This might take a few seconds longer, but it's math-free:
On your kneeboard, draw a quadrant (like this: +).
Draw a line through it for your runway(s).
Draw an arrow to represent the wind.
The answer will be apparent.
Do it enough times, and you'll be able to visualize the drawing without actually doing it.
It's also a great technique for calculating holds.
aviation.stackexchange.com/users/50/Brian Tusi
Is there a trick to determine best runway quickly without doing the math?
Aside from "Asking the other pilots in the pattern / UNICOM", none I'm aware of.
The closest thing to a "trick" I can offer you if you're going in to a completely unattended field are the following suggestions: If your directional gyro (DG) has a heading bug, set the heading bug to the wind direction.
Now find the runway alignment closest to the bug.
That's the runway you want.
(If your DG doesn't have a heading bug you may still be able to do this visually easier than doing math - of course this relies on you flying in a plane with a DG or a vertical card compass...).
Break out your E6B , dial in the wind direction, and find the closest runway heading.
Same logic as (1), but for when you're stuck in a Piper Cub with only the wet compass.
One drawback - it only works with mechanical flight computers...
If you have your sectional out, lay your pen or ruler on it to show the wind direction.
See which runway alignment is closest to the ruler.
That's the runway you want.
Count on your fingers.
(Seriously, this is what I do most of the time.
I'm an engineer, I can't add and subtract!)
aviation.stackexchange.com/users/64/voretaq7
In uncontrolled airports I've avoided problems simply by asking on CTAF which runway is in use when 10-7SM out.
This has worked out well because often times there are aircraft in the pattern on the wrong runway (from the perspective of crosswind) because conditions changed and traffic has been busy, or someone is just doing their own thing.
I've even had a unicom station respond with a recommendation when nobody in the air responded.
It doesn't hurt to ask and if you get no response a quick glance at the heading indicator can save you the math by just visualizing the runways over the indicator and choosing the one that's closest to the wind.
aviation.stackexchange.com/users/36/kevin42
When I arrive at an uncontrolled airport, and there's nobody there to tell me what everybody else is doing, I overfly the airport to get the lay of the land and to look at the wind sock.
This should be SOP for everybody.
One glance at the wind sock will tell you which runway the winds favor.
No math or diagrams required.
You should also be looking for a tetrahedron .
This will also give you information about the pattern.
Nominally, this is the authoritative answer about landing direction, but I've known airports where the tetrahedron was inoperative.
If the wind is strong and the wind sock contradicts the tetrahedron, consider trusting the wind sock instead.
Or better yet, consult the locals.
aviation.stackexchange.com/users/87/Edward Falk
The only way you can avoid doing the math is if someone else has already done it for you and you have the results of their work available.
Towered airports, of course, will control the runway direction from the ground, and will handle any lighting systems.
At non-towered but fairly busy airports there will be an accepted pattern in use, and when anyone notices the windsock is pointing the other way the pilots can coordinate to "turn the airport around"
(I'm actually curious how that happens; for strips that always have a left-hand or right-hand pattern, the answer is simply to not turn to final and instead just circle to the other end, but for airstrips where, for instance, powered planes must always stay to one side of the airport to avoid a residential neighborhood, you can't circle that way, and must instead make a 180 away from the airport to reverse the pattern direction).
However, your question infers that no radio chatter or other traffic is available to follow, and you have to determine it for yourself.
You can still get some help in these cases.
Non-towered airports can still be lit; end lights and the LDI tetrahedron can be controlled from a simple automated weather station, and activated on request (to save energy) by pilots tuning to a station and clicking the mike.
If the pattern is truly empty, you can maneuver around the strip, look for the windsock, and approach in the direction closest to its tail.
Use a compass card; any will do, you have several in your cockpit, or you could even have a literal "compass card", a rose drawn on an index card on your clipboard or the inside cover of your notebook (whatever you're using for quick reference or shorthand notes on your flight).
You know wind is from 225* and your options for runways are 13(0) or 31(0).
A quick look at the dial will show you which runway choice is closer to the wind.
Just remember not to get confused by the numbers on the rose; to land on runway 31, you have to go around to the southeast end, even though 310* is marked on the northwest quadrant of the compass rose; runways are labelled according to the heading you'll be on while using them.
aviation.stackexchange.com/users/7629/KeithS
Rather than calculating off the wind direction, start with the runway headings.
13-9=4 and 13+9=22.
If the wind is 040-220 use 13, otherwise use 31.
I have an HSI
so I set the bug to the wind heading and the CDI to the runway, then press vectors-to-final to get an extended centerline.
Both easy peasy
aviation.stackexchange.com/users/3504/rbp
Let's say I call up Wx and have the wind direction and I know the runway headings from my charts and the pattern is empty. I can do the math, but it's tedious and slow and even worse when there are multiple runways. This is what I usually do:   Runways are 13 and 31  Wind is 253° which rounds to 25  $25-13=12$  $31-25=6$  I'm going to use Runway 31   Is there a trick to determine best runway quickly without doing the math?
What's a quick way to determine which runway to use?
aviation.stackexchange.com
<runways><wind>
aviation.stackexchange.com/questions/126
aviation.stackexchange.com/users/120/guidoism
Draw a quadrant and a line through it for your runway. Draw an arrow to represent the wind and the answer will be apparent. Draw a quadrant, draw a line for the runway, draw a line to represent the wind and the answer will be apparent.
This user gives the simplest solution.