Air does not know where it is supposed to go
A trunk with six takeoffs off it is six parallel paths from one pressure to one room pressure. Air divides between them so that every path drops the same pressure, and the path that drops it most easily gets the most air. A twenty foot branch to the room next to the air handler and a hundred and ten foot branch to the bedroom over the garage are not remotely equal paths, so they do not get equal treatment, and the difference is often three to one before anyone touches a damper.
That is the entire mechanism behind the complaint everyone has heard: the room nearest the furnace bakes and the far bedroom never gets warm. It is not a broken damper or a weak blower. It is arithmetic, and the only way to change it is to make the easy paths artificially hard.
What the numbers on this page mean
Each branch is sized from its own airflow at whatever friction rate you set, then rounded up to a duct you can buy. That rounding matters: a branch needing 7.09 inches gets an 8 inch duct, which runs at a lower friction rate than the design target, so its path is easier than the design intended. The calculator uses the actual friction of the size you would actually install rather than the target, because that is what the air responds to.
The path loss for each branch is its effective length — straight duct plus the equivalent length you attribute to its fittings — multiplied by that actual friction rate and divided by a hundred. The branch with the largest path loss is the reference. It gets no damper. Every other branch has a surplus equal to the difference between its own loss and the reference loss, and its damper exists to absorb exactly that surplus.
The surplus is quoted in inches of water gauge because that is a real physical quantity you could measure. It deliberately is not quoted as a damper angle, because that number does not exist in a form anyone can calculate from a duct layout.
The fitting allowance is doing more work than it looks
The default in the fittings field is a single average applied to every branch, which is convenient and wrong in a specific way worth knowing about. A takeoff, two elbows and a boot on a six inch branch are not the same equivalent length as the same fittings on a twelve inch branch, and a sharp square takeoff and a bellmouth takeoff differ by a factor that can exceed the entire straight run behind them.
| Fitting | Relative penalty | What drives it |
|---|---|---|
| Bellmouth or conical takeoff | Low | Air turns into the branch gradually |
| Straight square takeoff | Moderate | Air has to make a sharp entry from the trunk |
| Long radius elbow | Low to moderate | Radius relative to diameter is the whole story |
| Tight or gored elbow | High | Separation on the inside of the turn |
| Boot with a sharp turn to the register | High | Ninety degrees in a few inches, right at the outlet |
If one branch has a bellmouth takeoff and a sweeping run while another has a square takeoff and three tight elbows, giving both the same fitting allowance hides the difference that actually explains the imbalance. Use per-branch numbers from a fitting loss table when you have them, and when you do not, at least raise the allowance for the branches you know are ugly.
Balancing is measured, not calculated
This page tells you what to expect and where the work is. It does not replace balancing, which is a loop: measure the flow at each register, adjust the dampers, measure again, and repeat until the numbers stop moving. It takes several passes because closing one damper pushes air into every other branch, which changes every reading you already took.
The practical order that shortens the loop is to leave the worst branch wide open throughout, start by setting the branches with the biggest surplus, work down to the smallest, and only then go back to the beginning. Balancing at the takeoff dampers rather than at the register faces keeps the throttling noise inside the duct, and the register and grille sizing calculator covers why that matters at the room end.
When the answer is that the layout is wrong
If a branch needs to absorb three quarters of the reference path loss, the damper is being asked to act as most of the resistance in that run. That works, but it is loud, it is sensitive to small adjustments, and it wastes blower energy that was spent producing pressure only to throw it away. A better fix is usually structural: run the long branch in a larger duct so its path loss falls, or split a long trunk so the short and long branches are not competing directly.
And if the sum of branch demands exceeds what the trunk carries, no amount of balancing helps. That is the case to check first, before touching anything, and it points at the blower and the total system resistance rather than at the branches. The duct static pressure calculator takes the whole path and compares it to the blower rating, the duct size calculator handles a single duct in more detail than this page does, and if any of these runs are flex, the flex duct penalty calculator will change the path losses more than any other single input.
Questions people ask
Why does the room furthest from the furnace get the least air?
Because it has the hardest path and air takes the easy one. Every branch off a trunk starts from the same pressure and ends in a room at roughly the same pressure, so the flow divides itself until each path is burning the same pressure difference. A short branch with two fittings burns that pressure at a high flow rate; a long branch with six fittings burns it at a low one. Work the example on this page and the twenty foot branch and the hundred and ten foot branch differ by roughly four to one in path resistance with the dampers open. The far room is not being neglected by anything. It is losing a race it was never in a position to win, and a balancing damper on the near branches is how you make the race fair.
How far do I close a balancing damper?
There is no calculable answer, and anyone offering you a degrees figure is guessing. The resistance of a damper depends on its type, the duct diameter, how the air arrives at it and how far along the blade travel you are, and the curve is extremely steep near closed, so the last fifteen degrees can do more than the first sixty. The practical method is a loop: leave the hardest branch fully open, set the others by measuring the flow at the register and adjusting, then go round again because each change moved the others. Two or three passes is normal. What this calculator gives you is the ordering and the rough magnitude, so you know before you start which branches need a lot of trimming and which are nearly right as built.
Can I just make the far branch bigger instead of dampering the near ones?
Yes, and it is generally the better fix when you can still change the ductwork. Increasing the diameter of a long branch cuts its friction rate sharply — friction falls with roughly the fifth power of diameter, so going up one nominal size can halve the path loss — which brings the hard path closer to the easy ones and reduces how much everything else has to be throttled. The reason it is not always done is that ducts have to fit in joist bays and soffits, and one size up is often one size more than the cavity has. Where the duct is already in the ceiling, dampers are what you have. Where you are still drawing it, sizing the long runs generously costs very little and removes the problem before it exists.
Do the branch demands have to add up to the trunk airflow?
They should be close, and this page flags it when they are not. If the branches ask for more than the trunk delivers, everything downstream is short and no balancing fixes it, because balancing only redistributes what arrives. If the branches ask for meaningfully less, either some airflow is going somewhere unaccounted for or the equipment is moving more air than the design needs, which shows up as higher velocities and more noise than expected everywhere. A small unallocated remainder is normal and healthy; a large one is a sign that the room-by-room numbers and the equipment selection came from different assumptions.
Does this work for return ducts too?
The pressure arithmetic is identical — parallel paths from a common point, dividing by resistance — so the sizing and the path loss figures apply directly. What differs is that returns rarely have dampers on them, so there is no throttling stage to compute, and the practical consequence of an unbalanced return is different: instead of a room being cold, a room becomes pressurised relative to the rest of the house because it gets supply air and cannot give it back. That drives air out through the envelope and pulls it in elsewhere. If you are working the return side, size on flow, keep the paths as equal as the building allows, and pay attention to the grille free area, which is usually the biggest single restriction in the whole return path.