PAG/NAG Gain Before Feedback Calculator
Enter the published PAG/NAG distances to see whether the layout has enough gain before feedback. The calculator also reverses the same model into usable microphone, loudspeaker, and open-mic limits.
Gain-before-feedback margin0.02
- Potential acoustic gain (PAG)
- 14
- Needed acoustic gain (NAG)
- 13.98
- Design result
- Pass
- Maximum talker-to-mic distance (ft)
- 2
- Minimum mic-to-speaker distance (ft)
- 7.98
- Maximum open microphones without automixing
- 1
- Effective open microphones in PAG
- 1
D0 affects the separately displayed PAG and NAG, but it cancels out of the pass/fail margin and inverse design limits.
How to use this calculator
- Choose feet or meters, then use that same unit for every distance.
- Enter D0 through D4 from the talker, microphone, loudspeaker, and listener positions.
- Enter the number of microphones open at once and whether an automatic mixer controls the effective NOM.
- Set the feedback stability margin, then compare PAG, NAG, margin, and the inverse design limits.
How the PAG/NAG result is calculated
Potential acoustic gain, or PAG, estimates how much level a sound system can add before acoustic feedback becomes likely. Needed acoustic gain, or NAG, estimates how much gain is required for the farthest listener to hear the talker at the same level as a nearer reference listener. A workable geometry needs PAG to be at least as high as NAG after the chosen feedback stability margin.
The calculator uses the standard distance-ratio procedure:
PAG = 20 × log10((D0 × D1) ÷ (D2 × D4)) − 10 × log10(Neff) − F
NAG = 20 × log10(D0 ÷ D3)
- D0 is talker to farthest listener.
- D1 is microphone to nearest loudspeaker.
- D2 is farthest listener to the loudspeaker serving that listener.
- D3 is talker to nearest listener.
- D4 is talker to microphone.
- Neff is the effective number of open microphones. With the automixer option selected, this calculator uses one effective open microphone.
- F is the feedback stability margin in dB.
The gain-before-feedback margin is PAG − NAG. Zero or positive means the modeled layout passes the selected margin; a negative value means it needs revision.
Why the inverse limits are useful
The same equation can be solved backward for practical design limits. When the margin is exactly zero, D0 cancels out: moving the farthest listener changes both PAG and NAG by the same amount. That is why the pass/fail margin depends on the local geometry around the talker, mic, loudspeaker, and reference listener rather than the farthest-listener distance alone.
The inverse limits are:
maximum D4 = (D1 × D3) ÷ (D2 × 10^(F ÷ 20) × sqrt(Neff))
minimum D1 = (D2 × D4 × 10^(F ÷ 20) × sqrt(Neff)) ÷ D3
maximum NOM = floor(((D1 × D3) ÷ (D2 × D4 × 10^(F ÷ 20)))^2)
Moving the microphone closer to the talker, moving loudspeakers farther from microphones, reducing the listener-to-loudspeaker distance, lowering the number of open microphones, or reducing the required safety margin all improve the modeled margin. Increasing the safety margin is conservative, but it can quickly turn a borderline layout into one that needs changes.
What this estimate leaves out
This is an inverse-square-law estimate. It does not model reverberation, reflections, equalization, delay, stage monitors, microphone polar patterns, loudspeaker directivity, placement angles, acoustic treatment, or frequency-specific feedback modes. Treat the result as a layout check before tuning, not as proof that the installed system cannot feed back.
Worked example
Suppose D0 is 30 ft, D1 is 8 ft, D2 is 12 ft, D3 is 6 ft, D4 is 2 ft, one microphone is open, no automixer is used, and the stability margin is 6 dB. PAG is 20 × log10((30 × 8) ÷ (12 × 2)) − 6, which is 14.00 dB. NAG is 20 × log10(30 ÷ 6), which is 13.98 dB.
The margin is 0.02 dB, so the modeled design just passes. The inverse limits show why it is tight: the talker-to-mic distance can be about 2.00 ft, the mic-to-speaker distance needs to be about 7.98 ft or more, and the geometry supports one open microphone without automixing.
Common questions
What are PAG and NAG in sound reinforcement?
Potential acoustic gain is the amount of system gain the layout can theoretically support before feedback. Needed acoustic gain is the amount of gain required for the farthest listener to hear the talker at the chosen reference level. The layout is workable in this model when PAG is at least as large as NAG.
How much gain-before-feedback margin is enough?
A 6 dB feedback stability margin is the conventional allowance in the published PAG procedure and is a reasonable starting point for speech systems. Difficult rooms, reflective stages, monitors, or uneven equalization may need more margin. Final gain before feedback should still be verified on the installed system.
Why does moving a microphone closer to the talker reduce feedback?
A closer microphone receives more direct sound from the talker, so the mixer needs less gain to reach the same reinforced level. In the PAG equation, reducing D4 increases potential acoustic gain. That is why headset and close lectern microphones usually provide more gain before feedback than distant microphones.
How do multiple open microphones affect feedback?
Each doubling of open microphones reduces potential acoustic gain by about 3 dB because more acoustic paths contribute to the system. This calculator applies the published NOM term as <code>10 × log10(N)</code>. The maximum-open-microphones result is floored so it never rounds a failing fractional value up.
Does an automatic mixer improve gain before feedback?
An automatic mixer can improve practical gain before feedback by reducing the number of microphones that contribute full gain at the same time. In this simplified calculator, selecting the automixer option sets the effective number of open microphones to one. It does not model a specific mixer gain-sharing algorithm.
Why can PAG/NAG predict a pass while the real system still feeds back?
The distance-ratio method is a simplified broadband geometry estimate. Real feedback depends on room modes, reflections, equalization, loudspeaker coverage, microphone pattern, placement angles, and frequency response. A passing result means the layout is plausible, not guaranteed.