How to Use the Resistor Noise Calculator
Every resistor generates a small random voltage across its terminals due to the thermal motion of electrons — a phenomenon known as Johnson-Nyquist noise, or simply thermal noise. This noise exists in any resistor at any temperature above absolute zero, even with no current flowing, and it sets a fundamental noise floor for analog circuits, sensors, and RF front ends. This calculator uses the standard Johnson-Nyquist formula to estimate the RMS noise voltage, RMS noise current, noise voltage density, and available noise power for a resistor given its resistance, temperature, and measurement bandwidth.
The Johnson-Nyquist Noise Formula
The open-circuit RMS thermal noise voltage generated by a resistor is Vn = √(4·k·T·R·Δf), where k is Boltzmann's constant (1.380649 × 10⁻²³ J/K), T is the absolute temperature in kelvin, R is the resistance in ohms, and Δf is the noise bandwidth in hertz. Because the resistor behaves as a Thevenin source with series resistance R, the short-circuit RMS noise current is In = Vn / R = √(4·k·T·Δf / R). Dividing the voltage formula by √Δf gives the noise voltage spectral density en = √(4·k·T·R), expressed in volts per root-hertz (V/√Hz) — a single number that lets you scale the noise to any bandwidth by multiplying by √Δf.
Why Noise Power Doesn't Depend on Resistance
When a noisy resistor is connected to a matched load (a second resistor of the same value), the maximum power transferred to that load is P = k·T·Δf, the available noise power. Notice that R cancels out entirely: a 100 Ω resistor and a 1 MΩ resistor deliver exactly the same available noise power at the same temperature and bandwidth. This is why RF engineers quote a universal noise floor of about −174 dBm/Hz at standard room temperature (290 K, or 16.85 °C) — it applies to any matched resistive source, and adding 10·log₁₀(Δf) gives the total noise floor for a given bandwidth.
Practical Notes for Low-Noise Design
- Thermal noise is unavoidable, but it scales with √R and √Δf, not linearly — use the smallest resistance and narrowest bandwidth the application allows.
- Metal-film and wirewound resistors behave close to ideal thermal-noise-only sources; carbon-composition and some thick-film resistors add extra 1/f ("excess") noise under DC bias that this calculator does not include.
- Independent noise sources combine by adding power (or voltage in quadrature): V_total = √(V1² + V2² + …), never by simple addition.
- Active devices (op-amps, transistors) add their own input-referred noise on top of a resistor's Johnson noise, so a full noise budget sums every contributor in quadrature.