Horn Flare Calculator for Exponential Horns

Horn Flare Calculator

Size exponential horn flare from throat, mouth, length, temperature, and target cutoff.

🎧 Quick Presets

🔧 Horn Inputs

All geometry fields use the same unit.
Sound speed changes with temperature.
Used to size the mouth and flare rate.
Round or square length along the axis.
Round uses diameter. Square uses side.
Small throat area raises the flare rate.
Use area-equivalent geometry here.
A larger mouth lowers the cutoff.
💡 Formula: exponential horn area follows S(x) = S0 e^(mx), with m = 4πfc / c. Minimum mouth area uses Sm = (c / 2fc)² / π.
Choose a preset or adjust the controls to size the horn flare.
Actual cutoff
0.0
Hz
From current geometry
Flare constant
0.000
m^-1
0.000 in^-1
Required length
0.0
in
For the target cutoff
Minimum mouth area
0.00
0.0 in²

Calculation breakdown

Air temperature20.0 °C
Sound speed343.3 m/s
Throat area0.00 m² / 0.00 in²
Mouth area0.00 m² / 0.00 in²
Area ratio0.00:1
Current length0.0 in
Target flare constant0.000 m^-1
Target mouth area0.00 m²
Target mouth diameter0.0 in
Target length at current mouth0.0 in
Equivalent area growth0.00x

📊 Horn Reference Tables

Cutoff m Min mouth Use
60 Hz2.202.60 m²Giant bass
100 Hz3.660.94 m²Bass horn
150 Hz5.490.42 m²Front load
250 Hz9.160.15 m²Mid horn
Temp c 100 Hz wave Note
0 °C331.3 m/s3.31 mCold room
10 °C337.4 m/s3.37 mCool room
20 °C343.3 m/s3.43 mRoom temp
30 °C349.4 m/s3.49 mWarm room
Horn family Cutoff band Length feel Comment
Bass horn60-120 HzVery longBig mouth area
Front loaded120-250 HzLongGood loading
Compression horn250-1000 HzMediumHigher flare
Waveguide1 kHz+ShortDirectivity control

📦 Horn Design Grid

60-100 Hz
Sub bass horn
Huge mouth area
Low flare rate
Longest path
120-250 Hz
Front loaded horn
Bass to low mid
Balanced loading
Moderate mouth
250-800 Hz
Compression horn
Compact geometry
Higher flare rate
Smaller mouth
1 kHz+
Waveguide
Directivity tool
Short path length
Control pattern

💬 Tips

Tip: Use the target cutoff to size the minimum mouth area before you worry about cabinet details.
Tip: If the mouth is too small, the horn will act more reactive below cutoff and lose loading.
This calculator assumes a classic exponential horn profile and uses air temperature to set sound speed.

Designing an exponential horn require an understanding of the mathematical relationship between the throat size, the mouth dimension, and the path length. An exponential horn gradually expand in area to load the driver and create improved sound output. The area of an exponential horn is calculate using the formula $S(x) = S_0 e^{mx}$, where the constant $m$ control the rate of expansion of the horn between the throat and the mouth.

This constant $m$ is mathematicaly linked to the horn’s cutoff frequency. If the value of the flare constant $m$ are set incorrectly, the horn will be reactive to the audio signal, which cause the horn to waste energy. The horn’s cutoff frequency, $fc$, represent the frequency below which the horn will not function as intended.

How to Design an Exponential Horn

Sound wave cannot propagate through the horn at frequencies lower than the cutoff frequency. At frequencies lower than the cutoff frequency, the horn acts as a stopped pipe that reflect the sound waves back to the driver. At frequencies more higher than the cutoff frequency, the horn increase the sensitivity of the driver.

The size of the horn’s throat determine the area from which the horn begin to expand. The throat size must match the specification of the driver. Drivers that require high level of pressure have a small throat size.

Drivers with low-cut frequency have larger throat sizes. The horns mouth must have a minimum area. If the mouth area is too small, sound output will be weak and there will be ripple at the horn’s cutoff frequency.

The temperature of the environment in which the horn will be used is another factor that need to be considered in horn design. The speed of sound in air is affect by air temperature. Changes to the temperature of the air change the speed of sound; changes in the speed of sound change the wavelength of the sound.

The temperature of the horn’s environment will impact the performance of the horn; thus, the temperature have to be accounted for in horn design. The length of the horn along its axis impact the expansion of the horn’s path. A shorter length require a higher value of the flare constant $m$ to achieve the same area expansion of the horn.

Depending on the specifications of the speaker cabinet in which the horn will be used, the area expansion might not have to be as great as the calculated factor suggest. Some horn design example can be applied to the mathematical principles described. For instance, a front loaded bass horn can be designed for 150 Hz with a 1.5-inch round throat and a 12-inch square mouth area.

The mouth area must be large enough for the horn to radiate sound effective. If the horn’s mouth area is too small for the horn’s diameter, the horn will become reactive. If you use a compression driver to create the horn, care must be taken to ensure that it does not operate below its frequency capability.

Using a compression driver with bass horns create challenges because bass horns need a very large mouth area to move the air required to create low frequency. The horn design tool include presets that can help to speed up the horn design process. A 60 Hz preset will calculate a horn with a very large mouth area and path length.

A 1 kHz waveguide preset will calculate a horn with a small throat and mouth area. The horn design tool can calculate the length of the horn that is required to achieve a target cutoff frequency. It can also calculate the growth factor of the horn.

If the calculated frequency is 20% higher than the targeted frequency, the designer can increase the path length of the horn or the horn’s mouth area can be expanded. Although the horn design formula can calculate the performance of a horn, there are other factor to consider in horn design. For instance, if the horn is in close proximity to a wall, that wall has the potential to double the mouth area of the horn.

Folding horn paths can save space on the speaker cabinet. However, folding the horn path introduce bends into the horn that may alter the sound of the horn. The material of the horn and the driver throat adapter impact the performance of the horn.

Different material have different impacts on the performance of the horn. The areas of the horn have to be equated correctly when the horn has different shape of its mouth opening. If the horn’s mouth area is not accurately equate to the area of the throat, that will lead to a loss of efficiency of the horn.

Finally, equating the horn’s cutoff frequency to the targeted frequency; calculating the minimum size of the horn’s mouth; and setting the length of the horn to the size constraints of the speaker cabinet can best improve the efficiency of the horn.

Horn Flare Calculator for Exponential Horns

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