Sound Intensity Calculator with Frequency Weighting
Use this sound intensity calculator to compute I = P / (4π·r²) at any distance from a point source, then apply A-weighting or C-weighting per IEC 61672. Includes ISO 226 threshold-of-hearing reference at the chosen frequency to determine audibility margin.
Input
Result
A & C Weighting at Common Frequencies
| Frequency | A-weighting | C-weighting | Threshold (MAF) |
|---|---|---|---|
| 20 Hz | −50.4 dB | −6.2 dB | 76 dB |
| 31.5 Hz | −39.5 dB | −3.0 dB | 65 dB |
| 63 Hz | −26.2 dB | −0.8 dB | 50 dB |
| 125 Hz | −16.2 dB | −0.2 dB | 35 dB |
| 250 Hz | −8.7 dB | 0 dB | 19 dB |
| 500 Hz | −3.2 dB | 0 dB | 9 dB |
| 1 kHz | 0 dB (ref) | 0 dB (ref) | 3.6 dB |
| 2 kHz | +1.2 dB | −0.2 dB | 1.4 dB |
| 4 kHz | +1.0 dB | −0.8 dB | −3.9 dB (most sensitive) |
| 8 kHz | −1.1 dB | −3.0 dB | 15.3 dB |
| 16 kHz | −6.6 dB | −8.5 dB | 13.4 dB |
| 20 kHz | −9.3 dB | −11.2 dB | ~40 dB |
About Sound Intensity & Frequency Weighting
Sound intensity (W/m²) is the acoustic power flowing through a unit area perpendicular to the wavefront. For a point source radiating into free space, the sound intensity formula is I = P / (4π·r²) — the inverse-square law in its purest form. Every time you double the distance from a source, the intensity drops by 6 dB. Intensity level in decibels is then computed as LI = 10·log₁₀(I / 10⁻¹² W/m²), using the standard reference intensity of 10⁻¹² W/m².
Why frequency weighting?
Human hearing is not equally sensitive to all frequencies. We hear best around 2–5 kHz and progressively worse at the extremes. A 60 dB tone at 100 Hz sounds about as loud as a 35 dB tone at 1 kHz — the equal-loudness contours (ISO 226 phon curves) describe this relationship across the audible spectrum. A-weighting applies a filter that approximates human sensitivity at moderate levels (~40 phon equal-loudness contour). When a measurement is reported as "dBA", it has been filtered this way and roughly corresponds to perceived loudness. For low-frequency machinery or industrial noise assessment, this distinction becomes critical.
A-weighting (dBA) vs C-weighting (dBC)
A-weighting heavily attenuates low frequencies (−50 dB at 20 Hz) and somewhat attenuates very high frequencies. It is the standard for environmental noise regulations, workplace OSHA/NIOSH exposure limits, and consumer product noise specifications. C-weighting is nearly flat across the audible band (−0.2 dB at 250 Hz to 4 kHz) and only rolls off below 30 Hz and above 6 kHz. It is used for peak and impulse measurements — gunshots, explosions, machinery startup transients — where low-frequency content matters and where A-weighting would discard real energy. You can use the dB Addition Calculator to combine multiple sources correctly once you have each source’s SPL.
Threshold of hearing (MAF, ISO 226)
The minimum audible field (MAF) is the quietest tone an average young listener with normal hearing can detect, measured binaurally in a free field facing the source. It varies dramatically with frequency: ~76 dB SPL at 20 Hz, ~3.6 dB SPL at 1 kHz, dipping to ~−4 dB SPL at 4 kHz (the most sensitive region of the cochlea), and rising sharply above 10 kHz. This tool uses the ISO 226:2003 standard threshold curve and interpolates between the standard frequencies shown in the reference table above.
"Audibility margin"
The audibility margin is how many dB above the threshold of hearing the unweighted SPLZ sits. Positive values are audible — about +20 dB is "clearly audible", +60 dB is "loud", and +100 dB approaches the threshold of pain (~130 dB SPL). Negative values are inaudible to typical listeners, but a strong infrasonic or ultrasonic source at high SPL can still pump energy into tissue even when no sound is perceived. For everyday noise compliance work, the audibility margin helps confirm that a calculated source level is safely below annoyance or legal thresholds at a given receiver distance.
Frequently Asked Questions
Why does dBA show ear-friendly numbers but dBC sometimes shows much higher?
What's the difference between Z, A, and C weighting?
Does the inverse-square law account for room reflections?
I = P/(4π·r²) assumes a point source in unbounded free space (anechoic outdoors). In a real room, reflections add energy, raising measured SPL above the free-field prediction. The room's reverberant field eventually dominates at distances beyond the critical distance, where direct and reverberant levels are equal. For typical living rooms this is 1-3 m. Use this tool's free-field result as a baseline; add 3-10 dB for normal-room behavior.Why is the threshold of hearing negative dB SPL above 1 kHz?
Does A-weighting account for hearing damage risk?
What's the relationship between sound intensity and sound pressure level?
I = p²/(ρc) where p is RMS pressure, ρ is air density (~1.2 kg/m³), and c is speed of sound (~343 m/s). So ρc ≈ 411 N·s/m³ (acoustic impedance of air). At 1 Pa RMS pressure: I = 1/411 ≈ 2.4 mW/m² ≈ 94 dB SPL. The dB scales are designed so that SPL and intensity level numerically coincide in air at standard conditions — convenient since it lets us measure pressure (microphones) and report intensity-equivalent dB.How do I convert sound power level (Lw) in dB to sound power in watts to use this calculator?
P (W) = 10⁻¹² × 10^(LW/10). For example, a lawnmower rated at 96 dB LW has P = 10⁻¹² × 10^9.6 ≈ 4 W. Enter that wattage in the Power field, set your distance, and this tool computes the expected SPL at that point. This is the standard method used in ISO 3744/3745 sound power measurement standards.When should I use half-space (2π) instead of full-space (4π) in the intensity formula?
I = P/(4π·r²), which assumes the source radiates equally in all directions into free space — suitable for a source suspended mid-air outdoors. If the source sits on a hard reflecting floor (the common real-world case), acoustic power is directed into a hemisphere rather than a full sphere, so the formula becomes I = P/(2π·r²), adding ~3 dB to the SPL. For sources in a room corner (1/8 sphere), add ~9 dB. Use the free-field result here as a conservative baseline and add the appropriate boundary correction for your scenario.