I need to replace my rear rim, but I have no idea if it conforms to a standard or what that standard may be called. I was told some time ago by my LBS that they could sell me a rim, but that was all they said and I really don't want to deal with them. I don't know if the mechanism you put the cassette on is called or even if there is more than one standard. I don't know if the centering is the same from one rim to another or if it will need to be re-dished. So can anyone help me learn how to identify what rim I have so I can buy a new one? Any help would be appreciated.

Rim or wheel or??
You have a rim, hub, spokes, nipples & rim tape to make a wheel.
Lots of different brands/models/sizes.
You don't even provide details of the size.
Is there a label on the rim?

Picture of rim?
Size of tire?
Type of bike?
Give us a clue, here.

It's a 700C wheel. The rim part says Araya Japan 700c p-45

The hub doesn't say who it is, but this cassette worked with it.

https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1

It is from a mid 90s Trek 720. I think it's 1994

It's likely an Araya PX-45, 36-hole.
Unlikely to find a new one.
ERD is listed as 610.4mm, but a note to measure to be sure.

You basically need a replacement rim of the same ERD and width.
A Sun Rims CR18 is listed at 612mm.
IF your spoke ends protrude SLIGHTLY ABOVE the bottom of the screw driver slot of the nipple, it'll probably work.

EDIT- I found another that shows that rim at 614mm.
Too much discrepancy to suit me.

What is an ERD?
Also, I'm not looking for a rim to lace to a hub, I am looking for a whole already built wheel which I can install my cassette onto and drop into the frame.

What's the spacing on the rear drop out.
Hubs have various distances between lock nuts.
Probably 135MM, but measure and let us know.
135mm = 5-5/16"
130mm = 5-1/8"
Approx......

Terminology gap. When you say you need to replace a rim, we automatically leap to building a wheel. If you need the entire wheel, you need to say that up front.

Hi Christo. To ensure that we have the right problem, you have an existing (original?) wheel and you bought a new cassette (shown in the Amazon ad you cited). The cassette fits the wheel. You want to replace that wheel with one that the new cassettes. Why are you replacing the wheel?

Also, ERD means "Effective Rim Diameter". Its the diameter that the spokes have to extend to. If you have the hub dimensions (number of holes, spoke hole circle diameter, flange spacing) and the ERD you can figure out spoke lengths needed.

But you want a new wheel. So... why?

Here is what you need to know to buy the right wheel.

Quick release, bolt on or through axle hub.
Rim size (700c, 26, 27, etc)
Rim width (example 35mm)
Brake type (rim brake, 6 bolt disc, center lock disc)
Frame spacing (example 135mm rear, 110mm front)
Cassette or freewheel
Double or single wall
Spoke count (only important if looking for a really good match)
Spoke lacing (straight laced, single cross, double cross etc. Only important if looking for a really good match)
Color (black or silver, also only important if looking for a really good match)

How do you measure the dropouts?

I took the following measurements

From the inside to the inside of the rear dropout is 13.5 centimeters about 5 and 3/8ths
From the middle to the middle is a little over 14.5 centimeters but just under 5 and 3/4
From the outside to the outside is just a hair over 15 centimeters or just under 6 inches

None of these measurements seem right to me. They are not measuring whole numbers of either Imperial or metric (I'm American).

This has got to be following some kind of standard. I want double wall, rim brake and I have a shimanno cassette. It's QR. I really wish I could but a bolt on though. But I don't think it will work.

If it will help, I will post a picture. It's just that I use a PC and would have to drag a camera.

EDIT: I was watching the video and I'm not sure if I have a double wall or not. My rim looks a lot more like the cut-away of the single walled rim. When I replaced a couple of spokes, the spoke did not go through 2 layers the way the double walled rim is shown in the video. So it's probably single walled.

Inside to inside.
13.5cm = 135mm, A STANDARD rear spacing.
Single has the nipple heads against the tube with a rim strip in between.

Do you have the old wheel?

You are asking some pretty basic questions and a new wheel costs too much to take a chance on not getting the right replacement. I'm thinking the smart move would be to take it to a bike shop.

The problem is that I know all these wheels are not the same, but I don't know if the standards (or how many standards there might be) have names. I don't know what the standards are. I don't know if the cassettes are around a standard either. I don't want to buy a rim with the wrong parts for attaching the cassette that I have which fits on my existing rim. All of the freewheel and ratchet stuff is in the rim and it is keyed to accept a particular type of cassette, but I have no idea if those cassettes conform to a or multiple standards.

There is only bike shop near my house and I can't stand them. They are really rude. But I haven't found the right rim on Amazon, so I might have to bite the bullet.

https://www.modernbike.com/product-2...yABEgIgpvD_BwE

You are still after all the posts in this thread using the term "rim" instead of asking about a new wheel. A rim is not a wheel. The freewheel and ratchet stuff are in the HUB, not the rim. A newer wheel will accept your older 7 speed cassette with the simple addition of a spacer

From the info you've posted, you need a 700c wheel with a 135mm over locknut dimension hub and a Shimano hyperglide compatible freehub body. This is extremely common and is what you'll find on most hybrid bikes without disc brakes or road touring bikes. If you have a 7 speed cassette you will need to install a 3.5mm spacer behind the cassette.

https://www.amazon.com/Wheel-Master-...g-goods&sr=1-6 would work, not particularly high quality but probably fine.

To get compatibility right you need to identify:
BSD: the diameter of the rim where the bead of the tire sits defines it's bead seat diameter, which is the most precise way to refer to rim size. Yours is 700c which is named after an obscure french tire sizing system, which has a BSD of 622. You'll often find both numbers printed on the tires. Other common standards are 630 (27"), 584 (27.5" MTB, 650B), and 559 (26"), among others. https://www.sheldonbrown.com/rim-sizing.html is a comprehensive list.
OLD: Over locknut dimension is the distance between the locknuts (not the axle) of the hub which rest against the inside of the frame. Yours is 135mm, which is common for most hybrid bikes and mountain bikes with a quick release. Other common sizes are 100 (front), 120 (5sp freewheel, single speed ), 126 (6sp rear), 130(7-12 speed road, 7 speed mountain), 142 (standard thru axle), 148 (boost thru axle), etc. https://www.sheldonbrown.com/frame-spacing.html goes into more detail although lacks some modern mountain bike standards.
Gearing compatibility: Generally, there are thread on single speed and fixed gear systems, multi speed thread on freewheel systems (most are ISO, but some vintage hubs have different regional thread pitches), and most splined multi speed are either Shimano HG compatible 7-10sp (road) or 8-12sp(mountain), 11 speed Shimano HG compatible (road, which is slightly longer), Campagnolo (8-12sp), or Sram XD (11-12sp mountain). https://bike.bikegremlin.com/1259/bi...compatibility/ is a pretty comprehensive article.
Brake compatibility: Generally either for use with rim brakes with a machined sidewall, and/or for disc brakes with either a 6 bolt ISO mounting standard or centerlock, which is a splined mounting standard.

It's also generally a good idea to roughly match the interior width of the rim with the tires you intend to use, though there's a lot of wiggle room here. For wider tires, generally use wider rims. The industry trend has been generally to use wider rims for the same tire widths than was traditional a few years ago.

I think I know why.-
You REFUSE to learn the proper terminology even when it's pointed out to you.
You can't translate 13.5cm to 135mm.
You won't even say what bike this is. That might tell us exactly what you have.