ElectroCalc

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

ResistanceNoise Voltage (rms)
100 Ω40.7 nV
1 kΩ128.7 nV
10 kΩ407 nV
100 kΩ1.29 µV
1 MΩ4.07 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