A- & C-Weighting Calculator (IEC 61672)

Understanding the A- and C-weighting calculator — concept and principle

Our ears are much less sensitive to low and very high frequencies than to the mid range. Sound level meters apply frequency weightings so that a single decibel number better reflects how loud or harmful a sound is. This calculator gives the A-weighting and C-weighting correction, in decibels, at any frequency, using the analytic curves defined in IEC 61672-1.

How it is calculated

With f in Hz and f² = f × f:

• R_A(f) = 12194² f⁴ / [(f² + 20.6²) × √((f² + 107.7²)(f² + 737.9²)) × (f² + 12194²)]
• A(f) = 20 log₁₀ R_A(f) + 2.00 dB
• R_C(f) = 12194² f² / [(f² + 20.6²)(f² + 12194²)]
• C(f) = 20 log₁₀ R_C(f) + 0.06 dB

The constants +2.00 and +0.06 normalise both curves to 0 dB at 1 kHz. To get a weighted level, add the correction to the unweighted level in that band.

The principle

Each term such as (f² + 20.6²) is the response of a simple first-order filter with a corner at 20.6 Hz, 107.7 Hz, 737.9 Hz or 12,194 Hz. Combining them gives a smooth curve that rolls off steeply at low frequency and gently above about 10 kHz. The A curve was originally modelled on human hearing at fairly low loudness (roughly the 40-phon equal-loudness contour), so it cuts bass strongly. The C curve is almost flat from about 31.5 Hz to 8 kHz and was intended for loud sounds, where the ear's response is flatter. Because the two differ mainly at low frequencies, the difference between C- and A-weighted levels indicates how much low-frequency energy a noise contains.

Worked example

1. Input: f = 100 Hz, so f² = 10,000.
2. R_A = 0.087650; 20 log₁₀(0.087650) = −21.145 dB.
3. A = −21.145 + 2.00 = −19.14495429 dB.
4. R_C = 0.959227; 20 log₁₀(0.959227) = −0.3616 dB.
5. C = −0.3616 + 0.06 = −0.3015721491 dB.

So a 100 Hz tone measured at 70 dB unweighted reads about 50.9 dB(A) but about 69.7 dB(C).

How to read the result

Typical A values: about −39.5 dB at 31.5 Hz, −30.3 dB at 50 Hz, −19.1 dB at 100 Hz, 0 at 1 kHz, a small boost of about +1.3 dB around 2.5 kHz and −2.5 dB at 10 kHz. C values stay within about −3 dB from 31.5 Hz to 8 kHz. Workplace and environmental noise limits are usually stated in dB(A); peak sound pressure for impulse noise is often assessed with C-weighting.

Common mistakes

• Subtracting the weighting instead of adding it (the values are already negative where the ear is less sensitive).
• Applying a single-frequency correction to broadband noise; weight each band, then sum energetically.
• Assuming dB(A) equals perceived loudness; it is a standardised approximation.

Frequently asked questions

Why is 1 kHz the reference?

It is the standard reference frequency for acoustical measurement, so all weightings are defined as 0 dB there.

What is Z-weighting?

Z means zero weighting: a flat response within the instrument's specified range.

Sources: IEC 61672-1:2013, Electroacoustics — Sound level meters — Part 1: Specifications · ISO 226, Acoustics — Normal equal-loudness-level contours