Sabine & Eyring Reverberation Time (RT60) Room Acoustics Formulas

Compare two approximate room models

RT60 describes a 60 dB decay after the source stops. These simplified equations use room volume in cubic meters, total internal surface area in square meters and mean absorption at a specified frequency band. The coefficient 0.161 is a rounded SI approximation near room temperature. Air attenuation and detailed room geometry are not included.

Both formulas rely on diffuse-field assumptions. Eyring is not a guaranteed true decay time for a heavily treated studio, anechoic chamber or nonuniformly absorbing room. Modal behavior and spatial absorption distribution can make either estimate unsuitable. Use measurements or a more detailed model when those effects matter.

Sabine estimate

Enter volume in B2, total surface area in B3 and area-weighted absorption in B4. For the same frequency band, mean absorption is SUM(area*coefficient)/SUM(area); a simple average is appropriate only for equal areas.

The example uses 300 m³, 280 m² and 0.25. Sabine gives 0.69 seconds. Treat this as a model estimate, not a measured decay.

=IF(COUNT(B2:B4)<>3,"Enter numeric inputs",IF(OR(B2<=0,B3<=0),"Use positive volume and area",IF(OR(B4<=0,B4>=1),"Use absorption between 0 and 1",0.161*B2/(B3*B4))))

Eyring estimate

The logarithmic reflection-loss denominator gives approximately 0.599620 seconds for the same inputs. At low absorption, -LN(1-alpha) approaches alpha, so the formulas approach one another; there is no exact agreement cutoff at 0.20.

At alpha approaching 1 the Eyring expression tends toward zero mathematically, but this does not establish accurate room behavior in that limit. Both example formulas deliberately require 0 < alpha < 1 and positive volume and area. Alpha=0 produces no finite decay time in this lossless model; alpha=1 makes the direct logarithmic expression undefined.

=IF(COUNT(B2:B4)<>3,"Enter numeric inputs",IF(OR(B2<=0,B3<=0),"Use positive volume and area",IF(OR(B4<=0,B4>=1),"Use absorption between 0 and 1",0.161*B2/(-B3*LN(1-B4)))))

Further reading

• COMSOL — Small Concert Hall Acoustics, Sabine and Eyring predictions
• ASHRAE Handbook — Sound and Vibration