Room Modes Calculator
The lowest standing-wave frequencies of a rectangular room, sorted, with each one marked axial, tangential or oblique.
Results
Frequency · which mode · type
34.30 100 A
42.88 010 A
54.91 110 T
61.25 001 A
68.60 200 A
70.20 101 T
74.77 011 T
80.90 210 T
82.26 111 O
85.75 020 A
91.96 201 T
92.36 120 T
101.47 211 O
102.90 300 A
105.38 021 T
Lowest mode of all
34.30
Hz
Axial mode along the length
34.30
Hz
Axial mode across the width
42.88
Hz
Axial mode floor to ceiling
61.25
Hz
Room volume
56.000
m³
Surface area of the room
90.400
m²
Length ÷ smallest dimension
1.7857
Width ÷ smallest dimension
1.4286
Height ÷ smallest dimension
1.0000
Biggest gap between modes
12.03
Hz
Where that gap starts
42.88
Hz
Modes listed
15
What this tool does
A room does not treat all bass notes alike. At certain frequencies a wave fits exactly between two surfaces and reinforces itself, and at those frequencies the bass is loud in some places and missing in others. The strongest are the axial modes, between one pair of walls; the tangential and oblique ones involve four and six surfaces and are weaker. What matters is not each mode but how evenly they are spread — a big gap in the list is a hole you will hear, and the page marks the largest one.
Formula
f = (c ÷ 2) √((p ÷ L)² + (q ÷ W)² + (r ÷ H)²), with p, q, r whole numbers not all zero
Variables
| Symbol | Meaning | Unit |
|---|---|---|
l | Room length | m |
w | Room width | m |
h | Room height | m |
c | Speed of sound | m/s |
n | How many modes to list | — |
TB | Frequency · which mode · type | — |
F1 | Lowest mode of all | Hz |
AL | Axial mode along the length | Hz |
AW | Axial mode across the width | Hz |
AH | Axial mode floor to ceiling | Hz |
VO | Room volume | m³ |
SU | Surface area of the room | m² |
RL | Length ÷ smallest dimension | — |
RW | Width ÷ smallest dimension | — |
RH | Height ÷ smallest dimension | — |
GP | Biggest gap between modes | Hz |
GA | Where that gap starts | Hz |
NM | Modes listed | — |
Worked example
- Room length5 m
- Room width4 m
- Room height2.8 m
- Speed of sound343 m/s
- How many modes to list15
- Frequency · which mode · type 34.30 100 A 42.88 010 A 54.91 110 T 61.25 001 A 68.60 200 A 70.20 101 T 74.77 011 T 80.90 210 T 82.26 111 O 85.75 020 A 91.96 201 T 92.36 120 T 101.47 211 O 102.90 300 A 105.38 021 T
- Lowest mode of all34.30 Hz
- Axial mode along the length34.30 Hz
- Axial mode across the width42.88 Hz
- Axial mode floor to ceiling61.25 Hz
- Room volume56.000 m³
- Surface area of the room90.400 m²
- Length ÷ smallest dimension1.7857
- Width ÷ smallest dimension1.4286
- Height ÷ smallest dimension1.0000
- Biggest gap between modes12.03 Hz
- Where that gap starts42.88 Hz
- Modes listed15
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 calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.