# PAG/NAG Calculator

### What is PAG/NAG?

PAG/NAG is a concept that can be used to determine if a sound reinforcement system can produce enough gain to provide an optimal listening experience before causing feedback. “PAG” stands for Potential Acoustic Gain, or the maximum amount of gain a system is capable of producing before causing feedback. “NAG” stands for Needed Acoustic Gain, or the amount of gain required for the farthest listener from the audio source to hear as well as the nearest listener. If PAG is greater than NAG, a system will operate without feedback; if PAG is less than NAG, a system will suffer from feedback before providing an optimal listening experience.

This tool will help you calculate a system’s PAG/NAG using the number of microphones and the distances between various elements of the system.

### How is PAG/NAG determined?

Both PAG and NAG are calculated using the distances between the various components of a sound system, including the sound sources and the listeners themselves. These variables are spelled out in the tool above. For the technically curious, this is the actual PAG equation:

PAG=20logD1 –20logD2 +20logD0 –20logDS –10logNOM-6

The equation can be solved quite easily using a logarithmic calculator. NAG is calculated by using the distance between the closest listener and the sound source, compared to the furthest listener from the sound source. (Ds, D3, and D0, as shown above). Remember, we are only trying to provide enough level to overcome what is lost due to the distance between the sound source (the “talker”) and the further listener.

### How do different microphone types affect PAG/NAG?

The PAG equation assumes omnidirectional components, so it is basically presenting a “worst-case scenario.” However, if the equation yields positive results under these conditions, you can feel very confident the system will operate successfully if you are using directional microphones. Highly directional microphones, such as the Shure MXA910 ceiling array, offer an even greater advantage, and can often succeed where the “hanging” microphone indicated above would not. However, careful design practices must be employed when attempting to provide voice lift with an overhead microphone. See this following white paper for more details.