Johnson Noise Voltage Calculator

Calculator Form

Resistor Value

Resistance Unit

Resistor Network

Network Count

Temperature

Temperature Unit

Bandwidth

Bandwidth Unit

Preferred Voltage Unit

Decimal Places

Example Data Table

Resistance	Temperature	Bandwidth	Voltage Density	Noise Voltage
100.000 Ω	290.00 K	1.000 kHz	1.266 nV/√Hz	40.019 nV
1.000 kΩ	290.00 K	10.000 kHz	4.002 nV/√Hz	400.194 nV
4.700 kΩ	300.00 K	20.000 kHz	8.824 nV/√Hz	1.248 µV
10.000 kΩ	350.00 K	100.000 kHz	13.903 nV/√Hz	4.396 µV
1.000 MΩ	300.00 K	1.000 MHz	128.716 nV/√Hz	128.716 µV

Formula Used

The Johnson or thermal noise RMS voltage is calculated with:

V_n = √(4kTRB)

Where k is Boltzmann’s constant, T is absolute temperature in Kelvin, R is equivalent resistance in ohms, and B is bandwidth in hertz.

The calculator also shows these related values:

Voltage spectral density: √(4kTR) V/√Hz
Current noise density: √(4kT/R) A/√Hz
Matched-load voltage: V_n / 2
Available noise power: kTB
Estimated peak-to-peak noise: about 6.6 × RMS

How to Use This Calculator

Enter the resistor value and choose its unit.
Select whether the resistors are single, series, or parallel.
Enter the number of identical resistors in the network.
Enter temperature and choose Celsius, Kelvin, or Fahrenheit.
Enter bandwidth and choose Hz, kHz, or MHz.
Pick the preferred display unit for voltage outputs.
Choose decimal places for cleaner reporting.
Press the calculate button to show results above the form.
Use the chart to inspect how bandwidth changes noise voltage.
Download the current result as CSV or PDF.

Notes

This tool uses the equivalent resistance from the selected network. A series network increases total resistance. A parallel network decreases it.

The matched-load voltage is lower because half the source noise voltage drops across the source resistance and half across the equal load resistance.

The graph holds resistance and temperature constant while sweeping bandwidth around your chosen value.

Frequently Asked Questions

1) What is Johnson noise voltage?

Johnson noise voltage is the random thermal noise produced by charge motion inside any resistor above absolute zero. It depends on temperature, resistance, and measurement bandwidth.

2) Why does bandwidth change the result?

A wider bandwidth includes more noise energy. Because voltage scales with the square root of bandwidth, doubling bandwidth does not double voltage; it increases by the square root of two.

3) Why is temperature converted to Kelvin?

The thermal-noise equation uses absolute temperature. Kelvin starts at absolute zero, so it correctly reflects the physical energy driving random electron motion inside the resistor.

4) What does matched-load voltage mean?

Open-circuit noise is the source voltage of the resistor alone. When a matched load is connected, the voltage across that load becomes half of the open-circuit RMS value.

5) Does higher resistance always mean more voltage noise?

Yes, voltage noise density rises with the square root of resistance. However, current noise density falls with resistance, so the important metric depends on the circuit you are analyzing.

6) Is Johnson noise present without applied current?

Yes. Thermal noise exists even with no external signal or current flow. It comes from random microscopic motion caused by temperature inside the resistor material.

7) How can I reduce Johnson noise in practice?

Use lower resistance when possible, narrow the measurement bandwidth, reduce operating temperature, and place amplification carefully so added circuit noise does not dominate the thermal noise floor.

8) What does the Plotly graph show?

The graph sweeps bandwidth while keeping your other inputs fixed. It shows how RMS noise voltage increases with bandwidth, helping you compare measurement windows or filter choices.