The Eyring formula is an equation that predicts reverb time (RT60) in a room, developed by Carl F. Eyring in the 1930s as a refinement to the older Sabine formula. While Sabine is simpler and widely used, Eyring is more accurate in highly treated or absorbent rooms.
The Eyring formula is:
RT60 = 0.161 × V / (-S × ln(1 – α))
Where:
- RT60 = reverberation time in seconds
- V = room volume in cubic meters
- S = total surface area in square meters
- α = average absorption coefficient (0–1)
- ln = natural logarithm
- 0.161 = constant for metric units
The key difference from Sabine is the natural logarithm term, which accounts for the statistical distribution of sound energy bouncing around a more absorbent room. This makes Eyring more accurate when rooms have higher overall absorption (lots of foam, treatment, furnishings).
Sabine vs. Eyring: When to Use Which?
Both formulas give approximate results. The choice depends on your room’s absorption level.
Use Sabine if your room has low-to-moderate absorption (average α below 0.2). Most untreated rooms, concert halls, and lightly treated studios fall here. Sabine is simpler and accurate enough. It’s also the industry standard—most people know Sabine; fewer know Eyring.
Use Eyring if your room is highly absorbent (average α above 0.2–0.3). Professional control rooms, heavily treated studios, and dead spaces use lots of absorption. Eyring’s logarithmic term accounts for this more accurately. In a very absorbent room, Sabine can underestimate RT60.
A practical rule: if you’re applying the formula to predict a studio renovation (adding lots of foam), use Eyring. If you’re designing a concert hall or untreated room, use Sabine.
In most cases, the difference between Sabine and Eyring is 5–20%. For rough planning, either works. For precision, measure your actual room’s RT60 with test signals. Read more about when to use each formula in room acoustics.
Components of the Eyring Formula
Volume (V) and surface area (S) are the same as in Sabine: multiply room dimensions and calculate all wall areas.
Average absorption coefficient (α) is also the same process: weight each material’s absorption by its surface area, then average.
The mathematical difference is the natural logarithm (ln). This function handles high absorption better. In highly absorbent rooms, the simple division used by Sabine overestimates how long sound bounces; the logarithm corrects for that.
For low absorption (α < 0.1), Eyring and Sabine give similar results. For high absorption (α > 0.4), Eyring is noticeably different.
Calculating RT60 With Eyring
Use the same room example as the Sabine article:
- Volume: 60 m³
- Surface area: 94 m²
- Average α: 0.26 (from earlier calculation)
Eyring: RT60 = 0.161 × 60 / (-94 × ln(1 – 0.26))
= 9.66 / (-94 × ln(0.74))
= 9.66 / (-94 × -0.301)
= 9.66 / 28.3
≈ 0.34 seconds
Sabine gave 0.40 seconds; Eyring gives 0.34 seconds. The difference is about 15%—meaningful in acoustic design.
Now add more absorption (the foam example from the Sabine article):
- New average α: 0.44
Eyring: RT60 = 0.161 × 60 / (-94 × ln(1 – 0.44))
= 9.66 / (-94 × ln(0.56))
= 9.66 / (-94 × -0.580)
= 9.66 / 54.5
≈ 0.18 seconds
Sabine gave 0.21 seconds; Eyring gives 0.18 seconds. Again, about 15% difference. In a highly treated room, Eyring’s logarithm kicks in more dramatically.
Eyring in Highly Treated Studios
Professional mixing and mastering studios often aim for RT60 around 1.2 seconds with targeted absorption throughout the room. The room has diffusers, bass traps, absorptive panels, and soft furnishings—high absorption overall.
Using Eyring to design this, you’d calculate backward: “I want 1.2 sec RT60. My room volume is 80 m³, surface area is 150 m². What average α do I need?”
Rearranging: 1 – α = e^(-0.161 × V / (0.161 × RT60 × S))
This is complex, so use a calculator tool for backward calculation. But the principle is: Eyring helps you predict absorption needs in treated rooms more accurately than Sabine.
For studio design where precision matters, Eyring is worth using. For rough estimates and concert halls, Sabine is standard.
Limitations of Eyring
Like Sabine, Eyring assumes:
- Sound bounces uniformly throughout the room (diffuse field)
- All surfaces contribute equally to absorption
- No standing waves, room modes, or geometric anomalies
- Averaged absorption across all frequencies
Real rooms don’t match these assumptions. Furniture, people, and room shape create irregular reflections. Very low frequencies (bass) develop modes that Eyring can’t predict. Very high frequencies diffract differently.
Eyring is better than Sabine for highly absorbent rooms, but it’s still an estimate. For definitive answers, measure RT60 in your actual space using test signals and sound level meters.
The formula is a design tool, not a guarantee. Use it for planning; verify with measurement.
Frequently Asked Questions
Is Eyring more accurate than Sabine in all cases?
No. Eyring is more accurate in highly absorbent rooms (α > 0.3). In moderately absorbent rooms (α < 0.2), Sabine is fine. They’re designed for different scenarios. Use Sabine for general purpose; Eyring for heavily treated studios.
How do I know my room’s average absorption coefficient?
Look up absorption values for each material in ISO 11654 or equivalent standards. Measure each surface, multiply by its absorption, sum, and divide by total surface area. This is tedious but necessary for either formula. See the Sabine article for a step-by-step example.
Can I calculate RT60 at different frequencies with Eyring?
Yes. Absorption coefficients vary by frequency. Eyring (like Sabine) can be applied per frequency band if you have absorption data at those frequencies. Most standard references give absorption at 125, 250, 500, 1000, 2000, and 4000 Hz. Run Eyring separately for each frequency to see how RT60 varies.
Does Eyring account for room shape or parallel walls?
No. Both Eyring and Sabine treat the room as a uniform acoustic space and ignore geometry. Parallel walls create standing waves and modes that the formulas can’t predict. For acoustic design, avoid parallel walls when possible and use diffusers to break up reflections—elements that Eyring and Sabine can’t model but that matter in practice.