Resistor Noise Calculator
Calculate RMS noise voltage of a resistor using Johnson-Nyquist formula. Free online thermal noise calculator with interactive charts and detailed breakdowns for electronics engineers and physics students.
About This Calculator
The Resistor Noise Calculator computes the Johnson-Nyquist thermal noise (RMS noise voltage) generated by any resistor. Thermal noise is an unavoidable phenomenon in electronic circuits — it arises from the random thermal motion of electrons within conductive materials. Whether you're designing sensitive audio preamplifiers, precision measurement equipment, or radio frequency circuits, understanding and calculating resistor noise is essential for achieving optimal signal-to-noise performance.
The calculation is based on the Johnson-Nyquist formula: E = √(4 × R × k_B × T × Δf), where k_B = 1.380649 × 10⁻²³ J/K is Boltzmann's constant, R is the resistance in ohms, T is the absolute temperature in Kelvin, and Δf is the bandwidth in hertz. The calculator also computes the noise level in two common audio reference scales: L_u in dBu (referenced to 0.77459667 V) and L_v in dBV (referenced to 1 V).
The RMS noise voltage depends on the square root of the bandwidth — doubling the bandwidth increases noise by only about 41%. This square-root relationship means that the first few hertz of bandwidth contribute the most noise reduction when filtering. The interactive chart shows this relationship visually, helping you understand how bandwidth affects the total noise in your circuit.
Regional Notes
Global (IN, US, UK): The resistor noise formula is universal and does not depend on region. The calculator uses SI units throughout: resistance in ohms (Ω), temperature in degrees Celsius (°C), and bandwidth in hertz (Hz). Results are displayed in volts (V) with automatic scaling to millivolts, microvolts, or nanovolts for convenient reading. Noise levels L_u (dBu) and L_v (dBV) use international standard reference voltages applicable worldwide.
Frequently Asked Questions
What is resistor noise (Johnson-Nyquist noise)?
Resistor noise, also known as Johnson-Nyquist noise or thermal noise, is the random AC voltage signal generated by the thermal agitation of electrons within a resistor. It is present in all resistors regardless of the current flowing through them and increases with temperature, resistance, and bandwidth.
How is RMS noise voltage calculated?
The RMS noise voltage is calculated using E = √(4 × R × k_B × T × Δf), where k_B = 1.380649 × 10⁻²³ J/K is Boltzmann's constant, R is the resistance in ohms, T is the absolute temperature in Kelvin, and Δf is the bandwidth in hertz.
What units are used for noise levels L_u and L_v?
L_u is measured in dBu with a reference voltage of 0.77459667 V (the voltage that dissipates 1 mW in a 600 Ω load). L_v is measured in dBV with a reference voltage of 1 V. Both are calculated as 20 × log₁₀(V / V₀) using their respective reference voltages.
Does a resistor still produce noise without current flowing?
Yes, thermal noise (Johnson-Nyquist noise) is present even when no current flows through the resistor. It is caused by the random thermal motion of electrons, which occurs at any temperature above absolute zero. This distinguishes it from other noise types like shot noise or flicker noise.
How does bandwidth affect resistor noise?
The RMS noise voltage is proportional to the square root of the bandwidth. Doubling the bandwidth increases the noise voltage by a factor of √2 (approximately 1.414). This is why limiting the bandwidth of a measurement system can significantly reduce the observed noise.
Why are low-noise resistors important in amplifier circuits?
Low-noise resistors are critical in amplifier input stages because any noise generated by the input resistor is amplified along with the desired signal. Metal film and wire-wound resistors produce significantly less noise than carbon composition resistors, making them preferred for sensitive audio and measurement applications.
What is the difference between thermal noise and current noise in resistors?
Thermal noise (Johnson-Nyquist noise) is caused by random electron motion and increases with temperature and resistance. Current noise (excess noise or 1/f noise) is caused by fluctuations in conductivity and decreases as frequency increases. Thermal noise is usually the dominant contributor in most applications.
What resistor types produce the least noise?
Thin film and metal foil resistors produce the lowest noise levels, making them ideal for precision analog circuits. Wire-wound resistors also have very low noise. Carbon composition and thick film resistors generate the most noise and should be avoided in sensitive signal paths.