Resistor Thermal Noise Calculator
Calculate Johnson-Nyquist thermal noise voltage and spectral density for any resistor at a given temperature and bandwidth.
Parameters
Results
Common Resistors at 25°C, BW = 1 MHz
| Resistance | Noise Voltage (rms) |
|---|---|
| 100 Ω | 40.7 nV |
| 1 kΩ | 128.7 nV |
| 10 kΩ | 407 nV |
| 100 kΩ | 1.29 µV |
| 1 MΩ | 4.07 µV |
Johnson-Nyquist Thermal Noise
Every resistor generates a small random voltage noise due to the thermal agitation of its charge carriers. This is called Johnson-Nyquist (or thermal) noise, and it sets a fundamental lower limit on the noise in any electronic circuit operating above absolute zero.
The noise power available from a resistor is independent of its resistance — it depends only on temperature and bandwidth. However, the noise voltage (across an open circuit) scales with the square root of resistance, so lower-value resistors produce less noise voltage.
Noise Voltage (rms)
Vn = √(4 × kB × T × R × BW)Spectral Density
en = √(4 × kB × T × R) [V/√Hz]Available Noise Power
Pn = kB × T × BW (independent of R)Key Points
- kB = 1.38 × 10⁻²³ J/K (Boltzmann constant)
- Lower resistance → less noise voltage (but not less noise power)
- Cooling to 77 K (liquid nitrogen) reduces noise by √(77/298) ≈ 0.51×
- Noise voltage adds in quadrature: Vtotal = √(V1² + V2²)
- This is why low-noise op-amps use small input resistors
- Noise power at room temperature, 1 MHz BW ≈ −144 dBm
Applications
- Low-noise amplifier (LNA) design
- Precision instrumentation amplifiers
- RF receiver noise figure analysis
- ADC input circuit noise budgeting
Practical Examples
Calculate the thermal noise voltage of a 10 kΩ resistor at 25°C in a 10 kHz audio bandwidth.
Vn = √(4 × 1.38×10⁻²³ × 298 × 10000 × 10000) = 1.29 µV RMS
An inverting amplifier with Rf = 100 kΩ and Rin = 10 kΩ. The feedback resistor noise referred to input in 100 kHz BW.
Vn_Rf = √(4kT × 100000 × 100000) = 40.7 µV · RTI = 40.7/10 = 4.1 µV
Did you know? Resistor thermal noise (Johnson–Nyquist noise) is an unavoidable physical limit set by temperature and bandwidth, not the resistor quality. At room temperature (290 K), a 1 kΩ resistor in a 1 MHz bandwidth generates about 4 µV RMS of noise — this defines the noise floor of precision amplifier inputs.