NTC Thermistor Divider

Vout = Vcc × Rntc / (Rntc + Rfixed)

Quick answer

This calculator solves Vout = Vcc × Rntc / (Rntc + Rfixed) for Output Voltage. With Supply Voltage 26.4 V, NTC Resistance 10 kΩ, Fixed Resistor 22 kΩ, the result is 8.25 V. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Output Voltage (V)
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Formula

Vout = Vcc × Rntc / (Rntc + Rfixed)

Description

The simplest NTC thermistor interface circuit is a voltage divider with a fixed resistor. As temperature increases, the NTC resistance decreases, changing the output voltage. The fixed resistor value is chosen to maximize sensitivity at the temperature range of interest, typically equal to the NTC resistance at the center of the desired measurement range. The output voltage is then measured by an ADC and converted to temperature using the Steinhart-Hart equation or a lookup table. This circuit provides a low-cost temperature measurement solution with good accuracy.

Variables

  • Vout — Voltage at the divider output (V)
  • Vcc — Supply voltage (V)
  • Rntc — NTC thermistor resistance at current temperature (Ω)
  • Rfixed — Fixed series resistor (Ω)

Practical Notes

Place the NTC in the upper position (connected to Vcc) for a positive temperature coefficient of voltage, or in the lower position (connected to ground) for negative. Choose Rfixed = Rntc at the midpoint of the measurement range for best linearity. Self-heating must be controlled by limiting current through the thermistor. A 10kΩ NTC at 25°C with 3.3V supply and 10kΩ fixed resistor dissipates only 0.27 mW, causing negligible self-heating.

Symbols and units

Symbol Meaning Default unit Accepted units
Vout Output Voltage V pV, nV, µV, mV, V, kV
Vcc Supply Voltage V pV, nV, µV, mV, V, kV
Rntc NTC Resistance kΩ mΩ, Ω, kΩ, MΩ
Rfixed Fixed Resistor kΩ mΩ, Ω, kΩ, MΩ

Step by step

  1. 1. What you know: Supply Voltage 26.4 V, NTC Resistance 10 kΩ, Fixed Resistor 22 kΩ
  2. 2. The relation: Vout = Vcc × Rntc / (Rntc + Rfixed)
  3. 3. Substitute: Vcc = 26.4 V, Rntc = 10 kΩ, Rfixed = 22 kΩ
  4. 4. Result: Output Voltage = 8.25 V

Related quantities from the same inputs

  • P = V² / R = 69.7 mW
  • I = V / R = 2.64 mA

Worked examples

Minimum range

Given: Supply Voltage 0.726 V, NTC Resistance 100 Ω, Fixed Resistor 0.22 kΩ

Result: Output Voltage = 0.2269 V

Low range

Given: Supply Voltage 7.26 V, NTC Resistance 1 kΩ, Fixed Resistor 2.2 kΩ

Result: Output Voltage = 2.269 V

Typical

Given: Supply Voltage 26.4 V, NTC Resistance 10 kΩ, Fixed Resistor 22 kΩ

Result: Output Voltage = 8.25 V

High range

Given: Supply Voltage 0.506 kV, NTC Resistance 100 kΩ, Fixed Resistor 0.22 MΩ

Result: Output Voltage = 158.1 V

Maximum range

Given: Supply Voltage 5.06 kV, NTC Resistance 1 MΩ, Fixed Resistor 2.2 MΩ

Result: Output Voltage = 1.581 kV

Solving for each variable

Solve for Output Voltage

Supply Voltage 0.726 V, NTC Resistance 100 Ω, Fixed Resistor 0.22 kΩ → 0.2269 V

Solve for Supply Voltage

Output Voltage 0.33 V, NTC Resistance 100 Ω, Fixed Resistor 0.22 kΩ → 1.056 V

Solve for NTC Resistance

Output Voltage 0.33 V, Supply Voltage 0.726 V, Fixed Resistor 0.22 kΩ → 0.1833 kΩ

Solve for Fixed Resistor

Output Voltage 0.33 V, Supply Voltage 0.726 V, NTC Resistance 100 Ω → 120 Ω

How Output Voltage changes with Supply Voltage

Supply Voltage (input) Output Voltage (result)
2.64 V 0.825 V
6.6 V 2.063 V
13.2 V 4.125 V
19.8 V 6.187 V
26.4 V 8.25 V
39.6 V 12.37 V
52.8 V 16.5 V
105.6 V 33 V
0.1848 kV 57.75 V
0.264 kV 82.5 V

The same result in other units

Unit Value
µV 8250000
mV 8250
V 8.25
kV 0.00825

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Frequently asked questions

How do you calculate NTC Thermistor Divider?

Use Vout = Vcc × Rntc / (Rntc + Rfixed). With Supply Voltage 26.4 V, NTC Resistance 10 kΩ, Fixed Resistor 22 kΩ, Output Voltage works out to 8.25 V.

What is the formula for NTC Thermistor Divider?

The formula is Vout = Vcc × Rntc / (Rntc + Rfixed). The simplest NTC thermistor interface circuit is a voltage divider with a fixed resistor.

How do you find Supply Voltage when you know the other values?

Rearrange for Supply Voltage: with Output Voltage 0.33 V, NTC Resistance 100 Ω, Fixed Resistor 0.22 kΩ, Supply Voltage is 1.056 V.

How do you find NTC Resistance when you know the other values?

Rearrange for NTC Resistance: with Output Voltage 0.33 V, Supply Voltage 0.726 V, Fixed Resistor 0.22 kΩ, NTC Resistance is 0.1833 kΩ.

What units does NTC Thermistor Divider use?

Output Voltage is shown in µV, mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Sensors & ADC formulas →
ADC Resolution (LSB) ADC Theoretical SNR Steinhart-Hart Temperature Wheatstone Bridge Linear Sensor Transfer Function Oversampling SNR Improvement RTD Callendar-Van Dusen NTC Thermistor Divider

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