Thermal Noise Calculator

Calculator Inputs

Example Data Table

Use your actual filter or measurement bandwidth for best accuracy.

Formula Used

• Thermal noise voltage (rms): V_rms = √(4 k T R B)
• Thermal noise current (rms): I_rms = V_rms / R
• Voltage density: e_n = √(4 k T R) in V/√Hz
• Matched noise power: P = k T B
• Resistor power option: P = V_rms² / R
• Noise figure and gain: P_out = P × F × G, where F = 10^(NF/10), G = 10^(Gain/10)

Here, k is Boltzmann’s constant (1.380649×10⁻²³ J/K), T is absolute temperature in Kelvin, R is resistance in ohms, and B is bandwidth in hertz.

How to Use This Calculator

1. Enter temperature and choose its unit.
2. Enter resistance representing the circuit path.
3. Set bandwidth to your filter or measurement range.
4. Pick the noise power model that matches your case.
5. Add noise figure, gain, and impedance for system estimates.
6. Press submit and review results above the form.
7. Use CSV or PDF exports for project documentation.

Professional Notes on Thermal Noise in Construction Electronics

Thermal noise (also called Johnson–Nyquist noise) is the unavoidable electrical “hiss” produced by resistive materials whenever they are above absolute zero. On construction projects, it matters most in low‑level signal paths: sensor loops, long cable runs, instrumentation panels, building automation networks, and temporary site monitoring setups. Knowing the expected noise level helps you separate normal physics from real faults such as loose terminations, damaged shielding, moisture ingress, or incorrect filtering.

This calculator estimates the rms noise voltage created by a resistance over a chosen bandwidth. Bandwidth is often the hidden driver: when bandwidth increases, noise rises with the square root of bandwidth. That means a 100× wider measurement bandwidth produces only 10× higher rms noise, but that increase can still dominate sensitive measurements. Temperature also matters, especially in hot plant rooms, outdoor enclosures, and sun‑heated panels. Resistance is a proxy for how much thermal agitation can convert into voltage.

For system budgeting, many engineers track noise power using the matched kTB model. If you are looking at a specific resistor in a circuit, the calculator can also report the equivalent power using V_rms²/R. Optional noise figure and gain fields help you estimate how receiver stages or conditioners elevate and amplify the noise floor. The impedance field converts output noise power into an easy‑to‑interpret rms voltage estimate for a given system reference impedance.

Example with realistic site values

Suppose a control loop has R = 1,000 Ω, ambient 27 °C, and an effective measurement bandwidth of 20,000 Hz. The expected input noise is about 0.576 µV rms, and matched noise power is about -130.8 dBm. These values are small, but they become relevant when signals are millivolts or lower, or when high gain is applied.

In practice, you reduce noise impact by narrowing bandwidth with proper filtering, keeping impedances appropriate for the sensor type, ensuring correct grounding and shielding, and avoiding unnecessary gain early in the chain. When measured noise is far above the estimate, investigate cable routing near VFDs, poor bonding, corroded terminals, or incorrect input ranges. Accurate expectations make troubleshooting faster and design choices safer.

FAQs

1) What is thermal noise in simple terms?

It is random voltage caused by electron motion inside resistive materials. It exists in every cable, resistor, and sensor circuit whenever temperature is above 0 K.

2) Why does bandwidth increase the noise?

Noise energy spreads across frequency. A wider measurement bandwidth collects more of that noise, so rms noise increases with the square root of bandwidth.

3) Which resistance should I enter for a field loop?

Use the effective resistance that dominates the noise you care about: sensor element resistance, termination, or the input resistance that the signal is referenced across.

4) When should I use the matched kTB power model?

Use it for system noise budgets, receiver sensitivity checks, and link-style calculations where noise is treated as available power delivered to a matched load.

5) What does noise figure do in this calculator?

Noise figure represents extra noise added by active stages compared with an ideal device. The calculator applies it as a power multiplier to estimate a higher output noise floor.

6) Is this the only noise source on construction sites?

No. Switching drives, poor shielding, ground loops, and EMI coupling can dwarf thermal noise. This tool estimates the unavoidable baseline so you can spot abnormal contributions.

7) How can I lower noise in practice?

Reduce bandwidth, shorten high-impedance runs, use proper shielding and bonding, separate signal and power routing, and avoid excessive gain before filtering and averaging.