Skip to content
ComputeVerse.ai

Communication Systems

Thermal Noise & Noise Figure Calculator

kTB thermal noise power, noise power spectral density, noise temperature from noise figure, and the receiver noise floor.

About this calculator

Every resistor at a temperature above absolute zero generates noise — the Johnson–Nyquist noise discovered experimentally by Johnson and explained by Nyquist in 1928. The available noise power from any matched source is N = kTB: Boltzmann's constant, absolute temperature, and bandwidth. Nothing about the resistor's value appears — only how hot it is and how much bandwidth you accept.

At the standard reference temperature T₀ = 290 K, the noise power spectral density kT₀ is −174 dBm/Hz — the single most-quoted number in receiver design. Every doubling of bandwidth adds 3 dB: a 1 MHz receiver channel starts from −114 dBm before the receiver's own noise is counted.

The receiver's own contribution is captured by its noise figure NF, defined at the 290 K reference (Friis, 1944). The input-referred noise floor is then kT₀B in dBm plus NF — the level a signal must exceed by the required SNR for the link to work. The same information can be expressed as an equivalent noise temperature Tₑ = T₀(F − 1), the form preferred for satellite receivers where noise figures are fractions of a dB.

This calculator evaluates all four quantities and shows how they connect, so a bandwidth, a temperature, and a noise figure turn into the one number a link budget needs: the noise floor.

Assumptions

  • Available noise power into a matched (conjugate-matched) load; mismatch reduces the delivered noise below kTB.
  • B is the equivalent noise bandwidth of the receiver, which for real filter shapes differs slightly from the −3 dB bandwidth.
  • The Rayleigh–Jeans approximation behind N = kTB, valid for radio frequencies at ordinary temperatures (hf ≪ kT).

When to use this calculator

Appropriate for

  • Estimating thermal noise power and the noise floor for a given bandwidth and temperature
  • Finding a receiver's noise figure contribution to the system noise budget
  • Teaching the kTB noise relationship and the −174 dBm/Hz reference

Not suitable for

  • Systems dominated by non-thermal noise (phase noise, quantization, interference, 1/f), which this does not model
  • Cascaded noise-figure analysis of a full receiver chain without applying the Friis formula stage by stage
  • Final sensitivity specification without measured device noise figures and the actual operating temperature

What this calculator does not cover

  • Thermal (Johnson–Nyquist) noise only — flicker (1/f) noise, shot noise, phase noise, and man-made interference all add on top of kTB.
  • The quantum correction matters at very high frequency or cryogenic temperature (hf comparable to kT) — beyond the Rayleigh–Jeans region this formula overestimates the noise.
  • Single-stage noise figure: the noise contribution of a cascade of stages requires the Friis cascade formula, which is not computed here.
  • As with every calculator on this site: results are preliminary and educational, are not verified for any specific installation, and must be reviewed against the applicable code edition and stamped by a licensed Professional Engineer before real-world use.

Frequently asked questions

Where does −174 dBm/Hz come from?

It is kT₀ at the IEEE reference temperature of 290 K expressed in dBm: 10·log₁₀(1.380649×10⁻²³ × 290 / 1 mW) ≈ −173.98 dBm/Hz. Add 10·log₁₀ of your bandwidth in hertz to get the thermal noise level in that bandwidth.

Why doesn't the resistor value appear in kTB?

A larger resistance generates a larger noise voltage but delivers it from a larger source impedance; into a matched load, the available power is independent of R. Only temperature and bandwidth set the available noise power.

Noise figure or noise temperature — which should I use?

They carry the same information: Tₑ = 290·(F − 1). Noise figure in dB is convenient for terrestrial receivers with NF of a few dB; noise temperature resolves small differences better and is standard for satellite ground stations, where a 0.1 dB change in NF is tens of kelvin.

References

  • Johnson, J. B., “Thermal Agitation of Electricity in Conductors,” Physical Review, vol. 32, 1928
  • Nyquist, H., “Thermal Agitation of Electric Charge in Conductors,” Physical Review, vol. 32, 1928
  • Friis, H. T., “Noise Figures of Radio Receivers,” Proceedings of the IRE, vol. 32, 1944
  • Pozar, D. M., Microwave Engineering, 4th ed., Ch. 10 (noise in microwave circuits)

Related calculators

Get the ComputeVerse.ai quick reference

A free engineering quick-reference PDF, plus a note when new calculators launch across the library — one or two emails a month, nothing else.