The Eyring formula estimates reverberation time by relating room volume to total surface area and average sound absorption. Its logarithmic absorption term is often considered when a room has more absorption than the simple Sabine model represents well.
The common metric form is:
T = 0.161 × V ÷ [−S × ln(1 − ᾱ)]
Here, T is estimated reverberation time in seconds, V is room volume in cubic metres, S is total room surface area in square metres, ᾱ is the area-weighted average absorption coefficient, and ln is the natural logarithm.
For a step-by-step room calculation, use the Reverb Calculator or RT60 Calculator. This page focuses on the Eyring equation and the meaning of its variables.
What is the Eyring formula?
The Eyring formula is a reverberation-time equation used in room acoustics. It modifies the way absorption is represented by placing the average absorption coefficient inside a logarithmic term.
The equation is commonly compared with the Sabine formula. Both formulas estimate room reverberation time from simplified room information. Neither formula automatically measures the acoustic decay of a real room.
The result is commonly called an RT60 estimate because it represents the time associated with a 60 dB decay in the model. A measured reverberation time requires a separate acoustic measurement process.
The Eyring equation
Metric form
T = 0.161 × V ÷ [−S × ln(1 − ᾱ)]
Where:
| Symbol | Meaning | Unit or role |
|---|---|---|
| T | Estimated reverberation time | seconds |
| V | Room volume | m³ |
| S | Total surface area | m² |
| ᾱ | Area-weighted average absorption coefficient | dimensionless |
| ln | Natural logarithm | mathematical function |
| 0.161 | Constant for the common metric form | Used with the units above |
The negative sign keeps the denominator positive because ln(1 − ᾱ) is negative when the average absorption coefficient is between 0 and 1.
How to calculate the average absorption coefficient
First calculate total equivalent absorption area:
A = α₁S₁ + α₂S₂ + … + αₙSₙ
Then divide by total surface area:
ᾱ = A ÷ S
The average must be area-weighted. Do not take a simple average of the material coefficients unless the surfaces have equal areas.
Use the Absorption Calculator to total surface contributions. The Absorption Coefficients guide explains why coefficient data must match frequency and installation conditions.
How to use the Eyring formula
1. Calculate room volume
For a rectangular room:
V = length × width × height
For example, a room measuring 6 m by 5 m by 3 m has a volume of:
V = 6 × 5 × 3 = 90 m³
Use internal dimensions where possible. Irregular rooms or connected spaces may need a simplified model or professional analysis.
2. Calculate total surface area
For a simple rectangular room, add the floor, ceiling, and four wall areas:
S = floor area + ceiling area + wall areas
For a room with length L, width W, and height H:
S = 2(LW) + 2(LH) + 2(WH)
Treat doors, windows, panels, and other distinct surface sections separately when their areas or absorption values differ.
3. Calculate total equivalent absorption
Multiply each surface area by its absorption coefficient and add the results:
A = α₁S₁ + α₂S₂ + … + αₙSₙ
The coefficient is frequency-dependent, so use values for the frequency band you want to estimate. Avoid mixing coefficients from unrelated bands.
4. Calculate average absorption
Divide the total equivalent absorption area by total surface area:
ᾱ = A ÷ S
This value represents the area-weighted average absorption used by the Eyring model.
5. Substitute the values
Insert V, S, and ᾱ into:
T = 0.161 × V ÷ [−S × ln(1 − ᾱ)]
Check that ᾱ is below 1. An average absorption coefficient of 1 makes the logarithm undefined because ln(0) is not a finite value.
Worked Eyring example
Suppose a room has:
- Volume: 120 m³
- Total surface area: 150 m²
- Total equivalent absorption area: 30 m² sabin
First calculate the average absorption coefficient:
ᾱ = 30 ÷ 150 = 0.20
Now apply the Eyring equation:
T = 0.161 × 120 ÷ [−150 × ln(1 − 0.20)]
Since ln(0.80) is approximately −0.2231:
T ≈ 19.32 ÷ 33.47 ≈ 0.58 seconds
This is an estimate for the supplied model inputs. It is not a universal value for a room of that size, because the result depends on the surface area and absorption data.
When is the Eyring formula considered?
The Eyring formula is often considered for rooms with higher average absorption or substantial acoustic treatment. Its logarithmic term changes the absorption relationship compared with the direct inverse relationship in the Sabine equation.
The choice still depends on the room, frequency band, data quality, and purpose of the calculation. A formula should not be selected only because it produces a shorter or longer result that seems desirable.
Read the RT60 Formula guide for a side-by-side comparison. Read How to Calculate Reverb Time for the complete calculation workflow.
Eyring versus Sabine
| Feature | Eyring | Sabine |
|---|---|---|
| Absorption term | −S × ln(1 − ᾱ) | Total equivalent absorption area A |
| Main inputs | Volume, total surface area, average absorption | Volume and total equivalent absorption |
| Mathematical form | Logarithmic | Direct inverse relationship |
| Common consideration | More absorptive rooms | Straightforward estimate for lower absorption conditions |
| Shared limitation | Simplified room model | Simplified room model |
The two equations can produce similar estimates when average absorption is relatively low. Their difference becomes more noticeable as average absorption increases.
Eyring formula assumptions and limits
Diffuse sound field
The model assumes a sufficiently diffuse sound field. Small rooms, strong directional effects, room modes, and non-uniform reflection patterns can reduce the accuracy of a simple diffuse-field estimate.
Surface and absorption data
The result depends on the surface areas and coefficient values entered. Coefficients vary with frequency, mounting, material construction, and installation. A single average value cannot describe every frequency response in the room.
Room geometry
The equation does not model every reflection path, irregular boundary, cavity, opening, or low-frequency standing-wave effect. It is a calculation model, not a complete acoustic simulation.
Average absorption below one
The Eyring term requires 1 − ᾱ to be greater than zero. Inputs that produce an average coefficient of 1 or greater are invalid for the equation. Check the surface data and units before calculating.
Why an Eyring result may differ from measured reverberation time
The Eyring equation predicts from a simplified description of a room. A measurement evaluates the actual decay response using a sound source, measurement positions, equipment, and analysis method. Furniture, uneven absorption, geometry, frequency response, air absorption, and installation details can all contribute to differences.
ISO 3382-2 describes methods for measuring reverberation time in ordinary rooms. An Eyring calculation is useful for planning and comparison, but it is not a standardized measurement or certification.
For more detail, read Why Actual Reverb Differs from a Calculator.
Common Eyring formula mistakes
- Using a simple average instead of an area-weighted average coefficient.
- Confusing total surface area S with equivalent absorption area A.
- Mixing frequency bands when selecting coefficient values.
- Using inconsistent units for volume and surface area.
- Entering an average coefficient of 1 or more.
- Treating the calculated value as a measured room response.
Frequently asked questions
What is the Eyring formula for reverberation time?
The common metric form is T = 0.161 × V ÷ [−S × ln(1 − ᾱ)], where V is room volume, S is total surface area, and ᾱ is the area-weighted average absorption coefficient.
How do I calculate average absorption for Eyring?
Calculate total equivalent absorption with A = Σ(αᵢSᵢ), then divide by total surface area: ᾱ = A ÷ S.
Why does Eyring use a logarithm?
The logarithmic term represents the absorption relationship differently from the direct absorption term in the Sabine equation. This can matter more as average absorption increases.
Is Eyring more accurate than Sabine for every room?
No. The suitable equation depends on the room, the absorption conditions, the frequency band, and the assumptions that fit the intended estimate. Neither equation guarantees a measured result.
Can the Eyring formula calculate a measured RT60?
No. It estimates reverberation time from room properties. Measured reverberation time requires a separate acoustic measurement procedure.
What happens if average absorption equals one?
The expression ln(1 − ᾱ) becomes ln(0), which is undefined. The input set is invalid for the Eyring equation and must be checked.
Further reading
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.