Let's say your trusty old furnace is at the end of its life. You've got to buy a new one, so you call your HVAC company and they rush over to make sure you don't freeze during the next cold snap. They go and take a look at your furnace and find its capacity. They come back and tell you that you have a furnace rated for 60,000 BTU per hour and then talk to you about some of the options.
You could replace the old one with one that has the same efficiency, 80 AFUE (Annual Fuel Utilization Efficiency, essentially the percent efficiency over the whole heating season). Then they show you the price of their high efficiency furnace, which is 95 AFUE. It's only $400 more and they convince you that since you're going to have the furnace for another 15 or 20 years, you'll quickly get that money back in savings on your gas bill.
So you tell them to go ahead and install the 95% furnace. Your old one, remember, was rated at 60,000 BTU/hour of input capacity. They look in their product catalog and find that the high efficiency model comes in a 46,000 BTU/hr model or a 69,000 BTU/hr model. There's not a 60,000 BTU/hr model, and they don't want you to freeze, so they install the 69,000 BTU/hr model.
Looking at the wrong capacity
Hmmm. See a problem here? Many HVAC sales people and techs think in terms of input capacity for furnaces. To them, the 69k model is a little bigger than the old 60k model they're replacing, but not too much bigger.
Actually it's worse than that.
The relevant capacity of the furnace isn't the rate of BTU input. It's how quickly those BTUs go into your home, the output capacity. Let's look at what happened to those numbers when you replaced the old furnace. You started with 60,000 BTU/hr at 80% efficiency, so your old furnace supplied 60,000 x 0.8 = 48,000 BTU/hr. The new furnace has an output capacity of 69,000 x 0.95 = 65,550 BTU/hr. To summarize the numbers:
Input: 60,000 (old furnace) ==> 69,000 BTU/hr (new furnace) — 15% increase
Output: 48,000 (old furnace) ==> 65,550 BTU/hr (new furnace) — 37% increase
So, your new furnace is 37% larger in terms of its ability to provide heat to your home. If you had started with an older furnace, perhaps only 60% or 68% efficient, the amount of oversizing would be even worse.
Why it matters
How does that affect you? Your furnace will be on for shorter periods of time.
How does that affect you? If you live in a high performance home with a well-insulated and air-sealed building enclosure, you may not notice much of a difference. Well, let me rephrase that. You won't notice much difference most of the time...when the furnace is off. But when it comes on, you'll feel a blast of Sahara Desert heat making you long for the cool on the other side of the pillow. (RIP, Stuart Scott.)
If you live in an older home with air leakage and insulation problems, you may notice that you're less comfortable. The furnace comes on and blasts you for a few minutes, possibly making you uncomfortably warm in some parts of your home. Then it goes off, and you feel the cold walls and the drafts.
What can you do?
If you're getting a new furnace, ask the HVAC companies you get bids from how they're planning to size the new system. There are a lot of ways to do it, and many of them are wrong. Some acceptable ways would be to do a Manual J heating and cooling load calculation, use manufacturers' sizing software, or monitor the amount of runtime of your current system, especially at design conditions.
Probably the least reliable way to do it would be just to look at what size you have now and install that size or larger. To make it worse, just look at input capacity and ignore the effect of installing a new system with higher efficiency.
Bigger isn't always better. When it comes to heating and cooling your home, it's often worse.