Thermal Noise Calculator
Enter resistance, temperature, and bandwidth. The Thermal Noise Calculator instantly computes Johnson-Nyquist RMS voltage noise and power spectral density.
About the Thermal Noise Calculator
The Thermal Noise Calculator is a precise, scientifically accurate tool that computes Johnson-Nyquist thermal noise — the unavoidable voltage noise present in any resistor due to thermal agitation of charge carriers. This Thermal Noise Calculator implements the exact Nyquist formula V_rms = √(4 k_B T R Δf), discovered experimentally by John B. Johnson and theoretically derived by Harry Nyquist in 1928. Proudly supported by Agri Care Hub.
Scientific Formula
Noise Power Spectral Density: S_v = 4 k_B T R (V²/Hz)
k_B = 1.380649 × 10⁻²³ J/K (Boltzmann constant)
Why This Calculator Is Essential
Thermal noise (also called Johnson or Nyquist noise) is the fundamental noise floor in all electronic circuits: • Sets the ultimate sensitivity of amplifiers and receivers • Limits precision in analog measurements • Critical in low-noise design (LNA, instrumentation) • Important in radio astronomy and quantum systems • Defines kT/C noise in switched-capacitor circuits • Universal — present in every resistor regardless of material Understanding and calculating thermal noise is essential for achieving the best possible signal-to-noise ratio.
How to Use
- Enter resistance R in ohms (source or equivalent noise resistance).
- Enter temperature T in Kelvin (300 K ≈ room temperature).
- Enter bandwidth Δf in Hz (frequency range of interest).
- Click “Calculate Thermal Noise”.
- Get RMS voltage noise and spectral density.
When Should You Use This Tool?
- Low-noise amplifier and receiver design
- Precision analog circuit noise budget
- Sensor and instrumentation systems
- Radio and microwave receiver sensitivity
- Quantum device readout noise analysis
- Teaching electronic noise fundamentals
Scientific Foundation
Johnson noise was discovered by John B. Johnson at Bell Labs in 1928 while measuring resistor noise. Harry Nyquist provided the theoretical explanation using thermodynamic equilibrium and the equipartition theorem. The formula is exact in the classical limit and holds from DC to very high frequencies (with quantum corrections at very low temperatures or high frequencies). Full theory at Thermal Noise on Wikipedia and all electronics textbooks.
Conclusion
The Thermal Noise Calculator brings the fundamental limit of electronic noise to your browser — with perfect accuracy and beautiful design. Whether you’re a student learning circuit noise, a researcher designing ultra-low-noise systems, or an engineer optimizing amplifier performance, this tool delivers precise results every time. For more electronics tools, visit Agri Care Hub.