The Eyring formula is an acoustic equation used to estimate reverberation time (RT60) by considering a room’s volume, surface area, and average sound absorption. It is an improved approach compared with the traditional Sabine formula, especially in rooms where surfaces absorb a significant amount of sound energy.
In room acoustics, predicting reverberation time helps designers understand how sound behaves in spaces such as recording studios, theaters, classrooms, and performance halls. The Eyring formula provides a more realistic estimation when acoustic treatment creates higher levels of absorption.
To understand the concept behind this calculation, first learn about RT60 and reverberation time.
What Is the Eyring Formula?
The Eyring formula is a mathematical model used to calculate the approximate time it takes for sound to decay by 60 decibels after the original sound stops.
This measurement is known as RT60 (reverberation time).
The formula was developed as an improvement to the Sabine equation because Sabine assumes a simpler relationship between absorption and sound decay. In highly treated rooms, where surfaces absorb more sound, the Eyring approach often provides a more accurate prediction.
The formula is commonly used in:
- Recording studios
- Concert halls
- Auditoriums
- Classrooms
- Architectural acoustic design
The Eyring Formula Equation Explained
The Eyring formula is:
Where:
| Symbol | Meaning |
|---|---|
| RT60 | Reverberation time in seconds |
| V | Volume of the room in cubic meters |
| S | Total surface area of the room in square meters |
| α | Average sound absorption coefficient |
| ln | Natural logarithm |
The equation estimates how quickly sound energy decreases based on the size of the room and how much sound is absorbed by its surfaces.
How Does the Eyring Formula Work?
When a sound is produced inside a room, sound waves reflect from walls, ceilings, floors, and objects.
Each reflection loses some energy because surfaces absorb part of the sound.
The Eyring formula considers:
- How much space the sound travels through
- How much surface area interacts with sound
- How effectively surfaces absorb sound energy
The absorption coefficient (α) is especially important.
A surface with:
- Low absorption → more reflections → longer reverberation
- High absorption → fewer reflections → shorter reverberation
Understanding absorption values is important when applying the Eyring equation. Learn more about sound absorption coefficients.
Eyring Formula vs Sabine Formula
The Eyring and Sabine formulas are both used to estimate reverberation time, but they make different assumptions.
| Feature | Eyring Formula | Sabine Formula |
|---|---|---|
| Main use | Rooms with higher absorption | Rooms with lower absorption |
| Absorption approach | Logarithmic | Linear |
| Accuracy | Better for highly treated spaces | Good for traditional rooms |
| Application | Studios, modern acoustic spaces | General acoustic estimates |
The Sabine formula assumes that sound absorption is relatively small and evenly distributed.
The Eyring formula uses a logarithmic correction that becomes more useful as absorption increases.
You can learn more about the alternative calculation method in this guide about the Sabine formula.
Why Was the Eyring Formula Developed?
The Sabine formula works well for many rooms, but it becomes less accurate when absorption approaches higher levels.
Modern acoustic spaces often include:
- Acoustic panels
- Bass traps
- Fabric surfaces
- Specialized acoustic materials
These treatments can significantly change how sound behaves.
The Eyring formula improves prediction by accounting for the diminishing effect of additional absorption.
In simple terms:
- Adding absorption to a reflective room creates a large improvement.
- Adding more absorption to an already highly treated room creates smaller additional changes.
The Eyring equation models this relationship more effectively.
When Should You Use the Eyring Formula?
The Eyring formula is particularly useful when designing spaces with significant acoustic treatment.
Examples include:
Recording Studios
Studios require controlled reverberation because excessive reflections can affect recording accuracy and mixing decisions.
Treated Listening Rooms
Rooms with many absorptive surfaces may benefit from Eyring calculations because absorption levels are higher.
Modern Acoustic Spaces
Spaces using extensive acoustic materials often require more advanced reverberation predictions.
For practical room treatment decisions, understanding acoustic treatment helps explain how materials influence RT60.
Limitations of the Eyring Formula
Although useful, the Eyring formula has limitations.
It Assumes Even Sound Distribution
The equation assumes sound energy is distributed relatively evenly throughout the room.
Real rooms may have:
- Uneven surfaces
- Irregular shapes
- Furniture
- Complex reflections
It Uses Average Absorption
The formula uses an average absorption coefficient, but different surfaces absorb different frequencies differently.
For example:
- Carpets affect higher frequencies differently than walls.
- Bass absorption behaves differently from high-frequency absorption.
It Does Not Replace Measurement
The Eyring formula provides an estimate, but professional acoustic design often uses actual measurements to verify results.
Real-world testing can reveal problems that calculations cannot fully predict.
Relationship Between Eyring Formula and Acoustic Treatment
The Eyring formula helps explain why acoustic treatment changes a room’s reverberation.
Adding materials such as:
- Acoustic panels
- Bass traps
- Absorptive ceiling treatments
increases absorption and reduces RT60.
However, the goal is not always the lowest possible reverberation time.
Different spaces require different acoustic characteristics:
- Recording studios need controlled decay.
- Classrooms need speech clarity.
- Concert halls need musical spaciousness.
The ideal RT60 depends on the purpose of the room.
Learn more about recommended reverberation targets in this guide about ideal RT60.
Frequently Asked Questions
What does the Eyring formula calculate?
The Eyring formula calculates estimated reverberation time (RT60) based on room volume, surface area, and average sound absorption.
Is Eyring more accurate than Sabine?
The Eyring formula can provide more accurate results in rooms with higher absorption, while the Sabine formula works well for many traditional spaces with lower absorption.
What is the difference between Sabine and Eyring formulas?
The main difference is how they treat sound absorption. Sabine uses a simpler linear relationship, while Eyring uses a logarithmic approach that better accounts for higher absorption levels.
Can the Eyring formula replace acoustic measurement?
No. It provides an estimate. Professional acoustic analysis often combines calculations with real measurements.
Noah Bennett is an audio engineering writer and acoustics specialist at Reverb Calculator. He focuses on reverb time calculation, room acoustics, studio sound design, and music production tools for producers, audio engineers, musicians, and home studio creators.