Signal-to-Noise Ratio Calculator
The general SNR tool: find signal-to-noise ratio from power or voltage, turn it into bits, and see the thermal noise limit of a receiver.
📶 What is Signal-to-Noise Ratio?
Signal-to-noise ratio, usually shortened to SNR or S/N, compares the level of a wanted signal with the level of the unwanted background noise that comes with it. It is a ratio, so it has no units of its own, and it is most often quoted in decibels because the signals involved span many orders of magnitude. A higher SNR means the signal stands out more clearly from the noise: a clean voice recording, a sharp radio link or a precise sensor reading all have high SNR, while a hissy tape, a weak cell signal or a noisy sensor have low SNR.
SNR is a fundamentals idea used in nearly every measurement field. Audio engineers quote it to describe how much hiss sits under the music, radio and telecom engineers use it to judge whether a link will carry data, and instrument designers use it to decide how many bits a converter needs. Scientists use it to decide whether a faint feature in data is real or just noise, and imaging and astronomy work with it constantly. Thermal noise, the random motion of charge carriers set by temperature, gives every receiver a lower limit on noise that no design can remove.
A few points are easy to get wrong. Power ratios use 10 log10 and amplitude ratios use 20 log10, because power goes as voltage squared. SNR is not the same as the signal level: a strong signal in strong noise still has a poor SNR. It also depends on the bandwidth in which the noise is measured, since wideband noise power grows in proportion to bandwidth. And SNR is different from SINAD, which includes distortion, from Eb/N0 for digital links, and from the photon counting SNR of astronomical detectors. For those, use the specialist pages for ADC SNR and ENOB, the matched filter output SNR and the photon counting detector SNR.
This general calculator has four modes. Power levels finds the SNR from signal and noise power in watts or in dBm or dBW. RMS amplitudes uses voltages or other amplitudes. SNR and bits gives the rough link between SNR and converter resolution, and Thermal noise floor computes the k T B noise limit for a given temperature, bandwidth and noise figure, then compares a signal against it.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Signal and Noise Power in Milliwatts
Signal 5 mW, noise 0.05 mW
Example 2 — Receiver Levels in dBm
Signal −60 dBm, noise −95 dBm
Example 3 — RMS Voltages
Signal 1 V RMS, noise 0.05 V RMS
Example 4 — SNR and Bits
Convert 86 dB to bits, and 14 bits to dB
Example 5 — Thermal Noise Floor of a 20 MHz Receiver
290 K, 20 MHz bandwidth, 6 dB noise figure, signal at −85 dBm
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for signal-to-noise ratio?
SNR = P_signal / P_noise as a ratio, or 10 log10(P_signal / P_noise) in decibels. For amplitudes, SNR in dB = 20 log10(V_signal / V_noise). A signal of 5 mW over 0.05 mW of noise is 100:1, or 20 dB.
How do I calculate SNR in dB from RMS values?
Use 20 log10(Vsignal RMS / Vnoise RMS). With 1 V RMS signal and 0.05 V RMS noise the amplitude ratio is 20 and the SNR is 26.02 dB. The power ratio is the square of the amplitude ratio, 400:1.
Why is the SNR formula 10 log for power and 20 log for voltage?
Power is proportional to voltage squared, and log(x squared) = 2 log(x). So 10 log10 of a power ratio equals 20 log10 of the corresponding amplitude ratio. Both give the same decibel value.
What is a good signal-to-noise ratio?
It depends on the application. Above about 20 dB the signal clearly stands out of the noise, while many digital links need 10 dB or more and high-fidelity audio and measurement systems aim for 60 dB or more. Below 0 dB the noise exceeds the signal.
Can signal-to-noise ratio be negative?
Yes. A negative SNR in dB means the noise power is larger than the signal power. Some spread-spectrum and coded systems can still recover signals below 0 dB thanks to processing gain.
How do I convert SNR to bits of resolution?
For an ideal converter with a full-scale sine wave, N = (SNR - 1.76) / 6.02. An SNR of 86 dB is about 13.99 bits, and 14 bits gives 86.04 dB. Each extra bit adds 6.02 dB.
What is the thermal noise floor?
Thermal noise power is k T B, with Boltzmann constant 1.380649e-23 J/K, temperature in kelvin and bandwidth in hertz. At 290 K it is -174 dBm per hertz, so a 20 MHz bandwidth has a floor of -100.96 dBm before any receiver noise.
How does noise figure affect SNR?
A receiver with a noise figure of F dB adds F dB to the thermal noise floor. With kTB of -100.96 dBm and a 6 dB noise figure the floor is -94.96 dBm, and a -85 dBm signal then has an SNR of 9.96 dB.
What is the difference between SNR, SINAD and Eb/N0?
SNR compares signal power with noise power alone. SINAD also counts distortion, and Eb/N0 compares energy per bit with noise density in digital links. Use the matching specialist calculator when you need those.
How do I improve the signal-to-noise ratio?
Increase the signal power, reduce the noise bandwidth, cool or improve the receiver, or average repeated measurements. Averaging N independent samples improves SNR by 10 log10(N) dB for random noise.
How is this different from the SNR and ENOB calculator?
This page covers SNR in general: power and RMS ratios, dB, a rough bits conversion and the thermal floor. The SNR and ENOB calculator is specific to analog-to-digital converters and works from bit depth and measured SINAD.