Reverberation Time Calculator
Free Reverberation time Calculator for acoustic waves. Enter variables to compute results with formulas and detailed steps.
Calculator
Adjust values & calculateRoom Modes (Lowest Frequencies)
Formula
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.
Last reviewed: December 2025
Worked Examples
Example 1: Classroom Reverberation Assessment
Example 2: Concert Hall Design Target
Background & Theory
The Reverberation Time Calculator applies the following established principles and formulas. Date and time calculations underpin a vast range of applications from financial settlement to scheduling and age verification. The complexity arises because civil timekeeping uses irregular units: months have 28, 29, 30, or 31 days; years have 365 or 366 days; hours, minutes, and seconds use base-60 arithmetic; and time zones introduce offsets ranging from -12:00 to +14:00 relative to UTC. The Gregorian calendar's leap year rule is a compound condition: a year is a leap year if it is divisible by 4, except for century years, which must be divisible by 400. Thus 1900 was not a leap year but 2000 was. This rule keeps the calendar synchronized with the solar year to within about 26 seconds per year. For algorithmic date calculations, the Julian Day Number provides a continuous integer count of days since January 1, 4713 BCE, eliminating the irregularity of calendar months and making interval arithmetic straightforward. The Unix epoch, by contrast, counts seconds since 00:00:00 UTC on January 1, 1970, and is the basis of POSIX time used in most computing systems. ISO 8601 standardizes date and time representation as YYYY-MM-DD and combined datetime as YYYY-MM-DDTHH:MM:SS±HH:MM, ensuring unambiguous machine-readable interchange across locales that would otherwise differ in day/month/year ordering. Business day calculation requires excluding weekends and, optionally, a jurisdiction-specific list of public holidays. Duration calculations expressed in years, months, and days must account for the variable length of months, making them non-commutative: the interval from January 31 to February 28 is different from the interval from February 28 to March 31. Age calculation algorithms must handle the edge case of birthdays on February 29 and ensure that a person born on December 31 is not counted as one year older on January 1 of the following year until the clock passes midnight. Zeller's Congruence provides a closed-form formula to determine the day of the week for any Gregorian or Julian calendar date using only integer arithmetic.
History
The history behind the Reverberation Time Calculator traces back through the following developments. The need to track time and predict astronomical events gave rise to calendrical systems independently across many civilizations. The Babylonians, around 2000 BCE, developed a lunisolar calendar with 12 months of alternating 29 and 30 days, inserting an intercalary month periodically to keep pace with the solar year. They also divided the day into 24 hours and the hour into 60 minutes, a sexagesimal convention that persists in every modern clock. The Egyptian civil calendar used 12 months of exactly 30 days plus five epagomenal days, totaling 365 days. Though simple for administrative purposes, it drifted against the solar year by one day every four years. Julius Caesar, advised by the Egyptian astronomer Sosigenes, reformed the Roman calendar in 45 BCE. The Julian calendar introduced a 365-day year with a leap day every four years, a system that served Europe for over sixteen centuries. By the 16th century, the accumulated error of the Julian calendar had shifted the spring equinox ten days from its ecclesiastically mandated date, disrupting the calculation of Easter. Pope Gregory XIII commissioned the calendar reform that bears his name, and the Gregorian calendar was introduced in Catholic countries in October 1582. The transition required skipping ten days: October 4 was followed by October 15. Protestant and Orthodox countries adopted the reform slowly; Britain and its colonies switched in 1752, Russia not until 1918, and Greece in 1923. The expansion of railways in the 1840s created an urgent practical problem: each city operated on its own local solar time, making train timetables impossible to coordinate. British railways adopted Greenwich Mean Time as a standard in 1847. The International Meridian Conference of 1884 in Washington formalized the prime meridian at Greenwich and established the global framework of 24 time zones. Daylight saving time was first adopted nationally during World War I to reduce coal consumption. The development of atomic clocks after World War II led to the definition of Coordinated Universal Time (UTC) in 1960, accurate to nanoseconds. The Y2K problem of 1999-2000 demonstrated that two-digit year storage in legacy systems could cause widespread failures, prompting a global remediation effort costing an estimated 300 to 600 billion dollars.
Frequently Asked Questions
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\nTotal surface area = 2(10x8) + 2(10x3) + 2(8x3) = 160 + 60 + 48 = 268 m2\nTotal absorption A = 268 x 0.15 = 40.2 sabins\nSabine RT60 = 0.161 x 240 / 40.2 = 38.64 / 40.2 = 0.961 s\nEyring 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\nRearranging: A = 0.161 x V / RT60\nA = 0.161 x 12000 / 2.0 = 1932 / 2.0 = 966 sabins\nIf total surface area is approximately 4000 m2\nRequired average alpha = 966 / 4000 = 0.24\nCritical 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.
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.
Can I use Reverberation Time Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy