Howdy
Yup, looks like a 32 Hand Ejector, 3rd Model. Sometimes abbreviated as 32 HE, 3rd Model. Those grips are hard rubber. They look in pretty nice shape. Be careful, those old hard rubber grips are very brittle and crack easily. It's difficult to tell from the lighting of your photos, but it looks like your gun is nickel plated, with some flaking and pitting. It could just be the lighting, is the majority of the gun blue or silver colored? Does it look like nickel plating, or has all the blue worn away revealing the gray color of the steel underneath? The Serial Number of your revolver should show up in four places. The SN of record is on the bottom of the butt. The SN should also be stamped on the flat on the underside of the barrel, the rear of the cylinder, and on the underside of the extractor star. That last place is often difficult to see. If the other three SNs match the SN on the butt, that means the gun left the factory with those parts. Different Serial Numbers usually mean parts have been replaced. If you can very carefully remove the grips, you might also find the SN scratched on the inside of one of the grips, indicating the gun left the factory with those grips. Be careful, the grips are very brittle with age. These guns also sometimes have wooden grips.
I don't have one of that model, but here is a very similar model, a 32 Regulation Police. Built on the same size frame, but with a different grip style. Notice the large, mushroom shaped knob at the end of the ejector, just like yours. Later on, the knob became smaller. Also, the top down view of yours shows an early style of rear sight. Later guns did not have the round relief at the rear of the frame, it was squared off when viewed from the top.
Here is a photo of the 32 Regulation Police with a K frame 38 Military and Police, to show how much smaller the 32 revolver is.
Did you measure the barrel again? It looks like a 4 1/4" barrel. As I said before, 3 1/4", 4 1/4", and 6" were standard barrel lengths for this model. Measure the barrel from the front of the cylinder to the muzzle. What is marked on the left side of the barrel? 32 LONG CTG? A clear view of the other side of the revolver would be useful too.
These guns were quite common, there were 271,531 of them made from 1917 until 1942. There are a few on Gun Broker right now with asking prices as low as $275 and as high as $699. Way over priced in my opinion. If I came across yours in a shop, and it functioned perfectly, and the other side looked in the same condition as the side you are showing, I might go as high as $300 for it. And that is probably a bit too high.
If you want to know exactly when your 32 HE shipped, and where it was shipped to, you can go to the Smith and Wesson Forum and fill out the form for a Factory Letter. There is a pull down menu for Downloads and you can find the form there. S&W recently raised the price of a letter to $75 per gun. Sometimes it takes a long time to get the letter, depending on what the backlog is.
But I'm guessing your gun shipped in the late teens or early 1920s.
Hope this helps.