Resistor Noise Calculator

Every resistor generates tiny random noise from the thermal motion of electrons.

How the Math Works

The thermal noise voltage is calculated using the formula V_n = √(4·k·T·R·B), where k is Boltzmann's constant (1.38×10^-23 J/K), T is absolute temperature in Kelvin, R is resistance in ohms, and B is bandwidth in hertz. This equation derives from statistical mechanics, representing the root mean square (RMS) voltage generated by random electron motion in a resistor. The noise increases with resistance and bandwidth, but only with the square root of temperature, meaning it grows slowly as components heat up. The factor of 4 accounts for the two-sided power spectral density of white noise.

Practical Applications

Engineers use this calculation to design low-noise circuits in sensitive applications like audio amplifiers, medical devices, or radio receivers. By inputting component values and operating conditions, designers can predict noise floors and select optimal resistor values or bandwidth limits. For instance, in a high-gain sensor circuit, minimizing thermal noise ensures accurate signal detection. The formula also guides decisions on cooling systems or shielding to reduce temperature-related noise in precision measurements.

Day-to-Day Use

While invisible to users, thermal noise impacts the quality of everyday electronics. Your smartphone's microphone uses circuits designed with this calculation to minimize static in calls, and high-fidelity speakers rely on low-noise amplifiers for clear audio. Medical devices like portable ECG machines depend on these principles to capture heartbeats accurately. Even in wireless charging systems, controlling resistor noise prevents interference with other devices. Understanding this helps manufacturers produce more reliable, quieter consumer products we use daily.

Worked example

10 kΩ at 300 K over 20 kHz → about 1.8 µV.

FAQ