What Is η₀ (Eta Zero)?
η₀, also known as reference efficiency, represents how efficiently a speaker converts electrical power (watts) into acoustic power (sound energy). It is expressed as a percentage (%), indicating the fraction of input power that is actually turned into sound rather than lost as heat in the voice coil.
Most loudspeakers have relatively low efficiency, with typical values ranging from 0.1% to 10%. This means that in many cases, over 90% of the amplifier’s power is lost as heat, rather than being converted into audible sound.
Formula for η₀ (Reference Efficiency)
The reference efficiency of a speaker is calculated using the following equation:
Where:
- Fs = Free air resonance (Hz)
- Vas = Equivalent compliance volume (m³)
- Qes = Electrical quality factor (unitless)
- c = Speed of sound (343 m/s)
This formula shows that higher efficiency is achieved when a speaker has:
✅ A lower Qes (stronger motor control)
✅ A larger Vas (more compliant suspension)
✅ A higher Fs (higher resonant frequency)
Speakers with low Qes and high Vas tend to be more efficient, while those with high Qes and small Vas are generally less efficient. A higher η₀ means better efficiency, but this is influenced by trade-offs between motor strength (BL), moving mass (Mms), and suspension compliance (Cms).
Real-World η₀ Ranges for PA Speakers
PA drivers do not typically reach the 5-10% efficiency figures sometimes quoted, whilst historically some higher efficiency woofers were manufactured, they typically had very low power handling, very lightweight cones, and low excursion capability , which made them suitable for limited applications and required extreme care when they were used.
| η₀ (Efficiency) | Performance Category | Typical Applications |
|---|---|---|
| 4%+ | Very high | High-efficiency drivers, usually mid-range |
| 3% – 4% | High efficiency | High-performance PA bass drivers |
| 2% – 3% | Good efficiency | Good quality PA woofers |
| 1.5% – 2% | Average efficiency | General purpose PA drivers |
| 0.75% – 1.5% | Low efficiency | Budget applications, or optimization for low Fs |
| Below 0.75% | Very low efficiency | Often optimized for very low Fs |
🔹 Compression drivers and horn-loaded midrange drivers often exceed these values due to acoustic loading.
🔹 Large subwoofers with very low Fs tend to have low η₀, as their design prioritizes deep bass over efficiency.
η₀ vs. SPL – How Are They Related?
While η₀ tells us how much input power is converted into sound, sensitivity (SPL @ 1W/1m) is often a more practical measurement:
A higher η₀ typically results in higher SPL, meaning the speaker requires less amplifier power to reach the same volume. This does depend on cabinet design, frequency range and application. A well optimised infra-sub may well have efficiency lower than 1%, but at 30 Hz could outperform a general purpose woofer designed for kick-bass. The infra-sub would be sloppy, slow and inefficient around 100Hz, compared with the kick-bass driver which would be fast, precise and most likely 5 times louder.