Resistor Noise Calculator — Johnson-Nyquist Thermal Noise
Any resistor at a temperature above absolute zero generates random thermal noise due to the Brownian motion of charge carriers. Enter the resistance, temperature, and signal bandwidth to calculate the RMS noise voltage, noise spectral density, and noise power floor — essential for low-noise amplifier and sensor design.
Ω
°C
Hz
Johnson-Nyquist thermal noise: V_n = √(4·k_B·T·R·B)
- 1
Temperature in Kelvin
25 + 273.15 = 298.15 K - 2
Inner product 4·k_B·T·R·B
4 × k_B × 298.15 K × 10,000 Ω × 20,000 Hz = 0k_B = 1.380649 × 10⁻²³ J/K (Boltzmann constant, exact). - 3
RMS noise voltage (V)
√(0) = 0.00000181 V - 4
RMS noise voltage (nV)
0.00000181 × 10⁹ = 1,814.697
How does this calculator work?
Johnson-Nyquist thermal noise voltage V_n = √(4·k_B·T·R·B). At room temperature (25 °C) a 10 kΩ resistor in a 20 kHz audio bandwidth produces roughly 1.8 µV rms of noise. Noise density is √(4·k_B·T·R) nV/√Hz. Temperature, resistance, and bandwidth all raise noise proportionally to their square root.
Formula
How this is calculated
Thermal noise — also called Johnson-Nyquist noise or kTB noise — is an irreducible noise source present in every resistive element at finite temperature. It arises because free electrons in a conductor undergo random Brownian motion, creating fluctuating microscopic currents. John B. Johnson measured the effect in 1927 and Harry Nyquist derived the theoretical formula the same year.
The RMS noise voltage across a resistor is V_n = √(4·k_B·T·R·B), where k_B = 1.380649 × 10⁻²³ J/K (the Boltzmann constant, exact since 2019), T is the absolute temperature in kelvin, R is the resistance in ohms, and B is the noise bandwidth in hertz over which the noise is measured. The formula shows that noise grows with the square root of resistance, temperature, and bandwidth — doubling any one of them increases the noise voltage by √2 ≈ 41%.
The voltage noise density (nV/√Hz) is the noise per unit bandwidth and is the standard figure-of-merit for op-amp and amplifier noise specifications. The noise power delivered to a matched load is k_B·T·B, which at room temperature (290 K) equals −174 dBm/Hz — the fundamental noise floor of any receiving system. Cooling the resistor (e.g., to 77 K with liquid nitrogen) reduces noise but cannot eliminate it above absolute zero.
Frequently asked questions
Not significantly for thermal noise itself — it depends only on resistance, temperature and bandwidth, not on the resistor material. However, some resistor types (e.g., carbon composition) add excess "1/f" or "flicker" noise on top of thermal noise at low frequencies. Metal-film and wire-wound resistors have the lowest excess noise and are preferred in low-noise designs.
Voltage noise density (nV/√Hz) is the noise contribution per 1-Hz bandwidth. Multiply it by the square root of your system bandwidth to get the total RMS noise. Op-amp datasheets specify input noise density so engineers can predict how much noise an amplifier adds for any bandwidth.
Available noise power from a source resistance delivered to a matched load is k_B·T·B, regardless of R. Higher resistance produces a larger noise voltage but also a higher source impedance, so the power transferred to the load stays the same. This is why the noise floor of a receiver is −174 dBm/Hz at 290 K regardless of its input impedance.
Also known as
TG we-Calculate Editorial Team. (2026). Resistor Noise Calculator — Johnson-Nyquist Thermal Noise [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/resistor-noise-calculator
TG we-Calculate Editorial Team. "Resistor Noise Calculator — Johnson-Nyquist Thermal Noise." TG we-Calculate. 2026. https://we-calculate.com/calculator/resistor-noise-calculator.
TG we-Calculate Editorial Team, "Resistor Noise Calculator — Johnson-Nyquist Thermal Noise," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/resistor-noise-calculator
@misc{wecalculate_resistor_noise_calculator, title = {Resistor Noise Calculator — Johnson-Nyquist Thermal Noise}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/resistor-noise-calculator}}, year = {2026}, note = {TG we-Calculate} }
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