Resistor Thermal Noise Model
Every resistor generates random thermal noise (Johnson-Nyquist noise) due to the random motion of charge carriers at any temperature above absolute zero. The noise can be modelled as either a voltage source in series with an ideal noiseless resistor, or a current source in parallel.
k = 1.381 × 10−23 J/K (Boltzmann constant). Noise increases with resistance, temperature, and bandwidth.
Resistor Noise Calculator
Every resistor generates random electrical noise because its charge carriers are in constant thermal motion. This thermal noise (Johnson-Nyquist noise) exists at any temperature above absolute zero, regardless of resistor quality or construction. It sets the ultimate sensitivity floor for analogue circuits — audio preamps, sensor front-ends, RF receivers, and precision measurement systems all hit this limit. The calculator above computes RMS noise voltage, noise current, spectral density, noise power, and optional excess (1/f) noise from the Johnson-Nyquist formula.
The Johnson-Nyquist Formula
In = √(4kTΔf / R) — RMS noise current (Norton model)
en = √(4kTR) — voltage spectral density (nV/√Hz)
Pn = kTΔf — available noise power (independent of R)
k = Boltzmann’s constant = 1.3806 × 10−23 J/K. T = absolute temperature in Kelvin. R = resistance in ohms. Δf = bandwidth in Hz. The Thévenin model (voltage source in series with noiseless resistor) and Norton model (current source in parallel with noiseless resistor) are electrically equivalent — use whichever suits your circuit analysis.
Calculator Inputs
R (Resistance) — the resistor value. Higher R produces more noise voltage but less noise current. A 10 kΩ resistor generates ~10× the noise voltage of a 100 Ω resistor at the same temperature and bandwidth.
T (Temperature) — operating temperature in °C or Kelvin. Defaults to 25 °C (298.15 K). Noise voltage scales with √T — cooling from 25 °C to −40 °C only reduces noise by ~11%.
Δf (Bandwidth) — system or measurement bandwidth in Hz, kHz, or MHz. Noise voltage scales with √Δf — halving bandwidth reduces noise by ~29%. Narrowing bandwidth (with a filter or slower ADC) is the most practical way to reduce measured noise.
NI (Noise Index) — optional, in dB from the resistor data sheet. Accounts for excess noise (1/f or flicker noise) caused by DC current flowing through the resistive element. Only active when DC voltage is also provided.
VDC — optional, the DC voltage across the resistor. Combined with Noise Index to calculate excess noise, since 1/f noise is proportional to the applied voltage.
Worked Example — Audio Preamp (10 kΩ, 20 kHz)
Vn = √(3.293 × 10−13)
Vn ≈ 1.81 μV RMS
Spectral density = √(4 × 1.38×10−23 × 298.15 × 10000) = 12.8 nV/√Hz
1.81 μV is the thermal noise floor of a 10 kΩ resistor across the audio band. Any signal below this level is buried in resistor noise. A low-noise op-amp with input noise well below 12.8 nV/√Hz (such as 1–5 nV/√Hz) ensures the resistor, not the amplifier, sets the noise floor.
RF Receiver Front-End (50 Ω, 1 MHz)
Vn ≈ 0.91 μV RMS
Spectral density = 0.91 nV/√Hz
The 50 Ω source resistance sets the noise floor for the receiver. A low-noise amplifier (LNA) with a noise figure of 1–2 dB adds only slightly to this thermal baseline.
High-Impedance Sensor (1 MΩ, 100 Hz)
Vn ≈ 1.28 μV RMS
Spectral density = 128.6 nV/√Hz
Despite the narrow 100 Hz bandwidth, the 1 MΩ source resistance pushes the spectral density to 128.6 nV/√Hz — much higher than the 50 Ω case. High-impedance sensor circuits need amplifiers with very low current noise (pA/√Hz range) to avoid degrading the signal further.
What Affects Noise — and What Does Not
Resistance (Dominant Factor for Voltage Noise)
Noise voltage scales with √R. Reducing resistance from 10 kΩ to 1 kΩ cuts noise voltage by √10 ≈ 3.16×. But lower resistance means higher noise current (In scales with 1/√R). Whether voltage noise or current noise dominates depends on the impedance of the circuit around the resistor. Understanding how resistors interact in a network is covered in our Series & Parallel Resistor Calculator.
Bandwidth (Most Practical Lever)
Noise voltage scales with √Δf. A 10× reduction in bandwidth gives a √10 ≈ 3.16× noise reduction. This is the easiest knob to turn — add a low-pass filter, use a narrower-band ADC, or average multiple readings.
Temperature (Secondary Factor)
Noise scales with √T (in Kelvin). Going from 25 °C (298 K) to −40 °C (233 K) reduces noise by √(233/298) ≈ 0.88 — only a 12% improvement. Cryogenic cooling (77 K liquid nitrogen) gives √(77/298) ≈ 0.51 — a 2× improvement. For most circuits, cooling is not a practical noise reduction strategy.
Resistor Construction (No Effect on Thermal Noise)
Thermal noise depends only on R, T, and Δf. Carbon film, metal film, thin film, wirewound — all produce identical thermal noise for the same resistance value. Construction type only matters for excess noise (below).
Excess Noise (1/f Noise)
When DC current flows through a resistor, an additional noise component appears that increases at lower frequencies — hence “1/f” or flicker noise. This excess noise depends on the resistor’s construction, the applied DC voltage, and the measurement bandwidth.
NI = Noise Index in dB (from data sheet)
Typical values: carbon composition −10 to 0 dB, thick film −20 to −10 dB, metal film −40 to −20 dB, thin film < −40 dB
Excess noise matters most in low-frequency, high-impedance circuits with significant DC bias — precision strain gauge amplifiers, DC-coupled sensor interfaces, and audio circuits with high-value feedback resistors. For RF and wideband circuits, thermal noise dominates and excess noise is negligible.
Total Noise (Thermal + Excess)
Thermal noise and excess noise are independent, so they combine as root sum of squares:
The calculator computes this automatically when both Noise Index and DC voltage are provided.
Noise Models — Thévenin vs. Norton
The Thévenin model represents the noisy resistor as a noise voltage source Vn in series with a noiseless resistor R. The Norton model represents it as a noise current source In in parallel with noiseless R. Both are equivalent. Use Thévenin when analysing series circuits (voltage dividers, series feedback networks). Use Norton when analysing parallel circuits (transimpedance amplifiers, current-mode signal chains).
Practical Design Implications
Choose Resistance Carefully
In voltage-mode circuits, lower resistance = lower noise voltage. Use the smallest resistance that meets other design constraints (gain, bias current, power dissipation). In current-mode circuits (transimpedance amplifiers), higher resistance = lower noise current but higher noise voltage — optimise for the impedance that minimises total noise at the output.
Filter Aggressively
Every Hz of bandwidth you do not need adds noise. Place the anti-alias or band-limiting filter as early in the signal chain as practical. A 1 kHz bandwidth instead of 100 kHz reduces noise by 10×.
Pick the Right Resistor Type
For DC and low-frequency precision circuits, use metal film or thin film resistors — their excess noise is 20–40 dB lower than carbon composition or thick film. For AC-only or high-frequency circuits where 1/f noise is filtered out, construction type does not matter.
Frequently Asked Questions
Last updated: March 2026