Sound Transmission Loss Calculator (Mass Law)
Calculate sound transmission loss TL = 20 log(f × m) − 47 using the mass law.
Estimate STC ratings for walls and predict noise reduction across frequencies.
The mass law for sound transmission
For a single solid panel that is large compared to the wavelength of sound, the amount of sound it blocks is approximated by the mass law:
TL = 20 × log₁₀(f × m) − 47 dB
Where TL is transmission loss in decibels, f is the sound frequency in hertz, m is the panel’s surface mass density in kilograms per square meter (kg/m²), and the constant 47 reflects SI unit normalization and the acoustic impedance of air. For imperial units (lb/ft²), the constant becomes 33 instead of 47.
The 6 dB per octave rule falls out of this formula immediately. Doubling f or doubling m adds 20 × log₁₀(2) ≈ 6 dB to TL. A wall that blocks 30 dB at 500 Hz blocks roughly 36 dB at 1000 Hz, 42 dB at 2000 Hz, and so on. Symmetrically, doubling the mass of the wall raises every TL value by about 6 dB.
Why mass matters
Sound transmits through a panel by setting it vibrating. The panel’s inertia (resistance to acceleration) determines how much it vibrates for a given pressure. Heavy panels accelerate less, vibrate less, and re-radiate less sound on the other side. Light panels move freely with the pressure waves and pass most of the sound through.
This is why concrete walls beat drywall, why two layers of drywall beat one, and why heavyweight curtains over a doorway can reduce noise enough to be perceptible. The relationship is roughly logarithmic, so doubling mass for an extra 6 dB has rapidly diminishing returns: each doubling subjectively halves the loudness, but costs proportionally more material.
Where mass law breaks down
The mass law assumes an infinite limp panel with no internal stiffness, no edge support, and a uniform plane wave hitting it. Real walls violate all of these assumptions:
- Resonance frequencies: a panel of finite size has resonant frequencies where it vibrates easily and transmits sound much more freely than mass law predicts. Drywall panels resonate around 50 to 200 Hz, which is exactly where bass and traffic rumble live.
- Coincidence dip: at the coincidence frequency, bending waves in the panel match the projected wavelength of sound in air, and the panel becomes nearly transparent to sound. For 16 mm gypsum drywall this is around 2500 Hz; for 6 mm glass it is around 2000 Hz.
- Edge effects: stud connections, screws, drywall edges all create paths around the limp-panel idealization.
In practice, real wall TL is well below mass law at low frequencies (because of resonances) and dips below it at the coincidence frequency, but matches or exceeds it in the mass-controlled middle range.
Reference: typical surface densities
| Material (single layer) | Surface density (kg/m²) |
|---|---|
| 12 mm (1/2 inch) gypsum drywall | ~10 |
| 16 mm (5/8 inch) gypsum drywall | ~13 |
| Double 16 mm gypsum drywall | ~26 |
| 25 mm (1 inch) wood plank | ~12 |
| 6 mm window glass | ~15 |
| 100 mm (4 inch) concrete block | ~140 |
| 200 mm (8 inch) solid concrete | ~480 |
| 16 mm plywood | ~10 |
| Steel sheet, 1 mm | ~8 |
| Lead sheet, 1 mm | ~11 |
For typical residential construction, single drywall on a 2x4 stud wall delivers about 33 to 37 STC (Sound Transmission Class). Doubling the drywall plus filling the cavity with insulation can reach 45 to 50 STC. Genuinely soundproof construction (recording studio, theater wall) reaches STC 55 to 70+ through multiple layers, decoupled studs, mass-loaded vinyl, and resilient channels.
STC vs TL
Sound Transmission Class (STC) is a single-number rating derived from TL measurements across 16 third-octave bands from 125 Hz to 4000 Hz. STC is what building codes specify (e.g., apartment walls in many jurisdictions must achieve STC 50 or better). The rough heuristic: STC is approximately TL at 500 Hz, but the actual STC calculation weights low-frequency performance heavily, which is why bass-leaking walls have lower STC than mass law alone would predict.
| STC rating | Perceived quality |
|---|---|
| 25 | Normal speech easily understood through wall |
| 35 | Loud speech audible but not intelligible |
| 45 | Loud speech faintly heard, normal speech inaudible |
| 50 | Loud speech inaudible (apartment-wall code minimum in many places) |
| 60 | Very loud sounds barely perceptible |
| 70+ | Studio-grade isolation |
Worked example: doubling up drywall
A single 16 mm drywall sheet (m ≈ 13 kg/m²) at 500 Hz transmission loss: TL = 20 × log₁₀(500 × 13) − 47 = 20 × log₁₀(6500) − 47 = 20 × 3.81 − 47 = 76.2 − 47 = 29.2 dB
Add a second layer (now m = 26 kg/m²): TL = 20 × log₁₀(500 × 26) − 47 = 20 × log₁₀(13000) − 47 = 20 × 4.11 − 47 = 82.3 − 47 = 35.3 dB
About 6 dB more TL, as the mass law predicts. The cost of the upgrade is one extra sheet of drywall, the screws, and the tape and mud labor. The benefit is a clearly perceptible reduction in noise transmission, approximately equivalent to making the loud side 4× quieter (since perceived loudness halves every 10 dB or so).
When to use this calculator
The mass law formula gives a quick, first-order estimate of how much sound a single solid barrier will block. Use it to:
- Estimate before-spending: is doubling the wall material worth the cost?
- Compare materials: a 1 mm lead sheet (m ≈ 11 kg/m²) blocks roughly the same as 12 mm drywall (m ≈ 10) but with about 1/12 the thickness.
- Sanity-check a quoted STC rating: if a marketed product claims STC 50 with only 8 kg/m² mass, the mass-law-derived TL at 500 Hz is only 25 dB, so the STC claim probably comes from cavity decoupling or resonant cancellation rather than mass alone.
- Design educational demos showing why bass-heavy music is so much harder to block than treble.
For commercial building design and code compliance, get measured STC ratings from manufacturer test data (ASTM E90, ISO 10140). The mass law is the analytical foundation, but real assemblies need real test reports to certify against codes.