Thermal (Johnson–Nyquist) Noise
Every resistor generates a random noise voltage from the thermal motion of its charge carriers. This tool gives the RMS noise voltage and current across a resistance over a bandwidth, and the available noise power delivered to a matched load — the famous kTB, which is −174 dBm/Hz at room temperature and sets the noise floor of every receiver.
Equations & Parameters ▸
\(v_n = \sqrt{4 k T R B},\qquad i_n = \sqrt{\dfrac{4kTB}{R}}\)
\(P_{\text{avail}} = k T B \quad(\text{W}),\qquad \dfrac{P}{B} = kT = -174\ \text{dBm/Hz at }290\,\text{K}\)
\(P_{\text{avail}} = k T B \quad(\text{W}),\qquad \dfrac{P}{B} = kT = -174\ \text{dBm/Hz at }290\,\text{K}\)
| R | Resistance (Ω). |
| T | Absolute temperature (K). 290 K is the standard reference (≈17 °C). |
| B | Noise bandwidth (Hz). |
| vn | Open-circuit RMS noise voltage; the available power (to a matched load) is vn²/4R = kTB. |
| k | Boltzmann constant = 1.381×10⁻²³ J/K. |
References: J. B. Johnson, Phys. Rev. 32, 1928; H. Nyquist, Phys. Rev. 32, 1928. · D. M. Pozar, Microwave Engineering, 4th ed., Wiley, 2012.
Inputs
Ω
Source resistanceK
290 K ≈ 17 °CHz
Noise bandwidthResults
Noise source
RMS noise voltage vn—
RMS noise current in—
Voltage density—
Available power
Noise power kTB—
Noise power (dBm)—
Density kT—
Diagram