Thermal Voltage

VT = k · T / q

Quick answer

This calculator solves VT = k × T / q (≈ 25.85 mV at 300 K) for Thermal Voltage. With Temperature 300 K, the result is 25.85 mV. It solves in 2 directions, so you can enter the values you have and get the one you need.

Calculator

Thermal Voltage (mV)
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Formula

VT = k × T / q (≈ 25.85 mV at 300 K)

Description

The thermal voltage is the natural voltage scale of a semiconductor junction, set by temperature and the fundamental constants. It appears in the diode equation, transistor transconductance, and small-signal emitter resistance. At room temperature it is about 26 mV, and it rises directly with absolute temperature, which is why junction behaviour drifts with temperature.

Variables

  • VT — Thermal voltage (V)
  • T — Absolute temperature (K)
  • k — Boltzmann constant 1.381×10⁻²³ J/K
  • q — Elementary charge 1.602×10⁻¹⁹ C

Practical Notes

VT ≈ T/11600 volts. It sets gm = Ic/VT and re = VT/Ie, so amplifier gain has an inherent temperature dependence that bias and feedback must compensate.

Symbols and units

Symbol Meaning Default unit Accepted units
Vt Thermal Voltage mV pV, nV, µV, mV, V, kV
T Temperature K K

Step by step

  1. 1. What you know: Temperature 300 K
  2. 2. The relation: VT = k × T / q (≈ 25.85 mV at 300 K)
  3. 3. Substitute: T = 300 K
  4. 4. Result: Thermal Voltage = 25.85 mV

Worked examples

Minimum range

Given: Temperature 7.7 K

Result: Thermal Voltage = 0.6635 mV

Low range

Given: Temperature 77 K

Result: Thermal Voltage = 6.635 mV

Typical

Given: Temperature 300 K

Result: Thermal Voltage = 25.85 mV

High range

Given: Temperature 400 K

Result: Thermal Voltage = 34.47 mV

Maximum range

Given: Temperature 4000 K

Result: Thermal Voltage = 0.3447 V

Solving for each variable

Solve for Thermal Voltage

Temperature 7.7 K → 0.6635 mV

Solve for Temperature

Thermal Voltage 10 mV → 116 K

How Thermal Voltage changes with Temperature

Temperature (input) Thermal Voltage (result)
30 K 2.585 mV
75 K 6.463 mV
150 K 12.93 mV
225 K 19.39 mV
300 K 25.85 mV
450 K 38.78 mV
600 K 51.7 mV
1200 K 103.4 mV
2100 K 0.181 V
3000 K 0.2585 V

The same result in other units

Unit Value
µV 25850
mV 25.85
V 0.02585

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Frequently asked questions

How do you calculate Thermal Voltage?

Use VT = k × T / q (≈ 25.85 mV at 300 K). With Temperature 300 K, Thermal Voltage works out to 25.85 mV.

What is the formula for Thermal Voltage?

The formula is VT = k × T / q (≈ 25.85 mV at 300 K). The thermal voltage is the natural voltage scale of a semiconductor junction, set by temperature and the fundamental constants.

How do you find Temperature when you know the other values?

Rearrange for Temperature: with Thermal Voltage 10 mV, Temperature is 116 K.

What units does Thermal Voltage use?

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

Related Concepts

All Discrete Amplifiers formulas →
Thermal Voltage Small-Signal Emitter Resistance Transistor Transconductance Diode Dynamic Resistance Common-Emitter Voltage Gain BJT Alpha–Beta Relationship Darlington Pair Current Gain Emitter-Follower Input Impedance

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