Johnson Noise Calculator

Calculator Inputs

Resistance

Resistance Unit

Temperature

Temperature Unit

Bandwidth

Bandwidth Unit

Voltage Output Unit

Current Output Unit

Reset Calculator

Formula Used

Johnson noise is thermal noise generated by a resistor. This calculator uses the standard rms voltage, rms current, and available noise power relationships for a resistive source.

Vn(rms) = √(4 × k × T × R × B)

In(rms) = √(4 × k × T × B ÷ R)

Pn = k × T × B

Pn(dBm) = 10 × log10(Pn ÷ 1 mW)

Voltage density = √(4 × k × T × R) V/√Hz

Current density = √(4 × k × T ÷ R) A/√Hz

Where k is the Boltzmann constant, T is absolute temperature in kelvin, R is resistance in ohms, and B is bandwidth in hertz.

How to Use This Calculator

Enter the resistor value and choose the correct resistance unit.
Enter the operating temperature and select Kelvin, Celsius, or Fahrenheit.
Enter the effective noise bandwidth and choose its unit.
Select preferred display units for voltage noise and current noise.
Click Calculate Johnson Noise to show the result above the form.
Review rms voltage, rms current, spectral density, power in watts, and power in dBm.
Use the CSV and PDF buttons to export the calculated summary.
Inspect the Plotly graph to see how noise changes with bandwidth.

Example Data Table

Resistance	Temperature	Bandwidth	RMS Noise Voltage	RMS Noise Current	Noise Power
50 Ω	290 K	1 MHz	0.895 µV	17.897 nA	-113.98 dBm
1 kΩ	300 K	1 kHz	0.129 µV	0.129 nA	-143.83 dBm
10 kΩ	300 K	100 kHz	4.070 µV	0.407 nA	-123.83 dBm
1 MΩ	300 K	1 Hz	0.129 µV	0.129 pA	-173.83 dBm

FAQs

1. What is Johnson noise?

Johnson noise is the random electrical noise produced by thermal agitation of charge carriers inside a resistor. It exists even without applied voltage and increases with temperature, resistance, and bandwidth.

2. Why does bandwidth matter?

Noise power accumulates across the observation bandwidth. A wider measurement bandwidth includes more random noise energy, so rms noise voltage and current increase as bandwidth increases.

3. Why must temperature be absolute?

The formula uses thermodynamic temperature. That means the calculation must internally use kelvin, even if you enter Celsius or Fahrenheit values at the form level.

4. Does higher resistance always mean higher voltage noise?

For the same temperature and bandwidth, yes. Open-circuit rms voltage noise grows with the square root of resistance, while short-circuit rms current noise falls with the square root of resistance.

5. What does noise power in dBm mean?

It expresses available thermal noise power relative to 1 milliwatt. This is useful in RF and instrumentation work where designers compare weak signals and noise floors on a logarithmic scale.

6. What is spectral density?

Spectral density shows noise per square root of hertz. It helps compare components independent of total bandwidth and is commonly listed as nV/√Hz or pA/√Hz.

7. Can this calculator replace full circuit noise analysis?

No. It handles the resistor thermal-noise part only. Real circuits may also include amplifier noise, source impedance effects, filtering, matching losses, and frequency-dependent behavior.

8. When is this calculator most useful?

It is useful during sensor, amplifier, RF, data-acquisition, and low-level measurement design. It quickly estimates whether thermal noise will limit the minimum detectable signal.