Why ratings cannot be averaged
A transmission loss rating is a logarithm. Turning it back into something you can add means converting to a transmission coefficient — the fraction of sound energy that passes through — which is ten raised to the power of minus the rating over ten. A rating of 55 becomes a coefficient of 0.00000316. A rating of 30 becomes 0.001. The 30 dB element passes three hundred and sixteen times as much energy per square foot as the 55 dB one.
Once everything is in coefficients you can do the obvious thing: multiply each element by its area, add them up, divide by the total area, and convert back with minus ten times the base ten logarithm. That is the whole calculation, and it is the only correct way to combine elements.
Work through a common case. A wall 16 feet by 8 feet is 128 square feet, and it holds a 3 by 7 door, so there are 107 square feet of wall and 21 square feet of door. At 55 for the wall and 30 for the door, the wall contributes 107 times 0.00000316, which is 0.000338, and the door contributes 21 times 0.001, which is 0.021. The total is 0.021338 over 128 square feet, giving a coefficient of 0.0001667 and a composite of 37.8 dB.
The wall was rated 55. The partition is 37.8. Sixteen percent of the area threw away seventeen decibels, and the door is carrying 98.4 percent of everything that gets through.
The ceiling the weak element sets
There is a limit no amount of work on the rest can beat. If one element of area A sits in a partition of total area T, the composite can never exceed that element rating plus ten times the base ten logarithm of T divided by A, because even with the rest of the partition perfect that element is still passing sound.
| Weak element | Its share of the partition | Best composite it permits, at 30 dB |
|---|---|---|
| 3 by 7 door in a 128 sq ft wall | 16.4% | 37.9 dB |
| Same door in a 250 sq ft wall | 8.4% | 40.8 dB |
| Double door, 42 sq ft in 128 | 32.8% | 34.8 dB |
| 10 sq ft of glazing in 128 | 7.8% | 41.1 dB |
The practical use of that column is triage. If the ceiling the door sets is already below where you wanted to be, upgrading the wall assembly is money spent on the wrong element. Fix the ceiling first — a better door assembly, or no door in that wall at all — and only then does the wall specification start to matter.
Holes have no rating
An unsealed opening is the special case, because its transmission coefficient is 1. It goes into the sum at full area with no discount whatever, while a 55 dB wall goes in at three millionths of its area. That is how something measured in square inches ends up competing with something measured in square feet.
Take the same 128 square foot wall at 55 with no door at all, and put a single square inch of clear air path through it. That is 0.00694 square feet at a coefficient of 1, against 127.99 square feet at 0.00000316. The sum is 0.00694 plus 0.000404, which is 0.00734, over 128. The composite is 42.4 dB. One square inch has taken 12.6 decibels off a 55 dB wall.
The list of things that are a square inch of clear air path is longer than people expect. A door undercut of half an inch across a 36 inch door is 18 square inches. Two outlet boxes cut into the same stud bay back to back are a direct path. A recessed light fitting, a duct, a transfer grille, and the gap where a cable passes through are all on the list. So is the perimeter of a door with no seals, which is usually the largest single opening in a domestic partition and the one nobody counts because it does not look like a hole.
What a single number does not tell you
Single figure ratings compress a measurement across many frequency bands into one number, and the weighting used favours speech frequencies. A home theatre is not a speech source. The energy that annoys the rest of the house comes from a subwoofer working two octaves below where the rating is paying attention, and low frequencies pass through construction far more readily than the single number implies.
Two assemblies with identical single figure ratings can behave completely differently under a film soundtrack for that reason, and the frequency curve in the test report tells you more than the headline figure does. Where the low end genuinely matters, the useful description is the curve and the useful evidence is a measurement, not a rating on a data sheet.
There is also a path this arithmetic does not model at all. Flanking is sound travelling around the partition rather than through it — along a continuous floor, through a shared ceiling cavity, up a stud that runs past the junction, through a duct that serves both rooms. A partition can be built exactly to its tested detail and still underperform because the energy went round it. Composite arithmetic assumes the only route is through the elements you listed, and in a real building that assumption is often the weakest part of the whole calculation.
Using this before you spend anything
The sequence that works is to list every element of the partition with its area, put the manufacturer figure against each one, and see which row carries most of the transmitted energy. Improve that row. Recalculate. Repeat until the row carrying the most is the one that is most expensive to change, and then decide whether the remaining gap is worth the money.
Ratings for the assemblies themselves come from the manufacturer test data or the laboratory report, never from a rule of thumb, and a laboratory number and a site result on the same detail regularly differ because the site version has penetrations, a real perimeter and a real installer. Where the outcome matters enough to have a target, it matters enough to involve an acoustical consultant and to measure the result. Once you know which element to improve, the soundproof wall takeoff calculator counts what the assembly takes in materials.
Questions people ask
Why does one hollow door ruin a heavy wall?
Because transmission is averaged by energy rather than by rating, and the rating is a logarithm. A 30 dB door passes about three hundred times as much sound energy per square foot as a 55 dB wall does, so 21 square feet of door outweighs 107 square feet of wall by roughly sixty to one in the sum. The composite for that wall comes out near 38 dB, which is much closer to the door than to the wall. A partition is not as good as its average; it is close to as good as its worst element, weighted by how much area that element occupies.
How much does a small gap actually matter?
More than almost anything else per square inch, because a gap has no rating at all. Its transmission coefficient is 1, so its area enters the sum undiscounted while a 55 dB wall enters at about three millionths of its own area. One square inch of clear air path through a 128 square foot wall rated at 55 brings the composite down to roughly 42 dB — a loss of about 13 dB from a hole the size of a postage stamp. The half inch undercut under a 36 inch door is eighteen square inches, which is why door seals and thresholds get discussed as though they were the whole job. On this kind of work they very nearly are.
Can I add the STC ratings of two layers together?
No, and the arithmetic does not work in that direction at all. Ratings do not add, and a wall with two rated components is not the sum of their numbers — it is a new assembly that has to be tested as a whole. Adding a second layer of board, or a damping layer, or resilient mounting changes the behaviour of the entire assembly rather than stacking two independent barriers. The only figures worth using are the ones from a test of the assembly you are actually building, published by the manufacturer or the test laboratory. This page combines elements that sit side by side in the same partition, which is a different question from stacking layers through it.
What is flanking and why is it not in this calculator?
Flanking is sound getting from one room to the other by going around the partition instead of through it — along a floor slab or joists that run continuously under both rooms, through a ceiling cavity shared above the wall, up a stud that carries past the junction, or through ductwork serving both spaces. It is not modelled here because it depends entirely on how the surrounding building is put together, and no formula based on the partition can see it. It is also the reason a wall built exactly to a tested detail can still disappoint. If a partition performs worse than the composite arithmetic says it should, flanking is the first thing to suspect, and finding it is a job for someone with measurement equipment.
Will a good composite rating stop the neighbours hearing my subwoofer?
Not reliably, and the single figure rating is part of why people expect it to. Rating systems weight the measurement toward speech frequencies, and a film soundtrack puts most of its transmitted energy far below that range, where construction is much more transparent and where structure-borne transmission through the floor becomes a bigger factor than airborne transmission through the wall. A partition that comfortably handles conversation can pass low frequency content that shakes the room next door. Where the low end is the actual complaint, the useful evidence is the frequency curve in the test report and a measurement in the real building, not a headline number.