Resistor Noise Calculator

Every resistor above absolute zero produces random electrical fluctuations because charge carriers are in continuous thermal motion. This unavoidable phenomenon is called Johnson-Nyquist noise, thermal noise, or simply resistor noise. It exists even in an ideal resistor with no applied voltage and establishes a fundamental noise floor for amplifiers, sensors, radio receivers, measurement equipment, and communication systems. The root-mean-square open-circuit noise voltage is the square root of four times Boltzmann's constant, absolute temperature, resistance, and bandwidth. This calculator uses the exact SI value of Boltzmann's constant, 1.380649 times 10^-23 joules per kelvin. Equivalent short-circuit noise current is the square root of four times Boltzmann's constant, temperature, and bandwidth divided by resistance. Available noise power delivered to a matched load is Boltzmann's constant times temperature times bandwidth. Noise grows with the square root of bandwidth. Doubling bandwidth does not double RMS voltage; it multiplies voltage by the square root of two. Noise voltage also grows with the square root of resistance and temperature. Noise current moves in the opposite direction with resistance because the same source can be represented by a Thevenin voltage or Norton current model. Voltage noise density removes the bandwidth term and is expressed in volts per square root hertz, making components easier to compare. At room temperature, a 10 kilohm resistor over the 20 kilohertz audio band produces only a few microvolts RMS, yet that can matter in a high-gain microphone preamplifier. A 50 ohm radio system has lower voltage density, but a bandwidth of hundreds of megahertz or more integrates substantial total noise. Narrowing bandwidth is therefore one of the most effective ways to improve signal-to-noise ratio when the application permits it. The formula assumes an ideal resistor, thermal equilibrium, and a frequency range where classical white-noise behavior applies. Real components and active devices add excess noise, shot noise, flicker noise, interference, and amplifier input noise. Temperature must be entered in kelvin rather than Celsius. Use the calculated thermal contribution as one term in a complete noise budget, combine independent RMS noise sources by root-sum-square, and account for transfer gain and filtering at every stage.