Bag sizes ok for cheapo airlines

Generally they say one carry on and that doesn't mean a carryon plus a personal bag. It depends a little bit on the airline. Ryanair is more than a little strict while EJ is touch looser but I would follow their instructions to the letter. And the Steve's rolling bag does fit.

Just be careful and double check everything. Since covid EasyJet have changed their rules and the only free hand luggage you get is a very small underseat bag. You can pay extra for a larger carry on which is about £35 each way so not cheap.

I don’t know the Ryanair rules as never fly with them. Too many horror stories.

What is allowed depends on what type of ticket you bought. Some have a base price that only allows 1 personal item and then anything else is charged extra.
Here is a grid for many airlines and allowances....also links to the airline website for more specifics. Keep in mind there may be a maximum weight....and yes, expect the item to ve measured and weighed. https://upgradedpoints.com/travel/airlines/carry-on-luggage-size-chart/

we have had no trouble with our Rick Steves carry on Ravenna bags with several cheapo airlines Easyjet, Vueling, and I think we did Ryan air once as well, and our Ravenna bags fit, on all the airlines we paid extra to allow us to take our carryon in the cabin, usually about 14 extra Euros gives you the "upgraded service" otherwise if you just show up with carryon they can charge you a spectacular amount to take it in the cabin so read rules carefully, we each had a carryon Ravenna bag and a crossbody bag for reference the Ravenna is 21X14X9 inches

On another thread you asked about Iceland Air. The RS bag will not fit their carryon. The carryon weight limit is 22 pounds, so make sure you are good with both size and weight. You get one carryon plus a personal item. The personal item size is quite small. This is from Iceland Air regarding personal item size.

"You may bring on board 1 small personal item such as a handbag, backpack, or laptop bag that must fit under the seat in front of you.
Maximum dimensions: 15.7x11.8x5.9 inches (40x30x15cm)."

There's not a safe shortcut here. You need to check the baggage rules on the website of any airline you are considering using. Airlines can change those, and have, so what worked for someone else in the past may not work for you now. Measure your bag, including wheels and handle; compare those numbers to the airline website. Use an online converter if the website gives measurements in centimeters and you have only a measuring tape marked in inches. Compare the numbers.

I would contact them directly to get the exact rules.

Besides looking at the bag dimensions, also measure your suitcase filled. Sometimes a bag can go outside the allowable dimensions because of the protruding top or front if packed very full.

Ditto what others are saying about checking the airline’s website and following the luggage rules for the most restrictive airline. Remember: backpacks and tote bags can be used. Combine them with packing cubes. You may need to think outside the traditional concept of luggage. You can surf Amazon.com for ideas. Type in “Ryan Air” bag and see what comes up. You still need to follow the airline’s rules, though. Don’t go by Amazon.com alone.

We got “burned” once because the airline changed its baggage policy just one day before we flew. We were following baggage policies listed prior to the change. (Bummed there was no “grace” period.)

The budget airlines enforce their rules as part of their revenue. That's one reason the original prices are "budget".

Do you own research so it’s not my fault. But the most restrictive of the two is Ryan Air
Which limits the free personal item to 15.75 x 9.84 (use 9 ¾”) x 7.87 (use 7 ¾”). There does not appear to be a weight limit on this bag.
And limits the extra cost carry on to 21.65 (use 21 5/8”) x 15.75 x 7.87 (use 7 ¾”). The weight limit is 22 lbs which is pretty fair for that size bag. But they intentionally (I bet) excluded 22” carryon bags.
https://help.ryanair.com/hc/en-us/articles/360017825358

The EasyJet bags are 17.72 x 14.17 x 7.87 and 33 lbs and 22.05 x 17.72 x 9.84 and 33 lbs. But …..
https://www.easyjet.com/en/help/baggage/cabin-bag-and-hold-luggage

I for one am happy that those that need more luggage subsidize my flight, so I think the baggage restrictions are a good idea. You guys that need that full size carry on often pay close to twice what I pay. But I do suggest a good pair of cargo pants.

I will throw out Wizz too, cause I like Wizz
Free: 15.3/4” x 11 ¾” x 7 ¾” 22 lbs
Extra: 21 5/8” x 15 ¾” x 9” 22 lbs

Don't try to be cheap, that will get you burned in the end. Just pay for a higher level of service, that you need, that is how those airlines work.

For example, on Ryanair, the price shown is for "Value" tickets, only allowing essentially a purse or day bag...that will not do. You can move up to "Regular", that allows a small carry-on type bag weighing no more than 22 pounds, and a purse or day bag (but not crammed full). I travel light, but that is tight, on a typical trip, I am just over. It has worked for me if I have a base and am doing round trip with only a few things, but for my full load, it is risky. For little more cost though, you can do "Plus", that gets you a 44 pound checked bag, and you carry on your day bag. Plus you get to check in at the airport, essential if you will not have data service or a phone (Yes, you can check in on wi-fi, then save a copy of the bar-code, etc.), and handy and convenient in any case.

The total cost of the "Plus" option is still darn cheap, and you travel worry free.

The OP didn’t say anything about the trip. I am flying Ryan in June; a 90-minute trip. I am not checking out of my accommodation; I will keep it until I return from the 5-day diversion and so I can travel lighter.

On my flight “Value” is $92 but the cheapest seat will cost you $12. So, $104.
“Regular” gives you a full size carryon and a free cheap seat, so $130
“Plus” add a checked bag to Regular and a few other bells and whistles for $170

Thanks all for great advice!

And the RS bag appears to be too large for Ryan

And the RS bag appears to be too large for Ryan.

It's too big for Icelandair, also.