Required Amplifier Power / SPL-Target Sizer

Reference: AMP-SIZER-01. A capstone that chains three ideas already on this site into one worked answer: the Inverse Square Law SPL Predictor run backward (target SPL at distance → required SPL at the speaker), the same dB-of-headroom thinking as the Amplifier Headroom & Crest Factor Sizer (here added directly in dB rather than as a crest-factor ratio), plus a new factor neither of those covers: power lost to speaker cable resistance over distance. Every step is shown, not just the final number — this is meant to be checked, not trusted blindly.

Speaker sensitivity (dB SPL @ 1W @ reference distance) Reference distance (m) Distance to farthest listener (m) Target SPL at that distance (dB) Headroom (dB) — 3–10 dB typical, 6 dB is a reasonable default Speaker nominal impedance (Ω) Cable length, amp to speaker, one-way (m) Cable resistance (Ω per meter) — e.g. 0.0132 for 16 AWG Calculate

This ignores room and audience absorption (open-air/free-field assumption, same as the Inverse Square Law calculator) and assumes a single point source, not an array. It's a sizing starting point, not a replacement for measuring the actual room.

Source: Boyce, D. C. Live Sound Reinforcement, §11.9 "Determining Amplifier Power." Rewritten in Ryan's own words from the source material, including its own worked example (97 dB/1W/1m sensitivity, 20 m throw, 95 dB target, 6 dB headroom, 6Ω load, 20 m of 16 AWG cable → ~1183 W) used to verify this calculator.