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We can use a simple voltage divider circuit to measure the voltage across the thermistor.

Vout = Rt / (Rt + Rs) * Vin

Say the fixed resistor is 10K and the variable resistor is called R - the voltage output (Vo) is:

Vout = Rt / (Rt + 10K) * Vin

Remember that when you measure a voltage (Vi) into an Arduino ADC, you'll get a number.

ADC value = Vi * 1023 / Varef

So now we combine the two (Vout = Vi) and get:

ADC value = R / (R + 10K) * Vcc * 1023 / Varef

References

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