Johnson Noise Calculator
Enter resistance, temperature, and bandwidth. The Johnson Noise Calculator instantly computes RMS thermal noise voltage and power spectral density.
About the Johnson Noise Calculator
The Johnson Noise Calculator is a precise, scientifically accurate tool that computes Johnson-Nyquist thermal noise — the fundamental voltage noise generated by thermal agitation of charge carriers in any resistor at equilibrium. This Johnson Noise Calculator implements the exact Nyquist formula V_rms = √(4 k T R Δf), discovered by John B. Johnson (1928) and theoretically explained by Harry Nyquist. Proudly supported by Agri Care Hub.
Scientific Formula
Noise Power Spectral Density: S_v(f) = 4 k_B T R (white noise)
k_B = 1.380649 × 10⁻²³ J/K (Boltzmann constant)
Why This Calculator Is Essential
Johnson noise is the ultimate thermal limit in: • Ultra-low noise amplifiers • Precision measurement and metrology • Radio astronomy receivers • Quantum computing readout • Sensor and detector systems • Analog circuit design It sets the irreducible noise floor for any resistive element and is independent of material (universal).
How to Use
- Enter resistance R in ohms.
- Enter temperature T in Kelvin (300 K = room temperature).
- Enter bandwidth Δf in Hz (measurement frequency range).
- Click “Calculate Johnson Noise”.
- Get RMS voltage noise and power density.
When Should You Use This Tool?
- Low-noise amplifier design
- Precision voltage reference noise budget
- Sensor readout electronics
- Radio receiver sensitivity calculation
- Quantum device characterization
- Teaching thermal noise fundamentals
Scientific Foundation
Johnson noise was experimentally discovered by John Bertrand Johnson at Bell Labs in 1928 and theoretically derived by Harry Nyquist using thermodynamic equilibrium and equipartition. The formula V_rms = √(4 k T R Δf) is exact for classical systems and valid down to very low temperatures (with quantum corrections at h f >> k T). Full theory at Johnson Noise on Wikipedia and all electronics textbooks.
Conclusion
The Johnson Noise Calculator brings the fundamental thermal noise limit to your browser — with perfect accuracy and beautiful design. Whether you’re a student learning circuit noise, a researcher designing ultra-sensitive instruments, or an engineer building low-noise electronics, this tool delivers precise results every time. For more physics tools, visit Agri Care Hub.