Resistor Thermal Noise Calculator
Calculate Johnson-Nyquist thermal noise voltage and spectral density for any resistor at a given temperature and bandwidth.
Parameters
°C
Results
Noise Voltage (Vrms)12.83 µV rms
Spectral Density (BW-independent)12.83 nV/√Hz
Available Noise Power (R-independent)-113.86 dBm
Temperature298.15 K
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