Treadmill vs street running?

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What's the difference? I do much better on a treadmill so I want to know how much better I need to do in order to build up my fitness. I was doing couch to 5k street running and could just about manage week 4 (the one with the 8 minute segments) but on a treadmill I just did 30 minutes running at about the same speed and covered 4km. It was doable whereas I would be purple in the face and wheezing running in the real world.

How can I calculate how much more I need to do on a treadmill to know that I'm ready for a 5k run or dye thing outside next month?

There's more resistance when running outside rather than on a treadmill, so it is harder. I can't offer you a calculation, but if you can do outdoor running, you'd get a feel for what you can do. Try not to increase distance by more than 10% a week to help avoid injury.

On the treadmill you have the belt "helping" you forward. You don't have hills or slopes. You don't jump up and down off kerbs or dodge dog poo. It's a straight run, steady pace, good for building fitness. But it is easier on a treadmill than outside.

Do you listen to music outside? Do you have a route planned or have to keep checking how far you've gone?

You have proved you can run 30 minutes lung capacity wise. So give it a go outside. Go for 15 minutes, then a three minute walk and then another 15 minutes. You'll be suprised.

I find it harder to run on the treadmill purely because it is so easy to just stop at any time.

I find myself getting obsessed with the stats and it seems to take FOREVER for it to clock up the kilometers. Out on the road, the stats are not so in your face and it's harder to stop when you find yourself 5 mile away from home - you just have to keep on going.

Definitely try it outside. If you are anything like me you will never want to run on a treadmill ever again, I would bet you could double that distance within a few weeks going outside.

Running on the treadmill is easier on the joints because it is not as hard as the sidewalk.

Treadmill doesn't present an uneven surface and keeps you at a constant speed, all of which makes your running smoother and easier.

Treadmill is also easier because you have your towel, tissues, and water bottle at your fingertips.

Other than that, running on the treadmill doesn't need less effort to stay at the same speed & run the same distance, as it doesn't "help you forward". All it does is counter the forward vector of your running velocity so that you stay in the same place.

treadmill needs a kind of mental toughness that I lack, can rarely do more than a couple of miles before my mind bends and snaps

but am persevering once a week because:
lower impact on elderly self (usually run on either achilles wrenching tracks or calf strain terrain - roads)
I sweat so it feels like I've worked hard!
it's very convenient way of keeping up a minimal mileage by including it in gym visit
it's easier to control pace and achieve negative splits so confidence boosting

I find the opposite and that I can run better outdoors than on the treadmill. I just set a new Parkrun pb and the average pace for time I ran would be unachievable for me for that time on a treadmill. I generally just use treadmill for interval work where I can control the speed, I have no idea why outdoor running is easier for me.

Can anyone recommend a good folding treadmill? Prepared to pay about 300/400, maybe a little more if well recommended. Thank you