Formula

Formula used (example: A-weighted overall level)

\( L_{A} = 10 \log_{10} \left( \displaystyle\sum_{i} 10^{\left(L_{Z,i} + A_i\right)/10} \right) \)

What the symbols mean

L_A — A-weighted overall level (dB(A))
L_{Z,i} — unweighted level of band i (dB)
A_i — A-weighting of band i (dB), defined by IEC 61672
i — band index (octave or third-octave)

Inputs

Type your spectrum band by band. Pick the weighting it is expressed in: the tool brings it back to Z (linear) then applies A and C.

Resolution

Weighting of the input spectrum

Examples: · —

Results

Overall Z (lin.)—dB(Z)

Overall A—dB(A)

Overall C—dB(C)

Type at least one band to compute.

Spectra: input (Z) and weighted

Z (lin.) A C

Spectra by weighting

Understand the theory — why the ear imposes its curvesinteractive

A sound level meter measures pressure; an ear perceives sound. The two disagree: at equal physical level, a ventilation hum at 63 Hz sounds far quieter than a voice at 1 kHz. Frequency weightings correct the measured level to approximate perception: the A curve mimics the ear's sensitivity at everyday levels, the nearly flat C curve only departs at the extremes, and Z (zero) touches nothing. Drag the cursor below: at 50 Hz, A-weighting removes more than 30 dB!

Key takeaway. dB(A) is the common language of noise: occupational limits, neighbourhood noise, building acoustics. dB(C) serves peak levels and low-frequency detection. dB(Z) is the raw measurement, essential for intermediate calculations. Weight band by band, then sum energetically — never arithmetically.

The ear is not linear: equal-loudness contours

In 1933 Fletcher and Munson had listeners compare pure tones and drew the equal-loudness contours (now standardised in ISO 226): to sound as loud as a 1 kHz tone at 40 dB, a 50 Hz tone must be played at about 75 dB. The ear is deaf to bass, excellent between 2 and 5 kHz (the ear-canal resonance), then declines at the highest frequencies. One more crucial fact: the contours flatten as level rises — at 100 phons, bass is barely penalised any more.

Where do A and C come from?

Weightings are the simplified inverse of those contours: A derives from the 40-phon contour (moderate levels), C from the 100-phon contour (high levels, hence almost flat). The B (60 phon) and D (aviation) weightings were dropped by modern standards. IEC 61672-1 defines A and C analytically, as a rational function built on four characteristic frequencies (20.6 Hz, 107.7 Hz, 737.9 Hz and 12,194 Hz):

\[ R_A(f) = \dfrac{12194^2 f^4}{(f^2+20{,}6^2)\sqrt{(f^2+107{,}7^2)(f^2+737{,}9^2)}\,(f^2+12194^2)} \]

\[ A(f) = 20\log_{10} R_A(f) + 2{,}00 \qquad C(f) = 20\log_{10}\!\left[\dfrac{12194^2 f^2}{(f^2+20{,}6^2)(f^2+12194^2)}\right] + 0{,}06 \]

The constant term (+2.00 dB for A, +0.06 dB for C) normalises the curve to 0 dB at 1 kHz — which is why every weighting crosses there. This tool computes these exact formulas at the exact mid-band frequencies (\(f_m = 1000 \cdot 10^{n/10}\) Hz), reproducing the standardised tables to within 0.1 dB.

Octave-band values

Band	A (dB)	C (dB)
31.5 Hz	−39.4	−3.0
63 Hz	−26.2	−0.8
125 Hz	−16.1	−0.2
250 Hz	−8.6	0.0
500 Hz	−3.2	0.0
1 kHz	0.0	0.0
2 kHz	+1.2	−0.2
4 kHz	+1.0	−0.8
8 kHz	−1.1	−3.0
16 kHz	−6.6	−8.5

From spectrum to weighted overall level

To get an overall dB(A) from an unweighted spectrum: add each band's weighting \(A_i\), then sum the bands energetically:

\[ L_A = 10\log_{10}\sum_i 10^{(L_{Z,i}+A_i)/10} \]

The reverse operation (recovering the Z spectrum from per-band dB(A) levels) is a simple band-by-band subtraction — that is what this tool does when you declare your spectrum as "entered in dB(A)". However, a single overall dB(A) figure cannot be "un-weighted": without the band distribution, the information is gone.

Same energy, very different perceptions

The spectrum below keeps a constant 80 dB overall Z level. Slide the spectral balance from bass to treble: dB(C) barely moves while dB(A) soars or collapses. This is exactly why a plant room "at 80 dB" can be quiet — or loud — in regulatory terms.

The C − A indicator: a low-frequency detector

The difference between the overall levels L_C − L_A is an instant spectral diagnosis: near 0 dB, the noise is dominated by mids/highs; beyond roughly 10 dB, low frequencies dominate — think ventilation, transformers, amplified music. A useful reflex before even opening the spectrum.

What regulations require where

Occupational noise law assesses daily exposure L_EX,8h in dB(A) and peaks L_p,C,peak in dB(C) (action values 80/85 dB(A) and 135/137 dB(C) in the EU). Neighbourhood noise, strategic noise maps (L_den) and building acoustics also speak dB(A). dB(C) appears wherever peaks or bass matter: concert venues, shooting ranges, hearing-protector ratings.

The limits of dB(A)

dB(A) applies a 40-phon curve to every level: it underestimates low-frequency annoyance at high levels, ignores prominent tones and says nothing about impulsiveness. The same dB(A) can cover very differently annoying situations — hence the complementary indicators (C − A, band analysis, tonal penalties).

Classic pitfalls.

Adding dB arithmetically — two 60 dB bands make 63 dB, not 120. Summation is always energetic.
"Converting" an overall dB ↔ dB(A) without a spectrum — impossible: the weighting depends on the frequency content.
Confusing Z with "lin" — the old "linear" depended on the meter; Z is defined (10 Hz–20 kHz, flat) by IEC 61672.
Assessing peaks in dB(A) — regulations require dB(C).

Keep going

Add decibel levels Convert third-octaves to octaves

Sources : IEC 61672-1:2013 Sound level meters; ISO 226 Normal equal-loudness-level contours; D. A. Bies & C. H. Hansen, Engineering Noise Control; J.-C. Pascal, Vibrations et Acoustique, ENSIM — Le Mans Université.