Formula Sheet

AVIXA / CTS-D engineering formulas with examples

Viewing Distance (4K)

VD = Screen Height × VTR

VTR=6 (4K), VTR=4 (1080p). Last row ≤ 6× screen height for readability.

Example: 84" screen → 42" H → max VD = 252" (21ft)

Image Height

IH = SW / AR

AR = 16/9 = 1.78 for widescreen. SW = screen width.

Example: 120" wide → IH = 120/1.78 = 67.4"

Throw Ratio

TR = D / W

D = throw distance (lens to screen), W = image width.

Example: 15ft throw, 10ft wide → TR = 1.5:1

Lumens (Ambient Light)

L = (fL × A) / G

fL = foot-lamberts (≥40 bright room), A = area ft², G = screen gain.

Example: 40fL × 60ft² / 1.0 gain = 2,400 lumens

LED Pixel Pitch

PP(mm) = VD(m) / 2500 to 3000

Also: min VD(m) ≈ PP(mm) × 1.5. Smaller pitch = closer viewing.

Example: 6m viewing → PP ≈ 6/2750 = 2.18mm → use P2.0 or P2.5

PAG (Potential Acoustic Gain)

PAG = 20log(D1) - 20log(D0) - 20log(D2) + 20log(DS) - 6.5

D1=src-to-listener, D0=mic-to-src, D2=spkr-to-mic, DS=spkr-to-listener

Example: Must exceed NAG by ≥6dB for stable gain

NAG (Needed Acoustic Gain)

NAG = 20log(D1) - 20log(D0)

If PAG > NAG + 6dB, system is stable.

Example: Src 20ft, listener 4ft → NAG = 20log(20) - 20log(4) = 14dB

70V Tap Load

Total Taps ≤ Amp Watts

Sum all speaker taps. Never exceed amp rating. Budget 80% for headroom.

Example: 8 speakers × 8W tap = 64W → need ≥80W amp

Conduit Fill (1 Cable)

Fill ≤ 53%

1 cable: 53%, 2 cables: 31%, 3+ cables: 40% (NEC Chapter 9, Table 1).

Example: 1" EMT ID=1.049" → area=0.864in² → 40% = 0.346in²

BTU/hr (Rack Heat)

BTU/hr = Watts × 3.412

Sum all equipment watts. 1 ton HVAC = 12,000 BTU/hr.

Example: 2,000W rack → 6,824 BTU/hr → ~0.57 tons cooling

Dante Bandwidth

BW = Ch × SR × BD × 1.25

SR=48kHz, BD=24-bit. ×1.25 for overhead. Per flow (unicast or multicast).

Example: 64ch × 48000 × 24 × 1.25 = 92.16 Mbps

Speaker Coverage (EPR)

EPR = 2 × H × tan(θ/2)

H = ceiling height - ear height (4ft). θ = speaker dispersion angle.

Example: 10ft above ear, 90° cone → EPR = 2×10×tan(45°) = 20ft dia