Reverberation Time Calculator
Free Reverberation time Calculator for acoustic waves. Enter variables to compute results with formulas and detailed steps.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Reverberation Time Calculator
Calculator
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Formula: RT60 = 0.161 V / A (Sabine) or RT60 = 0.161 V / (-S ln(1-alpha)) (Eyring)
Worked example — Sabine RT60: 0.961 s | Eyring RT60: 0.887 s (classroom target is 0.4-0.7 s, treatment needed)
Formula
RT60 = 0.161 V / A (Sabine) or RT60 = 0.161 V / (-S ln(1-alpha)) (Eyring)
Where RT60 is reverberation time in seconds, V is room volume in cubic meters, A is total absorption in sabins (sum of surface area times absorption coefficient), S is total surface area, and alpha is the average absorption coefficient. The factor 0.161 has units of seconds per meter.
Worked Examples
Example 1: Classroom Reverberation Assessment
Problem:A classroom is 10m x 8m x 3m with average absorption coefficient of 0.15. Calculate RT60 using both Sabine and Eyring equations.
Solution:Volume = 10 x 8 x 3 = 240 m3 Total surface area = 2(10x8) + 2(10x3) + 2(8x3) = 160 + 60 + 48 = 268 m2 Total absorption A = 268 x 0.15 = 40.2 sabins Sabine RT60 = 0.161 x 240 / 40.2 = 38.64 / 40.2 = 0.961 s Eyring RT60 = 0.161 x 240 / (-268 x ln(0.85)) = 38.64 / (-268 x -0.1625) = 38.64 / 43.56 = 0.887 s
Result:Sabine RT60: 0.961 s | Eyring RT60: 0.887 s (classroom target is 0.4-0.7 s, treatment needed)
Example 2: Concert Hall Design Target
Problem:A concert hall has volume 12,000 m3. What total absorption is needed for RT60 = 2.0 seconds?
Solution:Using Sabine: RT60 = 0.161 x V / A Rearranging: A = 0.161 x V / RT60 A = 0.161 x 12000 / 2.0 = 1932 / 2.0 = 966 sabins If total surface area is approximately 4000 m2 Required average alpha = 966 / 4000 = 0.24 Critical distance = 0.057 x sqrt(12000/2.0) = 0.057 x 77.5 = 4.4 m
Result:Total Absorption Needed: 966 sabins | Average alpha: 0.24 | Critical Distance: 4.4 m
Frequently Asked Questions
What is reverberation time (RT60) and why is it important in room acoustics?
Reverberation time RT60 is the time in seconds for sound to decay by 60 decibels after the source stops. It is the single most important parameter in room acoustics because it determines how sounds blend, overlap, and sustain in a space. A room with too long an RT60 causes speech to become unintelligible as syllables overlap each other. A room with too short an RT60 sounds dead and uncomfortable, lacking warmth and natural ambiance. Concert halls typically target 1.8-2.2 seconds for orchestral music, while classrooms need 0.4-0.7 seconds for clear speech. Recording studios often aim for very controlled, short reverberation times around 0.3-0.5 seconds.
What is the Sabine equation and when should it be used?
The Sabine equation, developed by Wallace Clement Sabine around 1900, calculates RT60 as 0.161 times the room volume divided by the total absorption in the room (RT60 = 0.161V/A). The total absorption equals the sum of each surface area multiplied by its absorption coefficient. This equation works best for rooms with relatively uniform, low-to-moderate absorption (average absorption coefficient below about 0.3). It is the most widely used reverberation formula due to its simplicity and adequate accuracy for most architectural spaces. However, it overestimates RT60 for highly absorptive rooms because it does not account for the fact that each reflection loses a greater proportion of energy.
How does the Eyring equation differ from Sabine and when is it more accurate?
The Eyring-Norris equation uses a logarithmic term instead of a linear one: RT60 = 0.161V / (-S ln(1-alpha)), where alpha is the average absorption coefficient and S is the total surface area. This formulation correctly predicts that RT60 approaches zero as absorption approaches one (a fully absorptive room), while the Sabine equation incorrectly predicts a small but finite RT60 even with perfect absorption. The Eyring equation is more accurate when average absorption coefficients exceed 0.2-0.3, such as in recording studios with heavy acoustic treatment. For low absorption (typical live rooms), both equations give nearly identical results because ln(1-alpha) approximates negative alpha for small alpha values.
What are optimal reverberation times for different types of rooms and uses?
Optimal RT60 varies dramatically by room function. Speech-focused spaces need short RT60: classrooms 0.4-0.7s, lecture halls 0.6-1.0s, conference rooms 0.3-0.6s. Music performance spaces need longer RT60: symphony halls 1.8-2.2s, opera houses 1.3-1.8s, chamber music rooms 1.4-1.7s, churches 2.0-4.0s. Multi-purpose rooms typically target 1.0-1.5s as a compromise. Recording studios need 0.2-0.5s for control rooms and 0.4-0.8s for live rooms. The optimal RT60 also depends on room volume, with larger rooms generally requiring longer reverberation to sound natural. These targets have been refined over decades of psychoacoustic research and architectural experience.
What is the absorption coefficient and how do common materials compare?
The absorption coefficient (alpha) ranges from 0 (perfect reflection) to 1 (perfect absorption) and describes what fraction of incident sound energy a surface absorbs rather than reflects. It varies with frequency, so materials are typically characterized across octave bands from 125 Hz to 4000 Hz. Concrete and glass have low absorption (0.01-0.05), reflecting most sound. Gypsum drywall absorbs moderately (0.05-0.10). Carpet on concrete absorbs 0.1-0.3 at low frequencies and 0.3-0.7 at high frequencies. Heavy curtains absorb 0.4-0.8 depending on spacing from the wall. Acoustic foam panels achieve 0.6-0.9 at mid and high frequencies. Fiberglass insulation panels are among the most absorptive at 0.8-1.0 across most frequencies.
What is the critical distance and how does it affect sound system design?
The critical distance is the distance from a sound source where the direct sound level equals the reverberant sound level. Beyond this distance, the reverberant field dominates and speech intelligibility drops significantly. The critical distance depends on both the room volume and the reverberation time, approximately equal to 0.057 times the square root of V/RT60. In a typical classroom with V=200m3 and RT60=0.7s, the critical distance is about 1.0 meter, meaning students beyond 1 meter from the teacher hear mostly reflected sound. Sound system designers use this parameter to determine speaker placement, directivity requirements, and the number of speakers needed to ensure adequate direct-to-reverberant ratio throughout the audience area.
How does air absorption affect reverberation in large spaces?
Air absorbs sound energy during propagation, with the absorption increasing with frequency, temperature, and humidity. At room temperature and moderate humidity, air absorption is negligible below 1 kHz but becomes significant above 2 kHz, especially in large spaces where sound travels long distances between reflections. In a cathedral or large arena with mean free paths of 10-20 meters, air absorption can reduce the high-frequency RT60 by 30-50 percent compared to wall absorption alone. This is why large reverberant spaces often sound warm and muffled, with strong low-frequency reverberation but rapidly decaying high frequencies. The Sabine equation accounts for this with an additional 4mV term, where m is the air attenuation coefficient in inverse meters.
What are room modes and how do they relate to reverberation at low frequencies?
Room modes are standing wave resonances that occur at frequencies where the room dimensions equal integer multiples of half wavelengths. There are three types: axial modes (between two parallel surfaces), tangential modes (involving four surfaces), and oblique modes (involving all six surfaces). Below the Schroeder frequency, the room response is dominated by individual modes creating uneven frequency response with peaks and nulls. Above the Schroeder frequency, modes overlap sufficiently to create a statistically diffuse sound field where the Sabine and Eyring equations are valid. The Schroeder frequency equals approximately 2000 times the square root of RT60/V. For a small room (50m3, RT60=0.5s), this is about 200 Hz, meaning modal behavior dominates the entire bass range.
How can reverberation time be measured in an existing room?
RT60 is measured by exciting the room with a broadband sound source and recording the decay after the source stops. The traditional method uses an impulsive source (balloon pop, starter pistol) or interrupted noise, with measurement microphones and analysis software calculating the decay rate from the impulse response. Modern methods use swept-sine signals or maximum-length sequences that provide better signal-to-noise ratio. Measurements should be taken at multiple source and receiver positions to account for spatial variation, especially below the Schroeder frequency. Standards like ISO 3382 specify procedures for measurement positions, source types, and analysis methods. Low-cost measurement systems using smartphones with calibrated microphones can achieve acceptable accuracy for basic assessments.
What practical steps can reduce excessive reverberation in a room?
To reduce RT60, add sound-absorbing materials to room surfaces. The most effective approach targets the largest untreated surfaces first. Adding acoustic ceiling tiles (alpha 0.5-0.9) to a hard ceiling dramatically reduces RT60 because the ceiling is typically the largest unobstructed surface. Wall-mounted absorptive panels covering 30-50 percent of wall area provide significant improvement. Carpet reduces high-frequency RT60 but has minimal effect at low frequencies. Heavy curtains spaced from walls absorb effectively at mid to high frequencies. For bass control, thick porous absorbers (minimum 10 cm) or membrane absorbers tuned to problematic frequencies are needed. Upholstered furniture and audience members also contribute absorption, which is why empty concert halls sound more reverberant than occupied ones.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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