Free · Physics models
Johnson Noise Voltage and Audio Levels
Calculate open-circuit RMS thermal noise of an ideal resistor over an effective noise bandwidth.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
noise = 0.40703548 microvolt; noise Lv = -127.80735; noise Lu = -125.58887.
Vrms = √(4 kB T R B); dBV = 20 log₁₀(V/1 V); dBu uses 0.774596670 V.
Worked example
Enter these known values and leave the other values blank.
- Resistance (R)
- 1000 Ω
- Temperature (T)
- 26.85 °C
- Bandwidth (ΔF)
- 10000 Hz
- Resistor noise (E)
- 0.407 μV
- Noise level Lᵤ
- -125.6 dBu
- Noise level Lᵥ
- -127.8 dBV
Assumptions and limitations
- Calculate open-circuit RMS thermal noise of an ideal resistor over an effective noise bandwidth.
- Temperature is absolute kelvin in the equation, even when entered in Celsius or Fahrenheit. The exact SI Boltzmann constant is 1.380649×10⁻²³ J/K.
- The classical white-noise approximation ignores excess noise, frequency-dependent impedance and loading. The dBu reference is the captured rounded √0.6 V convention, not a power delivered to a load.
- Inputs and inverse outputs share the displayed unit selectors. Clear a known field to solve for it, and lock quantities that must remain fixed. Singular inverses may have no finite result.
- Positive absolute temperature, resistance and effective bandwidth are enforced. DC voltage offsets and resistor tolerances are not included.
Common questions
Does this give noise after loading?
No. It is open-circuit voltage. A matched resistor load halves the voltage.
Can zero noise have a finite dB value?
No. Logarithmic levels require positive noise voltage; zero corresponds to an unbounded negative limit.
References
Calculate open-circuit RMS thermal noise of an ideal resistor over an effective noise bandwidth. Temperature is absolute kelvin in the equation, even when entered in Celsius or Fahrenheit. The exact SI Boltzmann constant is 1.380649×10⁻²³ J/K. The classical white-noise approximation ignores excess noise, frequency-dependent impedance and loading. The dBu reference is the captured rounded √0.6 V convention, not a power delivered to a load.