Reverberation Time (Sabine's Formula) Equation, Derivation & Rearrangements

Core idea

Overview

Sabine's Formula is the foundational equation in architectural acoustics used to determine the time required for sound to decay by 60 decibels. It establishes a quantitative relationship between a room's physical volume and the total acoustic absorption provided by its surfaces and contents.

When to use: Use this formula when designing large, reverberant spaces like auditoriums or concert halls where the sound field is diffuse. It is most effective when the average absorption coefficient of the room is relatively low (below 0.2).

Why it matters: This equation allows designers to calculate the exact amount of acoustic treatment needed to ensure speech intelligibility or musical clarity. It prevents rooms from being too 'echoey' for communication or too 'dead' for performance.

Symbols

Variables

$R T_{60}$ = RT60, V = Volume, A = Absorption

R T_{60}

RT60

s

V

Volume

m^{3}

A

Absorption

sabins

Walkthrough

Derivation

Formula: Sabine Reverberation Time

Sabine's formula estimates RT60 from room volume and total absorption.

Diffuse sound field approximation (uniform energy density).
Absorption is represented by total absorption area A (sabins).

1

Relate decay time to V/A:

Larger rooms reverberate longer (higher V), more absorption reduces reverberation (higher A).

R T_{60} = 0.161 \frac{V}{A}

Result

R T_{60} = 0.161 \frac{V}{A}

Source: A-Level Music Technology — Room Acoustics

Free formulas

Rearrangements

Solve for $R T_{60}$

Make RT60 the subject

R T_{60} = 0.161 \frac{V}{A}

RT60 is already the subject of the formula.

Difficulty: 1/5

Solve for $V$

Make V the subject

V = \frac{R T _{60} A}{0.161}

Start from Sabine's Formula for Reverberation Time. To make V the subject, first multiply both sides by A, then divide by 0.161.

Difficulty: 2/5

Solve for $A$

Make A the subject

A = 0.161 \frac{V}{R T _{60}}

Start from Sabine's Reverberation Time formula. To make A the subject, first multiply both sides by A to clear the denominator, then divide by $R T_{60}$ .

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph is a straight line passing through the origin, meaning that increasing the volume results in a constant, linear increase in the time required for sound to decay. For a student of Music Technology, this indicates that larger volumes lead to longer reverberation times, while smaller volumes result in a much faster decay of sound. The most important feature of this linear relationship is that doubling the volume will always result in a doubling of the reverberation time.

Graph type: linear

Why it behaves this way

Intuition

Imagine sound waves bouncing repeatedly off the walls, ceiling, and floor of a room, gradually losing energy with each reflection until the sound becomes inaudible.

R T_{60}

Reverberation Time (60 dB decay)

The duration it takes for sound in a room to decay by 60 decibels after the source stops. A longer RT60 means the room sounds 'live' or 'echoey', while a shorter RT60 means it sounds 'dead' or 'dry'.

V

Volume of the room

Represents the total space within the room where sound energy can propagate. Larger volumes generally mean sound takes longer to decay because it has more distance to travel before encountering absorbing surfaces.

A

Total sound absorption of the room

Quantifies how much sound energy is absorbed by all surfaces and contents within the room. Higher total absorption means more sound energy is removed with each reflection, causing the sound to decay faster.

Signs and relationships

V (in numerator): A larger room volume provides more space for sound waves to travel and reflect, meaning it takes longer for the sound energy to dissipate through absorption, thus increasing the reverberation time.
A (in denominator): Greater total sound absorption means more sound energy is removed from the room with each reflection, leading to a faster decay of sound and a shorter reverberation time.

Free study cues

Insight

Canonical usage

Used to calculate reverberation time in seconds, typically using cubic meters for volume and square meters for total absorption in the SI system, or cubic feet and square feet respectively in the Imperial (US customary)

Common confusion

A common mistake is using the constant from one unit system (e.g., 0.161 for SI) with variables (V and A) specified in another unit system (e.g., cubic feet and square feet).

Unit systems

$R T_{60}$ s · Reverberation time, measured in seconds.

$V$ m^3 (SI) or ft^3 (Imperial) · Volume of the room or space.

$A$ m^2 (SI) or ft^2 (Imperial) · Total acoustic absorption in the room, often expressed in Sabins (ft^2) or metric Sabins (m^2). It is the sum of (surface area * absorption coefficient) for all surfaces.

Ballpark figures

Quantity:

One free problem

Practice Problem

A recording studio control room has a volume of 150 m³ and a total calculated absorption of 30 Sabins. Calculate the RT60 reverberation time for this space.

Volume150 m^3

Absorption30 sabins

Solve for: RT60

Hint: Divide the volume by the total absorption before multiplying by the Sabine constant of 0.161.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

A large cathedral might have an RT60 of several seconds, while a small studio should be under 0.5s.

Study smarter

Tips

Ensure the volume (V) is calculated in cubic meters (m³) to maintain compatibility with the 0.161 metric constant.
Calculate total absorption (A) by summing the products of each surface area and its respective absorption coefficient.
Be aware that this formula assumes a uniform distribution of sound and may be less accurate in small, oddly shaped rooms.

Avoid these traps

Common Mistakes

Using incorrect units for volume or area.
Convert units and scales before substituting, especially when the inputs mix s, $m^{3}$ , sabins.
Interpret the answer with its unit and context; a percentage, rate, ratio, and physical quantity do not mean the same thing.

Keep going

Related Formulas

Common questions

Frequently Asked Questions

Sabine's formula estimates RT60 from room volume and total absorption.

Use this formula when designing large, reverberant spaces like auditoriums or concert halls where the sound field is diffuse. It is most effective when the average absorption coefficient of the room is relatively low (below 0.2).

This equation allows designers to calculate the exact amount of acoustic treatment needed to ensure speech intelligibility or musical clarity. It prevents rooms from being too 'echoey' for communication or too 'dead' for performance.

Using incorrect units for volume or area. Convert units and scales before substituting, especially when the inputs mix s, m^3, sabins. Interpret the answer with its unit and context; a percentage, rate, ratio, and physical quantity do not mean the same thing.