# Are replacement windows ever worth it? or What's wrong with my math?

Posted by Kitep on May 11, 2008, 6:59 pm

Window cost: \$44
Energy savings: \$.25/yr
Payback time: 15.6 years

Is this typical?

The \$44 is just the cost of the window, and does not include installation
costs (I'm not against installing it myself).

BTW, turns out finding the price for triple or quadruple glazed windows over
the internet is harder than I thought.  I couldn't find a single one.  The
above is for an Anderson Silver Line 8500 double-hung window, double glaze,
low-e.

----

Now for the math.  Feel free to change channels :)

R = 1 / u
loss per degree day = A * (1 degree) * (24 hours/day) / (1/u) = 24 u A
Note: I'll use DD for number of degree-days/year
loss per year = 24 u A (DD)
Note: I'll use C for cost per BTU
cost per year = 24 u A (DD) C
savings per year = 24 A (DD) C (u_old - u_new)

The window mentioned above is 28" x 54" = 2.333' x 4.5' = 10.5 ft^2
(I'm not married to that window, but it was one I could find both price and
u-factor for)
degree days = 4928 (heating) + 1135 (cooling) = 6163
cost per BTU (natural gas) = (\$.5184/ccf) * (1 ccf / 102000 BTU) = \$4.886
x 10^-6 / BTU

(I'm going to cheat, and not write out the units)
savings per year = 24 A (DD) C (u_old - u_new)
= 24 (10.5) (6163) (14.886 x 10^-6) (u_old - u_new)
= 23.119 (u_old - u_new)

u_new = .35 for above window
u_old = .75 (I'm guessing on this.  Looks like a single pane, aluminum clad.
But there's also a storm window, so shouldn't it be half this?)

savings per year = 23.119 (u_old - u_new) = 23.119 (.75 - .35) = \$.25/year
Payback time = \$44 / (\$.25/year) = 15.6 years

Even if I could get a super duper window (u=.20) for the same price, that
brings it to \$2.72/year, or 11.32 year payback time.

What am I missing?  Or have I just fallen for the hype about replacement
windows?

Posted by Eeyore on May 11, 2008, 7:58 pm

Kitep wrote:

I believe it is.

The fastest payback for any energy use reduction method is insulation.
Loft/attic insulation pays back in a couple of years for example and blown in
cavity wall insulation is up there somewhere too.

Graham

Posted by Kitep on May 11, 2008, 8:28 pm

More attic insulation was going to be next calculation.  But after being
disappointed with the windows calc, I didn't have the heart.  Plus I thought
maybe my math was off.

Posted by Eeyore on May 12, 2008, 1:10 am

Kitep wrote:

Current guidance in the UK is to use 10-12" of glassfibre or rockwool mat (or
equivalent other material) for loft insulation, way more than the 4 inches or so
most people think is adequate from 20-30 year old advice. And it's CHEAP too,
especially if you install it yourself. Just make sure you don't block any air
vents in the eaves in the process..

It's well known that new double glazed windows have a compatively long payback
period, although the advertising would have you believe otherwise. However if
you need to replace a rotten window, then make it double glazed anyway, as the
incremental cost in that case is low and will pay back in more like 5 years (or
less). Check out local suppliers too rather than rely on higher priced national
companies.

Graham

Posted by Kitep on May 12, 2008, 1:39 am

Guess I can always hope some kid puts a baseball through my window <fingers
crossed> :)