Signal-to-Noise Ratio Calculator | SNR, PSNR & Noise Figure in dB
Calculate signal-to-noise ratio (SNR), peak signal-to-noise ratio (PSNR), noise figure (NF), noise factor, and dynamic range for audio, electronics, and imaging applications. Converts between linear power ratios and decibels, and computes thermal noise floor.
What Is the Signal-to-Noise Ratio Calculator | SNR, PSNR & Noise Figure in dB?
Signal-to-Noise Ratio (SNR) measures the quality of a signal relative to the background noise level. It appears in audio engineering, radio communications, electronics, imaging, and finance (where "noise" means random price fluctuations). A higher SNR means a cleaner, more usable signal.
- ▸SNR Tab: compute SNR from signal and noise power, from voltages, or convert a known SNR in dB to a linear ratio.
- ▸Noise Figure Tab: compute the noise figure of an amplifier or RF system. The Friis formula calculates cascaded NF for a chain of stages.
- ▸Thermal Noise Tab: compute Johnson-Nyquist noise — the irreducible noise floor set by temperature and bandwidth.
- ▸PSNR Tab: compute Peak Signal-to-Noise Ratio for image quality assessment. Enter MSE or compute it from pixel values.
Formula
SNR and related metrics are computed from ratios of power or amplitude measurements, expressed on logarithmic (dB) scales.
SNR_dB = 10 · log₁₀(Ps / Pn)
Ps = signal power, Pn = noise power, both in same units.
SNR_dB = 20 · log₁₀(Vs / Vn)
Use 20× for amplitude, voltage, or field quantities; 10× for power.
P_noise = k·T·B
k = 1.381×10⁻²³ J/K, T in Kelvin, B in Hz. Vn = √(4kTBR).
F_total = F₁ + (F₂−1)/G₁ + (F₃−1)/(G₁G₂)
First stage dominates; maximize G₁ and minimize F₁ for best system NF.
PSNR = 10 · log₁₀(MAX² / MSE)
MAX = 255 for 8-bit images. Higher PSNR = better quality.
dBm = 10 · log₁₀(P_mW)
Power in milliwatts: P_mW = P_W × 1000. 0 dBm = 1 mW.
How to Use
- 1
Select the appropriate tab: SNR Calculator, Noise Figure, Thermal Noise Floor, or PSNR (Image).
- 2
For SNR: choose Power, Voltage, or From dB mode; enter the required values and click Calculate.
- 3
For Noise Figure: choose Single Stage or Friis Chain; enter noise factors (linear) and gains (dB) for each stage.
- 4
For Thermal Noise: enter temperature in Kelvin and bandwidth in Hz; optionally add resistance for noise voltage calculation.
- 5
For PSNR: enter the MSE between original and processed images; adjust MAX pixel value for bit depth (255 for 8-bit, 65535 for 16-bit).
- 6
Click Calculate to view results including SNR in dB, linear ratio, quality classification, and all intermediate values.
- 1
Choose a tab
Select SNR Calculator, Noise Figure, Thermal Noise Floor, or PSNR (Image) depending on your application.
- 2
SNR Tab: choose power or voltage mode
For power SNR enter signal power Ps and noise power Pn in the same units (W or mW). For voltage SNR enter signal and noise voltages. Or enter a known dB value to convert to linear.
- 3
Noise Figure Tab: single stage or Friis chain
For a single amplifier enter the noise factor F (linear, ≥ 1). For a cascaded system enter F₁, F₂, F₃ and gains G₁, G₂ in dB to get total system noise figure via the Friis formula.
- 4
Thermal Noise Tab: compute noise floor
Enter temperature T in Kelvin (room temperature ≈ 290 K) and bandwidth B in Hz. Optionally enter resistance R for noise voltage.
- 5
PSNR Tab: image quality
Enter the Mean Squared Error between original and compressed/processed image. 255 is the standard MAX for 8-bit images.
Example Calculation
Example 1 | Audio Amplifier SNR
An amplifier has signal power 1 W and noise power 0.001 W.
Example 2 | Friis Cascaded Noise Figure
Three-stage RF chain: F₁ = 1.5, F₂ = 3, F₃ = 5 with G₁ = 20 dB (linear 100), G₂ = 15 dB (linear 31.6).
= 1.5 + 0.02 + 0.00127 ≈ 1.521
NF_total = 10·log₁₀(1.521) ≈ 1.82 dB
Example 3 | Thermal Noise at Room Temperature
T = 290 K, B = 1 MHz = 10⁶ Hz.
= −113.97 dBm (standard room-temperature noise floor per MHz)
Understanding Signal-to-Noise Ratio | SNR, PSNR & Noise Figure in dB
SNR in Different Fields
- ▸Audio engineering: SNR of a preamp or DAC measures how clean the output is. Professional audio targets > 100 dB SNR.
- ▸Radio frequency (RF): Receiver sensitivity is determined by the noise figure and thermal noise floor. A 3 dB improvement in NF doubles effective range.
- ▸Digital imaging: Camera sensor SNR limits the dynamic range and determines how much detail is visible in shadows and highlights.
- ▸MRI and medical imaging: SNR determines image resolution and the ability to detect small anomalies.
- ▸Finance and data science: Signal-to-noise analogies describe how much meaningful information exists in noisy datasets versus random variation.
The dB Scale: Why It Matters
The decibel scale is logarithmic because human perception of sound and light is approximately logarithmic, and because signal powers in real systems span many orders of magnitude. A satellite signal might be −130 dBm (10⁻¹⁶ W) while a nearby transmitter might be +30 dBm (1 W). Working in dB compresses a 10-billion-to-one power ratio into a 160 dB linear range — far more practical for engineering calculations. Every 3 dB represents approximately a doubling or halving of power; every 10 dB is an exact factor of 10.
SNR Quality Guidelines by Application
| Application | Minimum SNR | Good SNR |
|---|---|---|
| Voice telephony | 15 dB | 25 dB |
| FM Radio | 30 dB | 50 dB |
| Wi-Fi (802.11) | 10 dB (1 Mbps) | 25 dB (54 Mbps) |
| Professional audio (ADC) | 96 dB (16-bit) | 120+ dB (24-bit) |
| JPEG image compression | 25 dB | 35–40 dB |
| MRI imaging | 20 dB | 30+ dB |
Frequently Asked Questions
Why is 10·log₁₀ used for power SNR but 20·log₁₀ for voltage SNR?
The decibel is defined in terms of power ratios: dB = 10·log₁₀(P₂/P₁). Since power is proportional to voltage squared (P = V²/R), a voltage ratio of V₂/V₁ corresponds to a power ratio of (V₂/V₁)². Taking the log: 10·log₁₀((V₂/V₁)²) = 20·log₁₀(V₂/V₁). The factor of 20 applies whenever you are taking a ratio of amplitude quantities (voltage, current, pressure, electric field), while the factor of 10 applies to power or intensity ratios.
What is the thermal noise floor and why does it matter?
Thermal noise (Johnson-Nyquist noise) is the irreducible noise generated by the random thermal motion of electrons in any conductor at a temperature above absolute zero. Its power is P = kTB where k is Boltzmann's constant, T is temperature in Kelvin, and B is bandwidth in Hz. This sets an absolute lower bound on the noise in any electronic system. At room temperature (290 K) and 1 Hz bandwidth, the noise floor is −174 dBm/Hz. Every 10× increase in bandwidth adds 10 dB of noise.
What does noise figure (NF) tell me about an amplifier?
Noise figure is the degradation of SNR caused by a device, expressed in dB. An ideal noiseless amplifier has NF = 0 dB (noise factor F = 1). A real amplifier with NF = 3 dB has F = 2, meaning the output SNR is half the input SNR — the device added as much noise as was present at the input. In receiver chains (LNA + mixer + IF amplifier), the first stage's NF dominates the overall system NF because subsequent noise contributions are divided by the first stage gain (Friis formula).
What is PSNR and how is it used in image compression?
Peak Signal-to-Noise Ratio (PSNR) = 10·log₁₀(MAX²/MSE) where MAX is the maximum possible pixel value and MSE is the mean squared error between the original and compressed image. It measures how much distortion a compression algorithm introduces. JPEG images at typical settings yield PSNR around 30–40 dB. Lossless compression has infinite PSNR (MSE = 0). PSNR > 40 dB is generally considered excellent quality and artifacts are not visible to the human eye.
How do I convert between dBm and watts?
dBm is a power ratio relative to 1 milliwatt. To convert: P(dBm) = 10·log₁₀(P_W × 1000). Key reference points: 0 dBm = 1 mW, 10 dBm = 10 mW, 30 dBm = 1 W, −30 dBm = 1 μW, −60 dBm = 1 nW. To convert back: P_W = 10^(dBm/10) × 10⁻³. This logarithmic scale is used universally in RF engineering because it turns multiplication of gains into addition, making cascade calculations trivial.
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