Critical Distance Calculator (Room Acoustics)
The distance from a loudspeaker or talker at which the direct sound and the room's reverberation are equally loud, from the room volume, RT60 and the source's directivity.
Results
The dashed line marks the value you entered.
What this tool does
Close to a loudspeaker or a talker you hear mostly direct sound; far away you hear mostly the reverberation of the room. The critical distance d_c is where the two are equal, and it is about 0.057 √(Q V ÷ RT60): bigger, drier rooms and more directional sources push it outward. At half that distance the direct sound is 6 dB stronger than the reverb, and at twice it the reverb is 6 dB stronger. Beyond d_c, moving the listener closer helps clarity far more than turning the volume up. Typical Q: 1 for a source in the middle of the room, about 2 against a wall or on the floor, 8 in a corner; loudspeakers list their own.
Formula
d_c ≈ 0.057 √(Q V ÷ RT60) (V in m³, RT60 in s) · A = 0.161 V ÷ RT60
Variables
| Symbol | Meaning | Unit |
|---|---|---|
q | Directivity factor Q (1 = same in all directions) | — |
v | Room volume | m³ |
rt | Reverberation time RT60 | s |
DC | Critical distance (direct = reverberant) | m |
DH | Where the direct sound is 6 dB above the reverberation | m |
DD | Where the reverberation is 6 dB above the direct sound | m |
AB | Equivalent absorption area of the room (Sabine) | m² |
Worked example
- Directivity factor Q (1 = same in all directions)2
- Room volume200 m³
- Reverberation time RT600.6 s
- Critical distance (direct = reverberant)1.47 m
- Where the direct sound is 6 dB above the reverberation0.74 m
- Where the reverberation is 6 dB above the direct sound2.94 m
- Equivalent absorption area of the room (Sabine)53.7 m²
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.