Johnson-Nyquist Noise Calculator
Enter resistance, temperature and bandwidth to compute the thermal (Johnson) noise voltage, current and power.
Input Data
Results
At a glance:Johnson-Nyquist (thermal) noise is the random voltage generated across a resistor by thermal agitation of charge carriers. The RMS noise voltage in bandwidth B is v_n = √(4·k·T·R·B), where k = 1.380649×10⁻²³ J/K is Boltzmann's constant, T temperature (K), R resistance and B bandwidth (Hz). The available noise power from a resistor into a matched load is P = k·T·B (independent of R), and the voltage spectral density is S_v = 4kTR (V²/Hz). The corresponding current noise (short-circuit) is i_n = √(4kT·B/R). It sets the fundamental noise floor of receivers and sensors; cooling and narrowing bandwidth reduce it. At 300 K, a 1 kΩ resistor in 1 Hz bandwidth gives ~4 nV RMS.
Formula
v_n = √(4kTRB)
i_n = √(4kTB/R)
P = kTB
S_v = 4kTR
$$v_n = \sqrt{4 k_B T R \Delta f}, \quad S_v = 4 k_B T R, \quad P = 4 k_B T \Delta f$$How to Use
- Enter resistance R (Ω), temperature T (K) and bandwidth B (Hz).
- The calculator returns the noise voltage (V and nV), current and power.
Case Studies
Receiver front-end
R = 50 Ω, T = 300 K, B = 1 MHz.
v_n = √(4×1.38e-23×300×50×1e6) ≈ 9.1 µV RMS.
Cooling to 77 K cuts it ~2×.
FAQ
Why does noise power not depend on R?
Although v_n grows with √R, the available power into a matched load is v_n²/(4R) = kTB, independent of R — the resistor's own R both generates and delivers the noise.
How do I reduce thermal noise?
Lower temperature (cryogenic), reduce bandwidth to only what's needed, or use lower resistance (with care for current noise). v_n ∝ √(T·B·R).
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.