In telecommunication or other systems, thermal noise (Johnson noise) is the noise generated by thermal agitation of electrons in a conductor. The noise power, P , in watts, is given by P = kT Δf , where k is Boltzmann's constant in joules per kelvin, T is the conductor temperature in kelvins, and Δf is the bandwidth in hertz.

• Thermal noise power, per hertz, is equal throughout the frequency spectrum, depending only on k and T .
• For the general case, the above definition may be held to apply to charge carriers in any type of conducting medium.

Source: from Federal Standard 1037C and from MIL-STD-188

Thermal noise is intrinsic to all resistors and is not a sign of poor design or manufacture, although resistors may also have excess noise. Electronics engineers often prefer to work in terms of noise voltage and noise current.

e_n = &radic kTR Δf

i_n = &radic kT Δf / R