# ISO 226 Normal Equal-Loudness-Level Contour Calculator

The ISO 226 standard is the Acoustics Standard for normal equal-loudness-level contours. Normal equal-level-contours are often referred to as equal-loudness-curves and provide technical data to establish the perceived loudness levels of humans with 'normal' hearing aged between 18 and 25 years of age. This article provides a handy calculator for anyone who wants to determine detailed data contours for Phons between 0 and 90.

## ISO 226 Summarized

What is ISO 226? The equal-loudness contour acoustics standard is determined through hearing tests of real people. The test subjects are chosen who have regular health and do not have any signs or symptoms of hearing impairment. The testing is carried out in optimal laboratory conditions in a free sound field. This is an area, typically a room, whose boundaries (the walls) have no noticeable effect on the sound source or the subjects listening ability.

Pairs of continuous tones are played, directly towards the test subjects, who in turn identify which one they perceived as louder, or whether the sounds are perceived as equally loud. The test data taken from the subjects is then analyzed and “normalized” to help understand the general workings of human hearing.

For example, when a person is tested and hears the 10kHz tone played at 54dB, they perceived it as being the same loudness as 100Hz at 64dB.

##### Did you ever wonder what the loudness button does on a home hi-fi amplifier?

When the button is pressed, the amplifier boosts low and high frequencies to help the listener “perceive” a higher volume than the actual SPL.

### What ISO 226 Means for Mixing Music

Firstly, it is important to remember that the data collected for the ISO Standard is 'averaged' and that people tend NOT to fit any particular phon contour exactly. As a mix engineer, the standard is useful because it helps us understand that humans hear high and low frequencies differently at lower “loudness” levels.

You can see this for yourself using the Contour Calculator. Compare the contours produced using 1 phon and 90 phon. The slope of the 1 phon curve from 20Hz to 400Hz is much steeper than that of the 90 phon curve.

The higher the volume level goes, the easier it is to recognize SPL differences - that's why it is important to mix at an optimal level. When your monitors are to quiet, you will find it challenging to judge low and high frequencies. When your monitors are too loud, you will damage your hearing.

The level recommended for the K-system when mixing is 83dB (86dB with both monitors). This level depends on your room too – for example, my studio monitors are calibrated to 79.3dB.

## ISO 226 Contour Calculator

Enter a Phon level, and press calculate. The page will refresh and the graph will update. The graph currently shows a contour at 40 Phon. Hover over the points on the graph to read the exact x and y values.

Valid Phons are between 0 and 90.

### 40 Phon Equal-Loudness-Level Contour

#### Here are a few examples of what the above 40 Phon curve shows:

1. A 100Hz tone played at 64.4dB is perceived as being the same loudness as 10kHz at 54.3dB.
2. A 400Hz tone played at 45.0dB is perceived as being the same loudness as 12.5kHz at 51.5dB.
3. A 1kHz tone played at 40.0dB is perceived as being the same loudness as 2.5kHz at 36.5dB.

4. A full set of results is tabulated at the bottom of the page (see Table 1).

## The Equal Loudness Contour Graph

### X-Axis

The x-axis shows frequency from 20 Hz to 100 kHz on a logarithmic scale. The reason that the x-axis is logarithmic is because frequency increases by octaves and octave frequencies double up as they increase. If the x-axis were linear, it would be squashed to one side (see Figure 1).

Figure 1: 40 Phon Equal Loudness Curve on Linear x-axis

### Y-Axis

The y-axis shows the sound pressure level (SPL) from -10 dB to 130 dB.

### The Curve

The calculated Phon is plotted (shown in RED) using 29 points between 20 Hz and 12.5 kHz. The calculation accepts any Phon number between 0 (zero) and 90. Numbers above 90 or below 0 are outside of the ISO standard.

## ISO 266 Equations

For completeness, here are the equations that are referenced in ISO 226.

##### The SPL Lp of a pure tone frequency f, with loudness LN , is calculated:
$${L_p =\left[ \frac{10}{a_f} \times \textrm{lg} A_f\right] \textrm{dB} - L_U + 94\textrm{ dB}}$$

where,

$${A_f = 4.47 \times 10^{-3} \times (10^{0.025L_N}-1.15) + \left[ 0.4 \times 10^\left[ ^\frac{T_f+L_U}{10} -9 \right] \right] ^{a_f}, }$$

Tf   is the exponent for loudness perception,

af   is the threshold of hearing,

and  LU   is the magnitude of the linear transfer function normalized at 1kHz.

### Tabulated Results of 40 Phon Equal Loudness Curve

Frequency [Hz] SPL [dB]
2099.85
2593.94
31.588.17
4082.63
5077.78
6373.08
8068.48
10064.37
12560.59
16056.70
20053.41
25050.40
31547.58
40044.98
50043.05
63041.34
80040.06
100040.01
125041.82
160042.51
200039.23
250036.51
315035.61
400036.65
500040.01
630045.83
800051.80
1000054.28
1250051.49

Table 1: Frequencies and Sound Pressure Levels for 40 Phon (40 dB SPL at 1KHz)

### ISO 226 Equation Values

HzAfLUTf
200.532-31.678.5
250.506-27.268.7
31.50.48-2359.5
400.455-19.151.1
500.432-15.944
630.409-1337.5
800.387-10.331.5
1000.367-8.126.5
1250.349-6.222.1
1600.33-4.517.9
2000.315-3.114.4
2500.301-211.4
3150.288-1.18.6
4000.276-0.46.2
5000.26704.4
6300.2590.33
8000.2530.52.2
10000.2502.4
12500.246-2.73.5
16000.244-4.11.7
20000.243-1-1.3
25000.2431.7-4.2
31500.2432.5-6
40000.2421.2-5.4
50000.242-2.1-1.5
63000.245-7.16
80000.254-11.212.6
100000.271-10.713.9
125000.301-3.112.3