Calculate resistor thermal noise voltage, resistance, temperature, or bandwidth from the other three values using RMS units and temperature conversions.

Resistor Noise Calculator

Enter any 3 values to calculate the missing variable

Resistor Noise Voltage Formula

Resistor noise voltage, also called thermal noise or Johnson noise, is the random RMS voltage generated by the thermal motion of charge carriers in any resistor. This calculator estimates that noise over a specified bandwidth so you can quickly judge whether a resistor, sensor network, or front-end stage will be noise-limited.

NV = \sqrt{4 k T R B}

Where:

Symbol Meaning Typical Unit
NV RMS noise voltage across the resistor over the selected bandwidth V RMS, nV RMS, or µV RMS
k Boltzmann constant 1.380649 × 10-23 J/K
T Absolute temperature K
R Resistance Ω
B Measurement or effective noise bandwidth Hz

The result increases with resistance, temperature, and bandwidth, but not linearly. Because the relationship is square-root based, a large change in any input produces a smaller proportional change in the final noise voltage.

Noise Density Form

When comparing components, engineers often use noise density rather than total integrated noise. The resistor’s voltage noise density is:

e_n = \sqrt{4 k T R}

If the bandwidth is flat, total RMS noise is found by multiplying that density by the square root of bandwidth:

NV = e_n \sqrt{B}

Useful rule of thumb: at about 300 K, a 1 kΩ resistor contributes roughly 4.07 nV/√Hz.

Equivalent Current Noise

The same thermal noise can also be represented as an equivalent input current source, which is useful when comparing resistor noise against source impedance or amplifier current noise.

i_n = \sqrt{\frac{4 k T}{R}}

Temperature Conversion

Thermal noise depends on absolute temperature, so Celsius or Fahrenheit must be converted to Kelvin before calculation.

T_K = T_{^\circ C} + 273.15
T_K = \frac{5}{9}\left(T_{^\circ F} - 32\right) + 273.15

How the Result Changes

Change Effect on Noise Voltage
Resistance increases 4× Noise voltage doubles
Bandwidth increases 100× Noise voltage increases 10×
Absolute temperature doubles Noise voltage increases by about 1.41×
Resistance, bandwidth, or temperature drops to one-fourth Noise voltage is cut in half

Example

For a 1 kΩ resistor at 300 K over a 1 kHz bandwidth:

e_n = \sqrt{4 k T R} \approx 4.07\ \text{nV}/\sqrt{\text{Hz}}
NV = e_n \sqrt{1000} \approx 128.7\ \text{nV RMS}

This shows why even simple resistor values matter in low-level analog design. A quiet amplifier cannot recover detail that is already buried under thermal noise generated ahead of it.

Quick Reference at 300 K

Resistance Approx. Voltage Noise Density
100 Ω 1.29 nV/√Hz
1 kΩ 4.07 nV/√Hz
10 kΩ 12.87 nV/√Hz
100 kΩ 40.70 nV/√Hz
1 MΩ 128.72 nV/√Hz

Bandwidth Matters More Than Many Users Expect

The bandwidth in the formula is the bandwidth through which noise is allowed to pass. In practical circuits, that usually means the effective noise bandwidth of the filter, amplifier, ADC front end, or measurement instrument. Narrowing the band is often the simplest way to reduce measured noise.

For a first-order low-pass filter, the equivalent noise bandwidth is slightly higher than the -3 dB cutoff frequency:

B_{ENBW} \approx \frac{\pi}{2} f_c

Practical Design Notes

  • Lower resistance usually means lower voltage noise, but it can increase loading, current draw, and power consumption.
  • Lower temperature reduces thermal noise, but in most everyday circuits bandwidth control is the easier design lever.
  • Use the resistor’s actual operating temperature if self-heating is significant.
  • Series and parallel resistor networks can often be evaluated from the equivalent resistance seen at the terminals, provided the network is passive and at a uniform temperature.
  • This calculator models thermal noise only. It does not include amplifier input noise, shot noise, quantization noise, EMI pickup, resistor tolerance, or excess 1/f noise.

Common Questions

Why is the result expressed as RMS voltage?
Thermal noise is random, not a steady DC value. RMS expresses its effective magnitude in a way that relates directly to signal and power calculations.
Why doesn’t the applied voltage appear in the formula?
Ideal thermal noise exists even with no applied signal. It is set by temperature, resistance, and bandwidth rather than the circuit’s DC voltage across the resistor.
Does a larger resistor always create more voltage noise?
For thermal voltage noise, yes. Higher resistance increases voltage noise density. However, the equivalent current noise decreases as resistance increases, which is why source impedance matters when selecting front-end components.
What bandwidth should I enter?
Enter the effective bandwidth over which the circuit or instrument actually passes noise. If a filter is present, use its equivalent noise bandwidth rather than only the nominal cutoff whenever possible.