Feedback calculator: PAG and NAG
Before anyone asks for "more pastor": will the system get loud enough without feeding back? Enter the distances and find out.
How it works
NAG = 20 log(D0 ÷ EAD)
NAG is how much louder the system has to make the talker so the farthest listener hears them as clearly as if they were standing at the equivalent acoustic distance. PAG is how much gain the system can deliver before it feeds back, based on how much louder the talker is at the mic than the loudspeaker is. If PAG is at least as big as NAG, the system can work.
Each doubling of open mics costs 3 dB of gain before feedback. The stability margin keeps the system backed off from the edge of ringing; 6 dB is the traditional figure.
The model assumes omnidirectional mics and loudspeakers in a free field. Directional mics, speaker pattern control and the room all change the real numbers, so treat it as a planning check, not a guarantee.
Field notes
- Ds is the big lever. Halving the distance from talker to mic buys 6 dB, more than any EQ. That's why headsets and lavs beat podium mics for gain before feedback.
- EAD is a judgment call. It's how close you'd want to sit to hear the talker unamplified. Around 10 ft is a reasonable starting point for speech in a quiet room; use a smaller figure for noisy or reverberant rooms, or where every word matters.
- Gate unused mics. Every open mic adds feedback paths. An automixer keeps NOM low.
- Monitors count. A wedge pointed at the talker is a loudspeaker with a very short D1. Run the numbers for it too.