Noise Figure Calculator
This noise figure calculator handles four common RF and microwave scenarios: computing NF from input and output signal-to-noise ratios (linear or dB), converting a linear noise factor to noise figure, and calculating the cascaded noise figure of a multi-stage receiver chain using the Friis formula. Choose your mode, enter the values, and get noise figure in dB, equivalent noise temperature, and a worked derivation instantly.
What is noise figure?
Noise figure (NF) is a decibel measure of how much a device or system degrades the signal-to-noise ratio (SNR) as a signal passes through it. A perfect, noiseless device would have NF = 0 dB (noise factor F = 1), meaning the output SNR equals the input SNR. Any real amplifier, mixer, filter, or cable adds thermal and electronic noise, raising the NF above zero. The noise figure is defined as NF = 10 log10(F), where the linear noise factor F = SNRin / SNRout. A noise figure of 3 dB means the output SNR is half the input SNR; 10 dB means the SNR has shrunk by a factor of ten. In receiver design, minimising noise figure is critical because a poor NF directly lowers the minimum detectable signal and reduces communication range.
The Friis formula and cascaded systems
When multiple stages (amplifiers, mixers, filters) are connected in a chain, the total system noise figure is not the sum of individual noise figures. It is computed with the Friis cascade formula: F_total = F1 + (F2 - 1) / G1 + (F3 - 1) / (G1 x G2) + ... where F1, F2, ... are the linear noise factors of each stage and G1, G2, ... are their linear power gains. Because each subsequent term is divided by the cumulative gain of all preceding stages, the first stage dominates the total noise figure. This is why real receivers always place a low-noise amplifier (LNA) at the antenna port, before any lossy components such as mixers or cables. Increasing the gain of the first stage suppresses the noise contributions of all later stages. Even a 10 dB LNA gain can reduce a subsequent 6 dB mixer NF contribution by a factor of 10, from 6 dB to just 0.6 dB referred to the input.
Noise figure vs. noise temperature
Noise temperature (Te) is an alternative way to express noise performance, preferred in satellite and radio-astronomy work where noise figures are very small and the differences between 0.1 and 0.5 dB matter a great deal. The relationship is Te = T0 x (F - 1), where T0 = 290 K is the IEEE reference temperature (close to room temperature). A noise figure of 1 dB corresponds to a noise temperature of about 75 K; 3 dB corresponds to about 290 K. System noise temperature is additive, making it convenient for summing antenna noise, LNA noise, cable loss, and sky noise in a single budget. Both NF and Te carry identical information and convert exactly into each other.
How to use each mode in this calculator
This calculator provides four modes. The "NF from SNR (linear)" mode is the most fundamental: enter the linear signal-to-noise ratios before and after the device, and the calculator applies F = SNRin / SNRout directly. The "NF from SNR (dB)" mode is equivalent but uses the fact that in decibels, NF = SNRin_dB - SNRout_dB. The "Noise factor to NF" mode converts a known linear noise factor F (from a datasheet) into its decibel equivalent. The "Cascaded system (Friis)" mode is the most practical: enter the noise figure and gain of each stage in dB for up to six stages, and the calculator applies the full Friis formula to give the total NF, total gain, equivalent noise temperature, the contribution of each stage, and a chart showing how NF and cumulative gain evolve stage by stage.
Noise figure quality benchmarks by application
| Application | Typical NF (dB) | First-stage device | Quality |
|---|---|---|---|
| Deep-space / radio astronomy | < 0.3 | Cryogenic LNA | Exceptional |
| Satellite ground station | 0.3 - 1.0 | Low-noise LNA | Excellent |
| Cellular base station LNA | 1.0 - 2.0 | GaAs/GaN MMIC | Excellent |
| Wi-Fi / 802.11 receiver | 2.0 - 4.0 | Silicon RFIC | Good |
| GPS receiver front-end | 1.5 - 3.0 | SiGe LNA | Good |
| Radar receiver | 3.0 - 6.0 | GaAs MMIC | Moderate |
| Cable TV (CATV) amplifier | 4.0 - 8.0 | GaAs FET | Moderate |
| General-purpose SDR dongle | 6.0 - 12.0 | CMOS RFIC | High |
Typical NF ranges for common RF and microwave receiver front-ends. Lower is better.
Frequently asked questions
What does a noise figure of 0 dB mean?
A 0 dB noise figure corresponds to a noise factor of exactly 1, meaning the device adds no noise whatsoever. The output SNR is identical to the input SNR. This is a theoretical ideal: no physical device at room temperature achieves it, though cryogenically cooled amplifiers can come very close. Any positive NF means the device is degrading the SNR by some amount.
Can noise figure be negative?
Only in the mathematical sense if you entered output SNR greater than input SNR. In practice this is not physically possible for a passive or active device at room temperature, because thermal noise is always added. Negative values indicate a measurement error or an incorrect input. Some optical amplifiers can appear to have sub-unity noise factors in specialised definitions, but the standard IEEE definition used here requires F >= 1 and NF >= 0 dB.
Why does the first stage matter most in a cascaded system?
In the Friis formula, the noise contribution of each stage beyond the first is divided by the cumulative gain of all preceding stages. If stage 1 provides 20 dB (factor 100) of gain, then a 10 dB noise figure in stage 2 contributes only 10 dB / 100 = 0.043 dB to the total NF. This is why receiver designers always place the lowest-NF device (the LNA) first and give it enough gain to suppress downstream noise. Swapping stage order can dramatically change the total system noise figure.
What is the difference between noise figure and noise temperature?
Noise figure and noise temperature are two representations of the same physical quantity. Noise figure is expressed in decibels: NF = 10 log10(F). Noise temperature is expressed in kelvin: Te = 290 x (F - 1). Noise temperature is preferred when NF values are very small (below about 1 dB) because small differences are easier to resolve in kelvin. For example, the difference between 0.1 dB (7.5 K) and 0.5 dB (35 K) is clearer in kelvin than in dB. Both convert exactly to and from each other.
How does cable loss affect noise figure?
A passive lossy element such as a cable or attenuator with loss L (linear) has a noise figure equal to the loss: F = L, so NF = 10 log10(L). For example, a 3 dB cable has NF = 3 dB and F = 2. In a cascaded chain, if the cable comes before the LNA, it directly adds to the total NF. Placing the LNA before the cable (at the antenna port) is the standard solution. If a 2 dB cable precedes a 1.5 dB LNA, the combined NF is about 3.5 dB. With the LNA first, the cable contribution shrinks to nearly zero.
What noise figure should I aim for in my design?
This depends on the application. Consumer Wi-Fi chipsets typically need 2-4 dB. Cellular base station LNAs target 1-2 dB. GPS receivers and satellite ground stations aim for 1-3 dB. Radio-astronomy and deep-space receivers push below 1 dB, sometimes below 0.3 dB with cryogenic cooling. A practical starting point is to compute the required minimum detectable signal from your link budget, then work back to the maximum allowable system noise figure using the noise floor formula: noise floor = -174 dBm/Hz + 10 log10(bandwidth) + NF.