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

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

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

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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
Paste diagram.json and sketch.ino into a new Wokwi ESP32 project, then trace the I2C bus.
You will see
The MPU6050 uses GPIO21 for SDA, GPIO22 for SCL, 3.3 V, and a common ground.
Why it matters
A valid offset trace begins with a known bus and power boundary.
Step 2
Do
Inspect the counts-per-g conversion, visible teaching bias, and stationary calibration loop.
You will see
The sketch uses 16,384 counts per g, averages 12 stationary samples, and subtracts one g only from the Z-axis offset estimate.
Why it matters
Gravity is a reference, not an error; removing it during calibration would corrupt later tilt and motion evidence.
Step 3
Do
Start the simulation and inspect the initialization line.
You will see
The sensor at address 0x68 acknowledges with the plus-or-minus 2 g scale.
Why it matters
An ACK and explicit scale bind the following register counts to a physical unit.
Step 4
Do
Keep the simulated board stationary and read the first uncorrected sample.
You will see
The visible teaching model reports 0.050 g, -0.020 g, and 1.020 g before calibration.
Why it matters
Keeping the before-state makes the correction auditable instead of hiding it inside a library call.
Step 5
Do
Read the calibration summary and the next corrected rest sample.
You will see
Offsets of 0.050, -0.020, and 0.020 g produce corrected acceleration of 0, 0, and 1 g.
Why it matters
The corrected rest vector retains gravity while removing the modeled sensor and mounting offsets.
Step 6
Do
Select the MPU6050 and set X acceleration to 0.5 g.
You will see
Corrected X becomes 0.500 g, magnitude becomes about 1.118 g, and state changes to MOTION.
Why it matters
A magnitude threshold tests motion while remaining independent of which axis was changed.
Step 7
Do
Restore X acceleration to 0 g.
You will see
The corrected vector returns to 0, 0, 1 g with magnitude 1.000 and state REST.
Why it matters
Returning to the reference pose checks repeatability without claiming that one pose calibrates every orientation.

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

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diagram.json

sketch.ino

Steps

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2 Step 2

3 Step 3

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7 Step 7

Chapter checks

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Step 2

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Step 7