Introduction
In hobbyist and industrial projects alike, raw analog or digital sensor readings often drift, display offset, or suffer from non‑ideal scaling. A common remedy is to calibrate the sensor so that the Arduino’s measured values map accurately onto real‑world units. When you have two known reference points, the simplest, most reliable approach is the two‑point linear calibration formula.
This guide walks you through the theory, offers a step‑by‑step Arduino sketch, dives into software filtering and algorithm optimization, and shows you how to apply the technique to a variety of sensors. By the end, you’ll be able to turn a noisy, uncalibrated input into a precise, repeatable measurement with minimal code overhead.
1. The Math Behind Two‑Point Linear Calibration
1.1 Linear Relationship Basics
For two points \((x_1, y_1)\) and \((x_2, y_2)\) on a straight line, the slope \(m\) and intercept \(b\) are:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\qquad
b = y_1 - m \cdot x_1
\]
The calibrated value \(y\) for any raw reading \(x\) is then:
\[
y = m \cdot x + b
\]
1.2 Applying to Arduino
- \(x\) – raw input (e.g., ADC reading, voltage, or raw sensor output).
- \(y\) – calibrated real‑world value (temperature in °C, distance in cm, etc.).
- \(x_1, x_2\) – raw readings at two known reference points.
- \(y_1, y_2\) – the corresponding true values.
Because the Arduino’s ADC is integer‑based, it’s common to keep all calculations in integer arithmetic to avoid floating‑point overhead. A standard trick is to scale the slope and intercept:
```cpp
const long SCALE = 1000; // 10⁻³ resolution
long m_scaled = ((y2 - y1) * SCALE) / (x2 - x1);
long b_scaled = (y1 SCALE) - (m_scaled x1) / SCALE;
```
Later, the calibrated value is obtained by:
```cpp
long calibrated = (m_scaled * raw + b_scaled) / SCALE;
```
This keeps the math in integer form while preserving sub‑unit precision.
2. Step‑by‑Step Arduino Implementation
Below is a complete sketch that demonstrates two‑point calibration for a TMP36 temperature sensor. The same principle applies to any sensor that produces a linear output.
```cpp
/* Two‑Point Linear Calibration Demo
- Sensor: TMP36 (3.0V -> 0°C, 1.5V -> 75°C)
- Arduino: AVR (Uno, Nano, etc.)
- Author: Your Name
*/
const int analogPin = A0; // TMP36 connected to A0
const long SCALE = 1000; // 10⁻³ resolution for integer math
// Reference points
// 1) 0°C at 1.5V (ADC ≈ 512)
// 2) 75°C at 3.0V (ADC ≈ 1023)
const long raw1 = 512; // ADC at 0°C
const long raw2 = 1023; // ADC at 75°C
const long real1 = 0; // °C
const long real2 = 75; // °C
// Pre‑calculated slope and intercept (scaled)
const long m_scaled = ((real2 - real1) SCALE) / (raw2 - raw1); // 751000 / 511 ≈ 147
const long b_scaled = (real1 SCALE) - (m_scaled raw1) / SCALE; // 0 - (147*512)/1000 ≈ -75
void setup() {
Serial.begin(9600);
Serial.println("Two‑Point Linear Calibration Demo");
}
void loop() {
long raw = analogRead(analogPin); // 0–1023
long calibrated = (m_scaled * raw + b_scaled) / SCALE; // °C
float voltage = raw * (5.0 / 1023.0); // For display
Serial.print