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What is thermal noise and why is it −174 dBm/Hz?

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Thermal noise is the random voltage produced by thermal agitation of charge carriers in any resistor, described by Johnson and Nyquist in 1928.[1][2] The available noise power is P = kTB, where k = 1.380649×10−23 J/K. At the standard reference temperature T0 = 290 K this is about −174 dBm in a 1 Hz bandwidth, the floor against which all receiver noise is measured.[3]

How is −174 dBm/Hz derived?

kT at 290 K = 1.38×10−23 × 290 = 4.00×10−21 W/Hz = 4.00×10−18 mW/Hz. 10·log10(4.00×10−18) = −173.98 dBm/Hz. Scale by bandwidth: N(dBm) = −174 + 10·log10(B), so 1 MHz gives −114 dBm and 20 MHz gives −101 dBm.

What is the noise voltage of a resistor?

The open-circuit rms noise voltage is vn = √(4kTRB). A 50 Ω resistor at 290 K in 1 MHz bandwidth produces about 0.90 µV rms; the voltage density is about 0.90 nV/√Hz. Into a matched load, the delivered power is kTB because only half the voltage appears across the load.[2]

Is thermal noise white?

Yes, to an excellent approximation at radio frequencies: the classical formula holds while hf ≪ kT, true up to the terahertz range at room temperature. Other noise sources include shot noise (in² = 2qIB) and flicker (1/f) noise, which matters for direct-conversion receivers and oscillator phase noise.[4]

Why does thermal noise matter?

It sets the minimum detectable signal. Receiver sensitivity is −174 + NF + 10·log10(B) + SNRmin. External noise picked up by antennas (galactic, atmospheric, man-made) can exceed thermal noise at HF and VHF; ITU-R P.372 tabulates it.[5]

Frequently asked questions

What is kT at room temperature?

At 290 K, kT ≈ 4.0×10⁻²¹ W/Hz, or −174 dBm/Hz.

Does noise depend on resistance value?

Available noise power does not; the open-circuit voltage scales with √R.

Why 290 K?

IEEE adopted 290 K as the standard reference temperature for noise figure; it is close to room temperature and makes kT a round number.

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

  1. “Thermal Agitation of Electricity in Conductors”. J. B. Johnson, Physical Review, vol. 32, pp. 97-109. 1928.
  2. “Thermal Agitation of Electric Charge in Conductors”. H. Nyquist, Physical Review, vol. 32, pp. 110-113. 1928.
  3. “Microwave Engineering, 4th ed.”. D. M. Pozar, Wiley. 2012.
  4. “RF Microelectronics, 2nd ed.”. B. Razavi, Prentice Hall. 2012.
  5. “Recommendation ITU-R P.372: Radio noise”. ITU-R. current version.
Categories: Fundamentals