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HVAC sizing

  (aka air conditioner sizing, heating system sizing)

Last update: February 2016

The Basics

an air conditioner simply means figuring out what size system is needed to cool your home properly.
  Sizing is important because a unit that's too small won't cool your house properly, and a unit that's too big will cost more than necessary.  Most contractors will try to sell you a system that's too big, either because they're trying to make more money, or because they don't know how to properly do the sizing work. (sources 1,2,3)  Learning about proper sizing is helpful so you can know if your contractor is trying to sell you a unit that's bigger than what you need.

Most systems that cool also supply heat as well.
  Those are called HVAC systems (Heating, Ventilation, & Air Conditioning).  So actually, you usually need to size for both heating and cooling.  First you figure out how much cooling you need, then figure out how much heat.  A system in Texas needs lots of cooling and not so much heat, while one in Pennsylvania needs lots of heat and not as much cooling.

The best way to size your system is to have a "Manual J" calculation done on your house.
  That's the gold standard for system sizing, taking into account things like how much insulation you have, what kind of windows and what direction they're facing, and everything else.  Many utility companies will do this for free (check with them), and if not, you can hire an energy auditor.  Don't go with an HVAC contractor for the Manual J, go with your utility or an energy auditor so you can trust that they did it right.  They'll tell you exactly what size you need, and you can shop accordingly.

You should also have the efficiency of your ducts tested, because installing properly-sized equipment won't do any good if you're going to gain or lose lots of BTUs through your ductwork.  The national average performance of ducts is only 57%. (source)  If your ducts are a problem, then have them serviced.  Of course, if your ducts are running through conditioned space, then duct losses are not a problem, because you "lose" the air right into the area that you were trying to condition in the first place.

The problems with oversizing are cost and comfort

The problems with oversized systems is that they cost more, which is just wasted money, and they're often not as comfortable.
  (They might blast you with too-hot air in the winter, and they cause uneven temperatures throughout the house, because they don't run as much, so the air isn't circulated as much as it would be with a right-sized system.)  Conventional wisdom is that oversizing also creates other problems besides cost and less comfort, but I consider those to be myths.
  1. MYTH: Oversized AC's don't control humidity as well.  The theory here is that oversized systems don't run long enough to dry the air.  But a university study of homes where grossly oversized units were replaced with right-sized units didn't result in lower humidity.  The researchers theorized that the longer running time of the right-sized units meant that the fans they were drawing in more moisture into the house through the building envelope and the attic. (source PDF)

  2. MYTH: Oversized systems wear out faster because of short-cycling.  The theory here is that big systems heat or cool the house so quickly that they shut off after just a few minutes, and the constant on/off cycling is hard on the equipment.  There are three problems with that:  First, I'm skeptical that there are really more cycles.  Whether it takes the AC takes 5 minutes to cool the house or 20, either way, that's one cooling cycle, no matter how long it took.  Second, even if the oversized equipment does run more cycles, it's hard to believe that the extra cycles would really make a big difference in equipment life.  The AC will likely be up for replacement just because it's old before it dies completely.  Finally, any stress added by extra cycles would be balanced by the fact that the equipment doesn't run as long.  Even if right-sized equipment cycles less, it'll be running longer, and longer runtime could mean a shorter life, also.

  3. MYTH: Oversized systems use extra energy.  The theory is that AC's need to run for several minutes to get efficient.  But the study above found that they don't use more energy overall.

BTU: The measurement of heat

Heat is measured in BTU's (British Thermal Units).  For example, a heater might supply 24,000 BTUs per hour to a house when it's operating.  To size a heating system, we figure how many BTUs of heat the house loses to the outside, and then get a system big enough to replace the BTUs that were lost.

We use BTUs for cooling, too, to measure how much heat an air conditioner removes from a house or a room.  For example, a small window-unit AC will remove about 5000 BTU per hour from a room.  When we size for cooling, we'll be figuring out how many BTUs of heat enter the house, and then get a system that can remove that much heat.

AC equipment is also measured in tons.  This has nothing to do with the weight of the equipment, it's just a measurement of heat.  One ton is 12,000 BTU.  So a 2.5-ton system would be 2.5 tons x 12,000 BTU/ton = 30,000 BTU.

Easy mistakes to make when sizing heaters

Many homeowners are bitten by a couple of big misunderstandings.
  The first is that they don't know that gas furnaces are rated by their input, not their output.  So a "60,000 BTU" gas furnace that's 80% efficient will supply only 48,000 BTU to your home.  If you've figured that you need a 60k BTU of heating and you buy a 60k BTU gas furnace, you're going to wind up with only 48k BTU of heat which is not enough.  So you have to calculate the output when you buy a gas furnace.  (Oil furnaces, on the other hand, are rated by their output, so a 60,000 BTU oil furnace will supply 60,000 BTUs.)

The other mistake is to ignore the efficiency when replacing old equipment.  Let's say you have an 70k BTU gas furnace at the end of its useful life.  Your contractor points out that your old unit was only 80% efficient, but he can sell you a new 70k unit that's 95% efficient and it will cost only $350 more, promising that you'll make the difference back quickly with the energy savings.

But regardless of the energy savings, the unit is bigger than what you need, so if you buy it you'll be paying more than you need to.  Your old unit put out 70k BTU x 80% = 56k BTU.  The new one puts out 70k BTU x 95% = 66.5k BTU.  So the new one is effectively 10.5k BTU larger than what you need—and you'll be paying for it.  Here again, you must shop by output, not input.  If you need only 56k BTU of heating and you go with a 95% efficient unit, then you should buy one in the neighborhood of (56k BTU ÷ 95% = ) 59k BTU.

How close do you have to match the calcs to the equipment?

Here's a problem you might have:  You've hired out the Manual J calculation and it's come back at 27k BTU for cooling and 53k BTU for heating.  But the contractors don't have 27k BTU air conditioners, they've got 24k and 30k, and they don't have the exact size furnace you need, either.  Do you go with the next size bigger or the next size smaller?

You generally go the next size bigger.  Going slightly bigger won't be a big price penalty, and it'll ensure that the system can handle the load on extreme temperature days.  If you go smaller, even a little smaller, you might be a little uncomfortable on the coldest and hottest days of the year.

The Manual S limit is to not go beyond 15% more BTUs than you need for cooling
(25% for heat pumps), and not more than 40% more BTUs than you need for heating. (source)

Just like "Manual J" is used to figure the heating & cooling load, "Manual S" is used to select the equipment to handle the load.  
The reason for this is that the actual BTUs delivered or removed by the unit might not match the rating of the unit depending on things such as temperature and humidity in your area.  However, matching your calculated BTUs from Manual J with the nameplate BTU rating on the equipment is probably sufficient for most situations.

Methods of sizing HVAC equipment

METHOD 1:  Go by square feet alone

The worst way to size a system is by square feet, though many contractors do just that.
  The first problem is that it doesn't take into account the climate (hot or cold), how much insulation you have, whether the house is shaded, how leaky the house is, etc.  The other problem is that it estimates only cooling; there's no rule of thumb for heating based on only square feet, because such an estimate would often be even farther off.

But for what it's worth, which is not much, the basic formula for cooling is 1 ton of cooling for every 600 s.f. of house.  So, for example, a 2400 s.f. home would need 2400 s.f. x 1 ton/600 s.f. = 4 tons.  Newer homes that are insulated well and aren't leaky would be closer to around 1 ton for every 1000 s.f.  You could invert the figures if that's more comfortable.  Another way of saying 1 ton for every 600 s.f., is 20 BTU per square foot.  Another way of saying 1 ton per 1000 s.f. is 12 BTU per square foot.

METHOD 2:  Go by square feet + climate

HVAC System Sizing

Green Yellow
1.5 tons
700-1100 sf 700-1050 sf 600-1000 sf 600-950 sf
600-900 sf
2 tons
1101-1400 sf
1051-1350 sf 1001-1300 sf 951-1250 sf
901-1200 sf
2.5 tons
1401-1650 sf 1351-1600 sf 1301-1600 sf 1251-1550 sf
1201-1500 sf
3 tons
1651-2100 sf
1601-2000 sf 1601-1900 sf 1501-1850 sf
1501-1800 sf
3.5 tons 2101-2300 sf 2001-2250 sf 1901-2200 sf 1851-2150 sf 1801-2100 sf
4 tons 2301-2700 sf 2251-2700 sf 2201-2600 sf 2151-2500 sf 2101-2400 sf
5 tons 2701-3300 sf 2751-3300 sf 2601-3200 sf 2501-3100 sf 2401-3000 sf

40-60 BTU/sf 35-50 BTU/sf 30-45 BTU/sf 20-40 BTU/sf 15-35 BTU/sf
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U.S. Heat Zone map
 Map from DoE.  Data from AC Direct with permission, with my modifications for heat.
By taking climate into account, you can estimate heating as well.  While some people will estimate cooling based on square feet alone even though it's not accurate, nobody will estimate heating by square foot alone, because the results can be even farther off.  At a minimum, heating estimates must take into account the climate as well as the area to be heated.  (A study of office buildings showed that a building in Chicago needed three times less cooling than one in Miami, but it needed 48 times more heating. (source))

You can see the estimates in the table at right.  To make this method a little less useless, I give it with ranges rather than a static number.  You'll need more powerful equipment if you don't have good insulation and windows, less if you do.

METHOD 3:  Size it to your existing system

If you're shopping for an HVAC to replace an existing system (rather than buying it for new construction), you can usually use the capacity of your existing system to gauge the size of the replacement system.  The main thing is to make sure your existing system is sized correctly.  A properly-sized system will run continuously (or nearly so) on the hottest and coldest days of the year.  If your unit is shutting off even in the most extreme weather, it's probably oversized.  Also, if you've installed energy efficiency upgrades (e.g., more insulation, double-paned windows) since you bought your system, it's probably oversized.

If your equipment doesn't appear to be oversized, just buy the same capacity equipment to replace it.  If your current equipment is oversized, you could go with one that's a little smaller, but it's better to have the Manual J calculation performed (see way above) find out exactly how much smaller you can go.

This method also works if you're replacing window units with a central or ductless mini-split system.
  I had a small house that could be cooled well by three window units, which were 5000, 5000, and 6400 BTU respectively.  So I didn't need more than 16,400 BTU of cooling capacity for the new system.  (And even though I told that explicitly to the contractors I invited to bid, they gave me quotes for 24,000- and 28,000-BTU systems.  Sadly typical.)

METHOD 4:  Online calculator

There are various calculators on the net that try to help you size your system, but I didn't like any of them enough to recommend them.  I'd like to build my own to offer to my readers, but I've been having a hard time finding the data to use for the calculations.  (Manual J is too big for this project; what I'm envisioning is more like a "Mini-Manual J".)  Any readers who have data to share are welcome to contact me.  Mostly, I need the formulas.  I can look up things like heating/cooling degree days, and U-values and R-values for various building materials, it's the formulas to assemble those into an answer that I lack.  I'd like to account for losses/gains from ceilings, walls, windows, doors, floors, occupants, electrical devices, ductwork, leakiness, and shading.

METHOD 5:  Manual J calculation

A "Manual J" calculation is the gold standard for sizing HVAC equipment.  It's not something a homeowner can do themselves (unless they're willing to throw down $500 for the software, and confident that they can use it accurately).  Many utility companies will do the calculation for you, and failing that, you can hire an energy auditor.  Don't rely on an HVAC contractor to do your Manual J, since contractors frequently churn out bad Manual J's because they used the wrong inputs—either because they're trying to upsell bigger equipment, or because they sincerely don't know how to use the software properly.

Other Technical Topics

BTUs:  Technical definition

A BTU is the amount of heat required to raise the temperature of one pound of water by one degree from 60° to 61°F at a constant pressure of one atmosphere. (Wikipedia)  Different substances require different amounts of heat to change their temperatures because each substance has a different molecular makeup.  It takes about four times as much heat to change the temperature of water as it does for air.  The property of a substance that dictates how much heat is required to change its temperature is called specific heat.

BTUs to heat air

I wanted to know how much energy is required to heat and cool air, so I could figure things like the penalty for running a clothes dryer considering that the dryer is sucking conditioned air out of the house, and undconditioned air in, which then has to be heated or cooled.

Incidentally, the figure for the energy required to condition air isn't really useful for figuring the energy needed to heat or cool a home itself.  For that, you don't figure how much heat is required to change the temperature of the air in the home, because the inside air is generally always conditioned to a certain temperature.  What you need to know is how much heat is entering or leaving, which is all the HVAC system has to deal with.  And if the inside temperature is not maintained (e.g., you left the AC off all day and now you want to turn it on because it's very hot inside), I presume we'd have to figure the amount of heat to add or remove from all the objects in the house too, not just the air, which would be very difficult to estimate.  (We could assume X lbs. of stuff per 100 sf, and figure that the specific heat of the objects is around half that of water, but those are just guesses.)

So here's my stab at calculating the BTUs required to heat air, and this is what I got.
  • Air weighs 1.184 kg/m3 at room temperature (Engineering Toolbox)
  • So air weighs 2.6 lbs./m3  (1.184 kg x 2.2 lbs/kg)
  • So one pound of air is 1/2.6m3 = 0.385m3
  • So one pound of air is 13.59 ft3 (0.385m3 x 35.3 ft3/m3, Google calculator)
So it would take one BTU to raise the temperature of 13.59 ft3 of air by one degree if water and air had the same specific heat, but as we saw earlier, they don't.  The specific heat of water is 4.14 times greater than that for air.  So, we should be able to heat (13.59 ft3 x 4.14=) 56.3 ft3 of air by 1°F with one BTU.

I calculated that because I couldn't easily find a reference figure for how much air could be heated with one BTU.  But after doing the calculation I found a reference:  55 ft3, from this 1909 book by the American Technical Society.  That's extremely close to the 56.3 ft3 figure we calculated above.  Good for us.

Cost to remove heat generated by appliance use

   It can be useful to know how much energy is required to remove heat from electrical appliances (like light bulbs), and how much it costs.
  • 1 kW = 3412 BTU
  • A 2.5-ton AC uses 3.5 kW and removes (2.5 tons x 12,000 btu/ton =) 30,000 BTU/hr
  • So it's 3.5 kWh per 30,000 BTU.  That's 3.5 kWh/30,000 BTU ÷ 3.5 = 1 kWh/8571 BTU
  • To remove the 3412 BTU generated by 1 kWh of appliance use, we'd use 1 kWh/8571 BTU x 3412 BTU = 0.4 kWh
  • 0.4 kWh x 16¢ kWh = 6.4¢ worth of AC to remove the heat generated by 1 kW of electricity use
  • If we wanted to be really thorough, we'd calculate the energy required to remove the heat we created by running the AC to remove the original heat, which is a recursive issue of course.

Converting horsepower to tons of cooling

By a moderator at Refrigeration Engineer:

    1. 16 EER means 16 Btu/hr of cooling for every watt of power used
    2. 1 watt = 3.412 Btu/hr, so
    3. 16 EER unit provides 16 ÷ 3.412 = 4.69 watts of cooling for every watt of power used.  This is the coefficient of performance (COP).
    4. 1 ton refrigeration = 4.712 horsepower, electric
    5. 1 hp electric = 4.69 / 4.712 = 0.995 tons refrigeration

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