---
title: "Hearing threshold (age and reference zero)"
description: "The age-related hearing threshold distribution of ISO 7029:2017 (median, spread and population fractiles by age and sex) and the ISO 389-7:2006 free-field and diffuse-field reference threshold of hearing, over the audiometric frequencies from 125 Hz to 8000 Hz."
---

Two standards describe where the hearing threshold sits. **ISO 7029:2017**
gives the **statistical distribution of the hearing threshold with age** for an
otologically normal population — the slow, high-frequency-first loss known as
presbycusis. **ISO 389-7:2006** fixes the **reference threshold of hearing**,
the audiometric zero (0 dB HL) expressed as a sound pressure level under
free-field and diffuse-field listening. Both are defined over the audiometric
frequencies from 125 Hz to 8000 Hz.

<img class="light-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/diagram_hearing_threshold.svg" alt="The hearing-threshold model: age, sex and a population fractile feed the ISO 7029 chain — the median deviation from age 18, the upper and lower spreads su and sl, and the fractile threshold — giving the expected hearing threshold level in dB HL, referenced to the ISO 389-7 free-field or diffuse-field audiometric zero" style="width:82%"><img class="dark-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/diagram_hearing_threshold_dark.svg" alt="The hearing-threshold model: age, sex and a population fractile feed the ISO 7029 chain — the median deviation from age 18, the upper and lower spreads su and sl, and the fractile threshold — giving the expected hearing threshold level in dB HL, referenced to the ISO 389-7 free-field or diffuse-field audiometric zero" style="width:82%">

## 1. Age-related threshold (ISO 7029)

For a person older than 18, the **median** hearing threshold deviation from the
value at age 18 grows as a power law of age (ISO 7029 clause 4.2, Table 1):

$$
\Delta H_{md} = a\,(Y - 18)^{b},
$$

with coefficients $a$, $b$ per frequency and sex. The spread around the median
is modelled by two half-Gaussians whose standard deviations $s_u$ (worse than
the median) and $s_l$ (better) are fifth-degree polynomials in $(Y - 18)$
(clause 4.3, Tables 2–5). Any **population fractile** $Q$ follows from the
standard-normal quantile $z(Q)$ (clause 4.4): $\Delta H_Q = \Delta H_{md} +
z(Q)\,s$, using $s_u$ when $z \ge 0$ and $s_l$ otherwise.

```python
import phonometry as ph

# Median threshold shift of a 65-year-old man, all audiometric frequencies.
result = ph.age_threshold(65, "male", fractile=0.5)
print(result.median.round(1))     # [ 6.6  7.6  8.  9.  10.4 13.4 16.3 21.6 26.2 33.7 39.5]
print(result.median[8].round(1))  # 26.2 dB at 4000 Hz

# The worst-hearing decile (90th percentile) at 4000 Hz:
print(ph.age_threshold(65, "male", fractile=0.9).threshold[8].round(1))  # 50.3
```

The loss is largest at the high frequencies and grows with age — the classic
downward-sloping presbycusis audiogram. Men and women follow different
coefficients (the `sex` argument), and a subset of the audiometric frequencies
can be requested with `frequencies=`.

## 2. Reference threshold of hearing (ISO 389-7)

The audiometric zero is not a fixed sound pressure level: it depends on how the
sound reaches the listener. ISO 389-7:2006 Table 1 gives the reference
threshold for **free-field** (frontal incidence) and **diffuse-field**
listening.

```python
import phonometry as ph

print(ph.reference_threshold("free-field"))
# [22.1 11.4  4.4  2.4  2.4  2.4 -1.3 -5.8 -5.4  4.3 12.6]
print(ph.reference_threshold("diffuse-field")[4])   # 0.8 dB at 1000 Hz
```

The two fields agree at low frequencies and diverge above about 1 kHz, where
the ear-canal resonance and head diffraction make the frontal free field the
more sensitive condition (a lower threshold) around 3–4 kHz.

<img class="light-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/hearing_threshold.svg" alt="Two panels. Left: the ISO 7029 median hearing-threshold deviation for men at ages 20, 40, 60 and 80 on an inverted audiogram axis, with the 10 to 90 percent fractile band around the 70-year curve; the loss deepens toward high frequencies and with age. Right: the ISO 389-7 free-field and diffuse-field reference threshold, coinciding below 1 kHz and diverging above, dipping to a minimum near 3 to 4 kHz" style="width:96%"><img class="dark-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/hearing_threshold_dark.svg" alt="Two panels. Left: the ISO 7029 median hearing-threshold deviation for men at ages 20, 40, 60 and 80 on an inverted audiogram axis, with the 10 to 90 percent fractile band around the 70-year curve; the loss deepens toward high frequencies and with age. Right: the ISO 389-7 free-field and diffuse-field reference threshold, coinciding below 1 kHz and diverging above, dipping to a minimum near 3 to 4 kHz" style="width:96%">

<details>
<summary>Show the code for this figure</summary>

```python
import matplotlib.pyplot as plt
import phonometry as ph
from phonometry.hearing import AUDIOMETRIC_FREQUENCIES as f

# One line for the age distribution:
ph.age_threshold(70, "male", 0.5).plot()
plt.show()

# By hand, both panels:
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))
for age in (20, 40, 60, 80):
    r = ph.age_threshold(age, "male", 0.5)
    ax1.plot(f, r.median, "o-", label=f"{age} yr")
ax1.set_xscale("log"); ax1.invert_yaxis(); ax1.legend()

ax2.plot(f, ph.reference_threshold("free-field"), "o-", label="Free-field")
ax2.plot(f, ph.reference_threshold("diffuse-field"), "s--", label="Diffuse-field")
ax2.set_xscale("log"); ax2.legend()
plt.show()
```

</details>

The `AgeThresholdResult` carries the `median`, the `spread_upper` and
`spread_lower`, and the `threshold` at the requested fractile, and its
`.plot()` draws the median with the 10–90 % band. The noise-induced permanent
threshold shift of ISO 1999 — which adds a noise component on top of this age
component — is a separate topic.

---

**Standards.** ISO 7029:2017, *Statistical distribution of hearing thresholds
related to age and gender* — the median (clause 4.2, Table 1), the spread
around the median (clause 4.3, Tables 2–5) and its application (clause 4.4).
ISO 389-7:2006, *Reference zero for the calibration of audiometric equipment —
Reference threshold of hearing under free-field and diffuse-field listening
conditions* (Table 1).
