The Thermistor

Learning Goals 5 min

1. Wire an NTC thermistor with a 10 kΩ partner resistor as a voltage divider, and explain why the voltage on A0 changes with temperature.
2. Convert an ADC reading to thermistor resistance using the divider equation, then to temperature in °C using the simplified Steinhart-Hart (β-parameter) formula.
3. Pinch the thermistor between your fingers and watch the printed °C climb in real time — your first quantitative real-world measurement.

Warm-Up 10 min

So far we've used the ADC to read "0–1023". That's a number, not a temperature. To get to °C we need two conversions and one formula. Together they aren't scary — but skipping the explanation leaves you with magic incantations. Today we earn the magic.

Quick puzzle

An NTC thermistor has resistance 10 kΩ at 25 °C. As it gets hotter, the resistance:

1. (a) goes up
2. (b) goes down
3. (c) stays the same

New Concept · Voltage divider + β equation 20 min

The voltage divider

The thermistor and a 10 kΩ resistor in series, between +5 V and GND, form a voltage divider. The voltage at the midpoint depends on the ratio of the two resistors:

V_out = 5 V × R_fixed / (R_thermistor + R_fixed)

When the thermistor is at 25 °C, it's 10 kΩ — same as the fixed resistor — so V_out = 2.5 V exactly. As the thermistor heats up and its resistance drops, R_fixed becomes the bigger of the two, so V_out rises toward 5 V. Cool the thermistor → its resistance rises → V_out drops toward 0 V.

Wiring it up

Two components, three wires, one analog reading. Don't worry about which way the thermistor faces — it's a passive resistor with no polarity.

From V_out back to thermistor resistance

The ADC reads V_out as a number 0–1023. We need to go backwards through the divider to get the thermistor's actual resistance. Rearranging the divider equation:

R_thermistor = R_fixed × (1023 / raw - 1)

(Quick sanity check: when raw = 511 — half-way — that gives 10000 × (1023/511 - 1) ≈ 10020 Ω, almost exactly 10 kΩ. Matches the 25 °C case. Good.)

From resistance to temperature — the β equation

The full Steinhart-Hart equation has three coefficients and an awkward logarithm. For Level 2 we use the simplified β-parameter form, which uses only one extra constant β (beta — typically around 3950 for hobby thermistors):

1/T_K = 1/T0_K + (1/β) × ln(R / R0)

where:

• T_K = current temperature in Kelvin (what we want).
• T0_K = reference temperature in Kelvin — usually 298.15 (which is 25 °C).
• R0 = thermistor resistance at the reference — for a 10 kΩ NTC, R0 = 10000.
• R = current thermistor resistance (we just computed it).
• β = the thermistor's "beta" constant — typically 3950 for the common 10 kΩ NTC modules sold for Arduino.

Solve for T_K, then convert to °C by subtracting 273.15. In C++:

float tK = 1.0 / (1.0/298.15 + (1.0/3950.0) * log(R / 10000.0));
float tC = tK - 273.15;

log here means natural log (base e) in C++ — the standard convention. Don't use log10 by accident.

Putting it together

int raw = analogRead(A0);
float R = 10000.0 * (1023.0 / raw - 1.0);
float tK = 1.0 / (1.0/298.15 + (1.0/3950.0) * log(R / 10000.0));
float tC = tK - 273.15;

That's the whole conversion. From here you can Serial.print(tC, 1) for one decimal place, compare to a threshold, trigger an alert, log it. Tomorrow's Personal Thermometer project does all of that.

Worked Example · Read the thermistor and print °C 20 min

Step 1 — wiring

Build the divider as described above. Thermistor between +5 V and A0; 10 kΩ resistor between A0 and GND. Three breadboard wires. Take a moment to double-check both ends of the divider make solid contact — a loose wire here gives a wandering reading.

Step 2 — the sketch

Save as thermistor-read.ino:

// L02-11: NTC thermistor → °C using β-equation
const int THERM = A0;
const float R_FIXED = 10000.0;     // partner resistor in ohms
const float R0      = 10000.0;     // thermistor R at reference temperature
const float T0_K    = 298.15;      // reference temperature in Kelvin (25 °C)
const float BETA    = 3950.0;      // thermistor beta constant

void setup() {
  Serial.begin(9600);
}

void loop() {
  int raw = analogRead(THERM);
  float R  = R_FIXED * (1023.0 / raw - 1.0);
  float tK = 1.0 / (1.0/T0_K + (1.0/BETA) * log(R / R0));
  float tC = tK - 273.15;

  Serial.print("raw: "); Serial.print(raw);
  Serial.print("   R: "); Serial.print(R, 0);
  Serial.print(" Ω   T: "); Serial.print(tC, 1);
  Serial.println(" °C");

  delay(500);
}

Step 3 — upload and read

Open Serial Monitor. With the thermistor sitting in still room air:

raw: 512   R: 9961 Ω   T: 25.0 °C
raw: 511   R: 10020 Ω  T: 24.9 °C
raw: 513   R: 9902 Ω   T: 25.1 °C

Should hover around your room temperature — ~25 °C if you're in an air-conditioned classroom; ~28 °C if it's a warm afternoon. Some jitter is normal; you can apply L02-08's smoothing to flatten it.

Step 4 — pinch the thermistor

Squeeze the thermistor between your fingertip and thumb. Watch the temperature climb steadily over 30–60 seconds toward 32–34 °C (your skin temperature). Release — it drops back to room temp over the next 30 seconds. The Arduino is now a thermometer.

Step 5 — sanity check with a real thermometer

If you have a kitchen thermometer or a phone with a temperature sensor, compare. The Arduino reading should be within ±2 °C of the truth across normal room ranges. If it's consistently 3 °C too high or too low, tweak BETA up or down by ~100 and re-test.

Try It Yourself 20 min

float tF = tC * 9.0 / 5.0 + 32.0;
Serial.print(tC, 1); Serial.print(" °C   ");
Serial.print(tF, 1); Serial.println(" °F");

float readTempC(int pin) {
  int raw = analogRead(pin);
  float R  = R_FIXED * (1023.0 / raw - 1.0);
  float tK = 1.0 / (1.0/T0_K + (1.0/BETA) * log(R / R0));
  return tK - 273.15;
}

Mini-Challenge · The cold-warm-hot indicator 15 min

Use the thermistor on A0, plus three LEDs (blue on D9, green on D10, red on D11 — each with its own 220 Ω). Wire them as in L02-05's RGB lesson but using three separate LEDs.

The sketch reads the temperature and lights exactly one LED:

• Blue if T < 24 °C (cool).
• Green if 24 ≤ T < 30 °C (normal room).
• Red if T ≥ 30 °C (warm/hot).

It works if:

• At rest in a typical Malaysian classroom (~26 °C) → green is on.
• Pinch the thermistor for 60 seconds → red turns on (your skin is warmer than 30 °C).
• Blow on the thermistor (the breath is cooler than skin) → may flicker between red and green as it cools.
• Submerge it briefly in a glass of ice water (carefully, don't splash the Arduino) → blue turns on.

const int THERM = A0;
const int BLUE  = 9;
const int GREEN = 10;
const int RED   = 11;
const float R_FIXED = 10000.0;
const float R0      = 10000.0;
const float T0_K    = 298.15;
const float BETA    = 3950.0;

float readTempC() {
  int raw = analogRead(THERM);
  float R  = R_FIXED * (1023.0 / raw - 1.0);
  float tK = 1.0 / (1.0/T0_K + (1.0/BETA) * log(R / R0));
  return tK - 273.15;
}

void setColour(int b, int g, int r) {
  digitalWrite(BLUE,  b);
  digitalWrite(GREEN, g);
  digitalWrite(RED,   r);
}

void setup() {
  pinMode(BLUE,  OUTPUT);
  pinMode(GREEN, OUTPUT);
  pinMode(RED,   OUTPUT);
  Serial.begin(9600);
}

void loop() {
  float t = readTempC();
  Serial.print("T: "); Serial.print(t, 1); Serial.println(" °C");

  if (t < 24)        setColour(HIGH, LOW,  LOW);    // blue
  else if (t < 30)   setColour(LOW,  HIGH, LOW);    // green
  else               setColour(LOW,  LOW,  HIGH);   // red

  delay(500);
}

Recap 5 min

A thermistor changes its resistance with temperature. Put it in series with a fixed 10 kΩ resistor across +5 V and GND, and the midpoint voltage carries the temperature information. The Arduino reads the voltage, you compute the thermistor's resistance from the divider equation, then you plug R into the β-equation to get Kelvin, subtract 273.15 to get Celsius. Wrap the maths in a helper function and you have a clean readTempC() you can use anywhere. Tomorrow we turn all of this into a polished Personal Thermometer project with thresholds and alarms.

Thermistor

A resistor whose resistance changes significantly with temperature. NTC = resistance drops as temperature rises. PTC = opposite.

NTC (Negative Temperature Coefficient)

The common kind in hobby kits. 10 kΩ NTC = 10 kΩ at 25 °C, lower above, higher below.

Voltage divider

Two resistors in series across a voltage. The midpoint voltage = V_total × R_lower / (R_upper + R_lower). Used to convert a variable resistance into a variable voltage.

β (beta) parameter

The single thermistor constant in the simplified Steinhart-Hart equation. Typically 3950 for the common 10 kΩ NTC.

Kelvin

Absolute temperature scale where 0 K is absolute zero. T(K) = T(°C) + 273.15.

log() (in C++)

Natural logarithm — base e. Not base 10. (Base 10 is log10().)

Homework 5 min

Three temperatures, three places. Run your thermistor sketch in three different spots and record what you see:

1. Inside the fridge for 30 seconds (carefully — keep the Arduino out, dangle just the thermistor leads through the door).
2. On your desk at room temperature.
3. Held against your skin for 60 seconds.

For each, note the displayed °C, your expected °C (use a kitchen thermometer or just common sense), and the difference. If the readings are within 2 °C across the board, your circuit is solid.

Bonus question: If your reading is consistently 2 °C high in all three measurements, what one constant would you change to fix it? (Hint — re-read the "watch out!" note on β.)

Bring back next class:

• Your three-temp comparison table.
• Your answer to the bonus question.
• Your hw-l02-11.ino sketch — bring it on your laptop. Tomorrow it becomes the personal thermometer.