How do I use this calculator?

Enter the required values; results and step-by-step derivation update automatically.

Where is Resistor Noise used?

Electricity, engineering, research, and related scientific disciplines.

What formulas does this use?

All standard resistor noise formulas are applied and shown step-by-step in the results.

Can I get step-by-step solutions?

Yes. The calculator shows a full step-by-step derivation when results are displayed.

How accurate are the results?

Results use standard floating-point arithmetic (~15 significant digits). Suitable for education and professional use.

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Resistor Noise

Johnson-Nyquist thermal noise: V_n = √(4kTRB). All resistors at T > 0 K generate white noise. Excess noise from DC current.

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V_n = √(4kTRB). 1 kΩ at 300 K, 1 kHz BW: V_n ≈ 4 nV. Spectral density √(4kTR) ≈ 0.13 nV/√Hz per √(kΩ) at 300 K. Excess noise: carbon comp high; metal film, foil low. SNR = 10 log₁₀(P_signal/P_noise) dB.

Key quantities

V_n = √(4kTRB)

Johnson Noise

Key relation

√(4kTR) V/√Hz

Spectral Density

Key relation

∝ I·√R·B

Excess Noise

Key relation

Signal/Noise power

SNR

Key relation

Ready to run the numbers?

Why: Low-noise amplifiers, sensors, and RF systems require noise budgeting. Johnson noise sets fundamental limit.

How: Thermal noise: V_n = √(4kTRB). k=1.38×10⁻²³ J/K. Excess noise index (dB) for carbon comp; metal film quieter.

V_n = √(4kTRB). 1 kΩ at 300 K, 1 kHz BW: V_n ≈ 4 nV.Spectral density √(4kTR) ≈ 0.13 nV/√Hz per √(kΩ) at 300 K.

Sources:IEEE - Noise in CircuitsNIST - Johnson Noise

Run the calculator when you are ready.

Calculate Resistor NoiseEnter resistance, temperature, bandwidth for Johnson-Nyquist and excess noise

🎚️ Low Noise Preamplifier Design

Designing input stage for precision audio amplifier with 10kΩ resistor

📡 Sensor Interface Circuit

Temperature sensor with 1kΩ pull-up resistor at 50kHz bandwidth

🔬 Precision Measurement System

High-precision voltage measurement with 100kΩ reference resistor

🔊 Audio Amplifier Input

Audio preamp with 47kΩ input resistor, 20Hz-20kHz bandwidth

📻 RF Receiver Frontend

RF frontend with 50Ω matching resistor at 1MHz bandwidth

🌡️ High Temperature Application

Resistor at elevated temperature (100°C) for industrial application

Input Parameters

Calculation Mode

Resistance (R) - Ω

Temperature

Temperature Unit

Bandwidth (Δf) - Hz

Signal Voltage (Vs) - V

Excess Noise Type

Frequency Spectrum Analysis (Optional)

Min Frequency - Hz

Max Frequency - Hz

Frequency Points

❓ Frequently Asked Questions

What is Johnson-Nyquist noise and why does it occur?

Johnson-Nyquist noise (also called thermal noise) is the random voltage fluctuations generated by all resistors due to the thermal motion of charge carriers. It occurs at any temperature above absolute zero and is white noise with constant spectral density. The noise voltage is proportional to the square root of resistance, temperature, and bandwidth.

How does excess noise differ from thermal noise?

Excess noise (also called current noise or 1/f noise) occurs when DC current flows through a resistor. Unlike thermal noise which is always present, excess noise depends on the resistor material, construction, and DC voltage. Wire-wound resistors have the lowest excess noise, while carbon resistors have the highest. Excess noise typically increases with frequency as 1/f noise.

What is noise spectral density and why is it important?

Noise spectral density (en) is the noise voltage per square root of bandwidth, measured in V/√Hz. It's frequency-independent for thermal noise (white noise), making it useful for noise analysis at any frequency. To find total noise voltage, multiply spectral density by the square root of bandwidth. Typical values range from 0.1 nV/√Hz to 100 nV/√Hz.

How do I reduce noise in my circuit design?

To reduce noise: (1) Use lower resistance values when possible (noise ∝ √R), (2) Reduce operating temperature, (3) Minimize bandwidth to only what's needed, (4) Choose low-noise resistor types (wire-wound or thin-film), (5) Avoid excess noise by minimizing DC voltage across resistors, (6) Use low-noise op-amps and proper grounding techniques.

What is a good signal-to-noise ratio (SNR)?

SNR requirements vary by application: Audio systems need 60+ dB for high quality, 40-60 dB is acceptable. Precision measurements require 80+ dB. RF systems typically need 20-30 dB minimum. The calculator shows SNR in both linear and dB scales. Higher SNR indicates better signal quality relative to noise floor.

How does temperature affect resistor noise?

Temperature directly affects Johnson-Nyquist noise - noise voltage increases with the square root of absolute temperature. At room temperature (293 K), noise is relatively low. Cooling resistors reduces thermal noise, which is why precision instruments often operate at reduced temperatures. Excess noise is less temperature-dependent but may increase slightly with temperature.

Which resistor types have the lowest noise?

For thermal noise, all resistors have the same Johnson-Nyquist noise at the same temperature and resistance. For excess noise: Wire-wound resistors have the lowest (-40 dB/decade), followed by thin-film (-30 dB/decade), thick-film (-20 dB/decade), and carbon resistors (-10 dB/decade). For low-noise applications, choose wire-wound or precision thin-film resistors.

📚 Official Data Sources

IEEE Standards Association

IEEE standards and publications on electronic noise, Johnson-Nyquist noise, and resistor specifications

Last Updated: 2026-02-07

NIST Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology standards for electronic components, noise measurements, and thermal noise

Last Updated: 2026-02-07

Electronics Tutorials

Comprehensive tutorials on resistor noise, thermal noise, excess noise, and noise analysis in electronic circuits

Last Updated: 2026-02-07

Analog Devices

Technical articles and application notes on low-noise design, resistor selection, and noise analysis

Last Updated: 2026-02-07

⚠️ Disclaimer: This calculator provides theoretical noise estimates based on standard Johnson-Nyquist and excess noise models. Actual noise values may vary due to resistor manufacturing tolerances, temperature gradients, parasitic capacitances, circuit layout, electromagnetic interference, and component aging. Excess noise indices are typical values and may vary significantly between manufacturers and production batches. For critical applications such as precision instrumentation, medical devices, or low-noise amplifiers, always verify noise measurements using calibrated test equipment and consult manufacturer datasheets. This calculator is for educational and design planning purposes only.

Please enter a valid resistance value greater than 0

For educational and informational purposes only. Verify with a qualified professional.

🔬 Physics Facts

📡

Johnson (1928) and Nyquist (1928) derived thermal noise from thermodynamics.

— IEEE

📐

White noise: flat spectrum up to ~100 GHz at room temperature.

— NIST

⚡

Excess noise: 1/f at low f; depends on current and material.

— Analog Devices

📊

Metal film resistors: ~0.1 μV/V excess noise; carbon comp >10 μV/V.

— Component specs

What is Resistor Noise?

Resistor noise is the random electrical noise generated by resistors due to fundamental physical processes. The primary source is thermal noise (Johnson-Nyquist noise), which arises from the random thermal motion of charge carriers. Additionally, resistors can exhibit excess noise (current noise) when DC current flows through them, which depends on the resistor material and construction.

Johnson-Nyquist Noise

Thermal noise is present in all resistors at any temperature above absolute zero. It's white noise with constant spectral density.

Key Characteristics:

Present in all resistors
White noise spectrum
Proportional to √R
Proportional to √T

Noise Spectral Density

Noise voltage per square root of bandwidth. This parameter is frequency-independent for thermal noise.

Units:

V/√Hz
nV/√Hz (typical)
Frequency independent
White noise

Excess Noise

Additional noise that occurs when DC current flows through a resistor. Depends on resistor material and construction.

Resistor Types:

Wire-wound: Lowest
Thin-film: Low
Thick-film: Moderate
Carbon: Highest

How Does Resistor Noise Work?

Resistor noise calculations involve understanding thermal noise (Johnson-Nyquist noise), noise spectral density, excess noise, and their impact on signal-to-noise ratio. The calculator uses fundamental physics equations to determine noise characteristics.

🔬 Calculation Methods

Johnson-Nyquist Noise

1Enter resistance value (R) in ohms
2Enter temperature (T) in Celsius or Kelvin
3Enter bandwidth (Δf) in Hz
4Calculate: Vn = √(4kTRΔf)

Noise Spectral Density

Calculate spectral density: en = √(4kTR)
Independent of frequency (white noise)
Useful for noise analysis at any frequency
Multiply by √bandwidth for total noise

When to Use Resistor Noise Calculator

Resistor noise calculation is essential for electronic engineers designing low-noise circuits, precision measurement systems, audio amplifiers, sensor interfaces, and RF receivers. Understanding noise characteristics helps optimize circuit performance and select appropriate components.

Low Noise Preamplifiers

Design input stages for audio amplifiers, instrumentation amplifiers, and low-noise signal conditioning circuits.

Applications:

Audio preamps
Instrumentation amps
Low-noise op-amps

Precision Measurement

Analyze noise in precision voltage references, ADC input circuits, and high-resolution measurement systems.

Benefits:

Noise floor analysis
ADC resolution limits
Measurement accuracy

RF Receiver Design

Optimize noise performance in RF frontends, matching networks, and receiver input stages.

Design Tasks:

Noise figure analysis
Matching network design
SNR optimization

Resistor Noise Calculation Formulas

Understanding resistor noise formulas is essential for electronic circuit design. These formulas relate noise to resistance, temperature, bandwidth, and signal levels.

📊 Core Noise Formulas

Johnson-Nyquist Noise (Vn)

V_n = \\sqrt{4kTR\\Delta f}

Thermal noise voltage in a resistor, where k is Boltzmann's constant (1.38×10⁻²³ J/K), T is absolute temperature in Kelvin, R is resistance in ohms, and Δf is bandwidth in Hz.

Noise Voltage Spectral Density (en)

e_n = \\sqrt{4kTR} = \\frac{V_n}{\\sqrt{\\Delta f}}

Noise voltage per square root of bandwidth. This is frequency-independent for thermal noise (white noise). Typical values range from 0.1 nV/√Hz to 100 nV/√Hz.

Noise Power (Pn)

P_n = kT\\Delta f

Available noise power from a resistor. Interestingly, this is independent of resistance value and depends only on temperature and bandwidth. At room temperature (293 K), this is approximately -174 dBm/Hz.

Signal-to-Noise Ratio (SNR)

\\text{SNR} = \\frac{V_s}{V_n} = 20\\log_{10}\\left(\\frac{V_s}{V_n}\\right) \\text{ dB}

Ratio of signal voltage to noise voltage. Higher SNR indicates better signal quality. Typical requirements range from 20 dB (acceptable) to 60+ dB (high quality).

Excess Noise (Vexcess)

V_{\\text{excess}} = V_{dc} \\times \\sqrt{\\frac{R}{1\\text{k}\\Omega}} \\times \\sqrt{\\frac{\\Delta f}{1\\text{Hz}}} \\times 10^{\\text{ENI}/20}

Additional noise that occurs when DC current flows through a resistor. ENI (Excess Noise Index) is typically -40 dB/decade for wire-wound resistors, -30 dB/decade for thin-film, -20 dB/decade for thick-film, and -10 dB/decade for carbon resistors.

Total Noise (Vtotal)

V_{\\text{total}} = \\sqrt{V_{\\text{johnson}}^2 + V_{\\text{excess}}^2}

Combined noise from thermal (Johnson-Nyquist) and excess noise sources. Since these are uncorrelated, they add in quadrature (square root of sum of squares).

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⬅️Jump in and explore the concept!

Resistor Noise

🎚️ Low Noise Preamplifier Design

📡 Sensor Interface Circuit

🔬 Precision Measurement System

🔊 Audio Amplifier Input

📻 RF Receiver Frontend

🌡️ High Temperature Application

Input Parameters

Frequency Spectrum Analysis (Optional)

❓ Frequently Asked Questions

What is Johnson-Nyquist noise and why does it occur?

How does excess noise differ from thermal noise?

What is noise spectral density and why is it important?

How do I reduce noise in my circuit design?

What is a good signal-to-noise ratio (SNR)?

How does temperature affect resistor noise?

Which resistor types have the lowest noise?

📚 Official Data Sources

IEEE Standards Association

NIST Electronics and Electrical Engineering Laboratory

Electronics Tutorials

Analog Devices

🔬 Physics Facts

What is Resistor Noise?

Johnson-Nyquist Noise

Noise Spectral Density

Excess Noise

How Does Resistor Noise Work?

🔬 Calculation Methods

Johnson-Nyquist Noise

Noise Spectral Density

When to Use Resistor Noise Calculator

Low Noise Preamplifiers

Precision Measurement

RF Receiver Design

Resistor Noise Calculation Formulas

📊 Core Noise Formulas

Johnson-Nyquist Noise (Vn)

Noise Voltage Spectral Density (en)

Noise Power (Pn)

Signal-to-Noise Ratio (SNR)

Excess Noise (Vexcess)

Total Noise (Vtotal)

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