• 🎚️ Resistor Noise Calculator

    Calculate Johnson–Nyquist thermal noise voltage, current, noise density, and matched-load noise power for audio and electronic circuits.

    1. Enter Resistor and Noise Settings

    The bandwidth should be the effective noise bandwidth of the measurement or filter. For a simplified ideal rectangular 20 Hz–20 kHz passband, use 19,980 Hz. The default 20,000 Hz is a convenient approximation.

    2. Thermal Noise Results

    Open-Circuit RMS Thermal Noise Voltage — Microvolts RMS (µV)
    —Noise Voltage (V RMS)
    —Noise Density (nV/√Hz)
    —Short-Circuit Noise Current (pA RMS)
    —Current Density (pA/√Hz)
    —Noise Voltage (dBV)
    —Matched-Load Noise Power (W)
    —Matched-Load Noise Power (dBm)
    —Absolute Temperature (K)
    —Noise Bandwidth (Hz)

    3. Noise vs. Resistance

    This chart shows RMS thermal noise voltage as resistance changes, keeping temperature and bandwidth constant. The highlighted point represents your selected resistance.

    4. Compare Resistor Noise

    Compare up to five resistance values using the same temperature and bandwidth selected above.

    ResistanceNoise (µV RMS)Density (nV/√Hz)Noise (dBV)

    5. Resistor Noise Formulas

    RMS Noise Voltage: Vₙ = √(4kBTRB)
    Voltage Noise Density: eₙ = √(4kBTR)
    RMS Short-Circuit Noise Current: Iₙ = √(4kBTB/R)
    Current Noise Density: iₙ = √(4kBT/R)
    Available Matched-Load Noise Power: Pₙ = kBTB
    Voltage Level: dBV = 20 log₁₀(Vₙ / 1 V)

    Boltzmann constant: kB = 1.380649 × 10⁻²³ J/K. These formulas describe classical thermal noise for an ideal resistor over a specified bandwidth.

    6. Important Notes

    Thermal Noise: All resistive materials at temperatures above absolute zero produce thermal noise. It is present even without an applied signal.

    Noise Voltage vs. Noise Current: Open-circuit voltage noise and short-circuit current noise are two equivalent representations of the same resistor noise source. They are not separate noises to add together.

    Bandwidth: Wider measurement bandwidth increases integrated RMS noise. Noise voltage rises with the square root of bandwidth.

    Matched-Load Power: The calculated available noise power assumes an ideal conjugate-matched load and is not the power delivered to an arbitrary audio circuit.

    Noise Density: nV/√Hz describes voltage noise spectral density amplitude and is useful when comparing low-noise audio circuits.

    Real Components: Actual circuits may also exhibit 1/f noise, excess resistor noise, amplifier noise, electromagnetic interference, and other noise sources.

    Audio Use: A resistor's thermal noise alone does not determine the overall noise floor of a microphone preamp or recording system.

  • A Resistor Noise Calculator helps audio engineers, electronics enthusiasts, recording studio technicians, and circuit designers estimate the amount of electrical noise generated by a resistor.

    Resistors naturally produce a small amount of electrical noise because of the random thermal motion of charge carriers. This phenomenon is called Johnson–Nyquist noise, or simply thermal noise.

    Thermal noise is especially important when designing sensitive audio circuits, including microphone preamplifiers, recording interfaces, mixing consoles, and other low-noise electronic equipment.

    This calculator estimates RMS thermal noise voltage, voltage noise density, current noise, noise power, and noise levels in decibels using resistance, temperature, and bandwidth.

    What Is Resistor Thermal Noise?

    Thermal noise is the random electrical fluctuation produced by resistance at temperatures above absolute zero.

    Unlike interference from power cables, nearby electronics, or wireless devices, resistor thermal noise is an inherent physical property of electrical resistance.

    It exists even when no music, voice, or other signal is passing through the circuit.

    The amount of noise depends primarily on resistance, temperature, and measurement bandwidth.

    How to Calculate Resistor Noise

    The standard Johnson–Nyquist noise voltage equation is:

    Vn = √(4kTRB)

    Where:

    • Vn = RMS thermal noise voltage

    • k = Boltzmann constant

    • T = Absolute temperature in Kelvin

    • R = Resistance in ohms

    • B = Effective noise bandwidth in hertz

    For example, a 10,000-ohm resistor at approximately 20°C produces about 1.80 microvolts RMS of thermal noise over a 20,000 Hz effective noise bandwidth.

    Although this voltage is extremely small, it can become important in sensitive audio circuits that amplify weak signals.

    Why Does Resistor Noise Matter in Audio?

    Microphones can produce relatively low electrical signal levels, especially when recording quiet voices, acoustic instruments, or distant sound sources.

    A microphone preamplifier must increase the signal level while minimizing unwanted noise.

    Thermal noise from resistive elements contributes to the overall electronic noise floor.

    In low-noise audio circuit design, engineers consider resistor values, amplifier noise characteristics, source impedance, bandwidth, and circuit topology to achieve the desired performance.

    Understanding Noise Density

    Noise voltage density describes how much RMS noise voltage is generated per square root of bandwidth.

    It is commonly expressed in nanovolts per square root hertz (nV/√Hz).

    This measurement is useful when comparing resistors, amplifiers, and electronic circuit components.

    For an ideal resistor, thermal noise voltage density remains approximately constant across the ordinary audio frequency range.

    How Resistance Affects Noise

    Thermal noise voltage increases with the square root of resistance when temperature and bandwidth remain constant.

    For example, increasing resistance by a factor of four doubles the RMS thermal noise voltage.

    This does not mean that choosing the lowest possible resistor value is always the best solution. Circuit loading, power consumption, signal levels, and other design considerations also matter.

    How Temperature Affects Resistor Noise

    Higher temperatures increase thermal noise.

    The calculation uses absolute temperature in Kelvin because thermal noise is proportional to thermodynamic temperature.

    The calculator accepts Celsius, Fahrenheit, and Kelvin values and converts them to the appropriate absolute temperature.

    How Bandwidth Affects Noise

    A wider measurement bandwidth includes more thermal noise energy.

    For example, increasing the bandwidth from 5,000 Hz to 20,000 Hz increases the RMS thermal noise voltage by a factor of two, assuming the same resistance and temperature.

    This is one reason bandwidth is an important consideration when measuring and comparing electronic noise.

    Resistor Noise vs. Other Audio Noise

    Thermal noise is only one possible contributor to an audio system's noise floor.

    Other sources include amplifier voltage and current noise, power supply interference, electromagnetic interference, component excess noise, and noise introduced by connected equipment.

    This calculator estimates ideal resistor thermal noise, not the complete noise performance of an audio recording system.

    When Is a Resistor Noise Calculator Useful?

    This calculator can help when studying microphone preamplifier circuits, analyzing electronic noise floors, comparing resistor values, designing audio filters, or learning about low-noise analog electronics.

    The comparison table makes it easy to see how different resistance values affect thermal noise under identical conditions.

    Tip: Try comparing 100 Ω, 1 kΩ, 10 kΩ, 47 kΩ, and 100 kΩ resistors using the same temperature and bandwidth. You'll see how thermal noise voltage increases as resistance increases. This is a useful exercise when learning about low-noise audio circuit design and microphone preamplifiers.

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