0.500,0.000,1.000 magnitude=1.118 state=MOTION". Expected: corrected X rises to 0.500 g and state changes to MOTION. The panel control read X=0.5 g.
Why it matters
The calibration offset remains applied during the change. The vector magnitude rises from 1.000 to 1.118. The state transition is based on that controlled input. The simulated change is not a measured real gesture.
Step 7
Do
In the MPU6050 control panel, restore X acceleration to 0 g.
You will see
Input: restore X acceleration to 0 g in the MPU6050 panel. Observed: "IMU raw=0.050,-0.020,1.020 corrected=0.000,0.000,1.000 magnitude=1.000 state=REST". Expected: corrected rest values return. The panel control read X=0 again.
Why it matters
The final corrected vector matches the earlier baseline. The state returns from MOTION to REST. The unchanged Y/Z values help isolate the X change. This verifies the simulator sequence only.

Chapter checks

These questions refer to the chapter’s examples. Use the return links to review their answers.

What physically moves inside a MEMS capacitive accelerometer when the device accelerates?
Return to the chapter’s knowledge check
An ADXL335 outputs 300 mV/g with 0 g at 1.5 V. Its axis reads 1.20 V while stationary. What is happening?
Return to the chapter’s knowledge check
Why can a single MEMS accelerometer not distinguish a slow tilt from a genuine horizontal acceleration?
Return to the chapter’s knowledge check

Return to IMU Motion and Barometric Calibration Limits · Browse Labs

Wokwi ESP32

Get the files

diagram.json

sketch.ino

Steps

1 Step 1

2 Step 2

3 Step 3

4 Step 4

5 Step 5

6 Step 6

7 Step 7

Chapter checks

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7