Room Modes Calculator
Enter the room dimensions and the air temperature to list the axial modes (the standing-wave resonances between pairs of parallel walls), from the lowest frequency up.
Formula
The resonant frequency of an axial mode (a standing wave between one pair of parallel walls) is
f = n × c ÷ (2 × L) (n = 1, 2, 3, …)
where L is the room dimension in that direction and c is the speed of sound. The speed of sound comes from the air temperature, c = 331.5 + 0.6 × temperature (°C) (the same formula as the Speaker Delay Calculator and the Sound Wavelength Calculator; humidity and pressure are not considered). Dimensions in feet or inches are converted exactly to meters (1 ft = 0.3048 m, 1 in = 0.0254 m) first, and a temperature in °F is converted exactly to °C with °C = (°F − 32) × 5 ÷ 9, so the same room entered in different units gives the same result.
The calculator lists orders 1 to 6 for the length, width and height (18 modes in all), from the lowest frequency up. Frequencies are rounded to one decimal place for display (the sorting uses the unrounded values). If two dimensions are the same, the same frequency appears more than once (in a cube, three modes share a frequency).
Example
For a room of 5 m × 4 m × 2.5 m (16.40 ft × 13.12 ft × 8.20 ft) at 20 °C (68 °F), the speed of sound is 343.5 m/s (about 1,127.0 ft/s), and the first-order modes are:
- Length (5 m): 343.5 ÷ 10 = 34.35 Hz
- Width (4 m): 343.5 ÷ 8 = 42.9375 Hz
- Height (2.5 m): 343.5 ÷ 5 = 68.7 Hz
What is covered
- Axial modes only. A room also has tangential modes (involving two pairs of walls) and oblique modes (three pairs). Axial modes are a subset of these.
- An ideal rectangular room with rigid walls. This is the condition of the formula in the reference (Wikipedia, "Room modes").
- Furniture, absorption, openings and wall materials are not considered. They change the resonances of a real room.
- Discrete modes are a useful guide at low frequencies. At higher frequencies the modes overlap closely.
- Dimensions can be from 0.1 m to 1,000 m (or the equivalent), and the temperature from −50 to 60 °C (−58 to 140 °F).
Notes
- This is a rough guide, not a basis for acoustic design.
- Absorption, reverberation time, the strength of each mode, and the best positions for speakers and listeners are not covered. For the reverberation time, see the RT60 Calculator.
- To convert between frequency and wavelength, see the Sound Wavelength Calculator. To convert between a note name and a frequency, see the Note Frequency Converter.
Frequently asked questions
What is a room mode?
A frequency at which sound reflecting between the walls of a room reinforces itself. It is set by the dimensions of the room, and the lowest frequencies are the ones that affect the character of a room most.
Why only orders 1 to 6?
The aim is to list the low-frequency resonances. Higher orders are just whole-number multiples of the basic frequency of each direction.
What about tangential and oblique modes?
They are not covered. This calculator gives the axial modes of an ideal rectangular room.
Do I get the same result in feet and in meters?
Yes. Dimensions are converted exactly to meters before the calculation, so equivalent dimensions give the same frequencies.