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NAL-R hearing aid insertion gain calculator

Enter the hearing thresholds at 250, 500, 1000, 2000 and 4000 hertz to get the three-frequency average, the NAL-R correction and the target insertion gain at each frequency for a linear hearing aid.

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Results

Three-frequency average (500, 1000, 2000 Hz)

40.0 dB HL

A moderate loss: the usual range for a hearing aid fitting
NAL-R correction X (0.15 × the three-frequency average)
6.0 dB
Insertion gain at 250 Hz
0.0 dB
Insertion gain at 500 Hz
7.3 dB
Insertion gain at 1000 Hz
19.4 dB
Insertion gain at 2000 Hz
20.5 dB
Insertion gain at 4000 Hz
22.6 dB

The NAL-R calculator gives the target insertion gain of a hearing aid at 250, 500, 1000, 2000 and 4000 hertz from the thresholds of the audiogram, with the three-frequency average and the correction X.

How the calculation works

  • Enter the five thresholds in dB HL.
  • Read the three-frequency average and X.
  • Read the gain at each frequency.

Example

With thresholds of 20, 30, 40, 50 and 60 dB HL, the three-frequency average is (30 + 40 + 50) / 3 = 40.0 dB HL, so X = 0.15 × 40.0 = 6.0 dB. The gain at 1000 Hz is X + 0.31 × 40 + 1 = 19.4 dB, at 2000 Hz it is X + 0.31 × 50 − 1 = 20.5 dB, and at 4000 Hz it is X + 0.31 × 60 − 2 = 22.6 dB. At 250 Hz the result is below zero and is set to 0.0 dB.

Why it matters

The calculator helps audiology and hearing aid dispensing students, hearing aid fitters and teachers who want to show how an audiogram turns into a prescription of gain.

Good to know

The NAL-R formula adds to a base of 0.31 times the threshold at each frequency a constant that depends on the frequency, and it adds a correction X that grows with the average loss in the speech range. The result is a gain for a speech input of average level, 65 dB SPL, so modern aids with compression give different gains at soft and loud inputs. Insertion gain is not the same as the full-on gain of the aid, and the real gain is verified on the ear of the user with a probe microphone and fine-tuned from the feedback of the user. The first fitting is often lower than the target to let the user adapt to the new sounds in a few weeks, and the gain at a given frequency can also be limited by feedback, by the size of the vent, by a dead region of the cochlea, or by the maximum output of the aid. Children, people with conductive loss and users of cochlear implants need other methods. The gains are given in decibels and should not be read as a prescription.

The ear canal calculator treats the resonance that the aid must restore, the air-bone gap calculator separates types of loss, the pure-tone average calculator grades the loss and the battery life calculator estimates the running cost.

Frequently asked questions

What is NAL-R?

NAL-R is a prescription formula by the National Acoustic Laboratories of Australia that gives the target insertion gain of a linear hearing aid so that speech of average level is made equally loud across the frequency bands, and as intelligible as possible.

What is insertion gain?

It is the difference between the sound level at the eardrum with the hearing aid and without it, measured with a probe microphone in the ear canal. It is different from the gain measured in a coupler on a test box.

Is it still used?

The newer NAL-NL2 and DSL v5 formulas handle compression, which is standard in modern aids, and take more variables into account. NAL-R remains a classic teaching example because its structure is simple.

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Results are estimates provided for information purposes. They do not replace professional advice.

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