Q: Save photos to icloud and eliminate them from ios device

Is there a way to have all the photos in iCloud without deleting them?

If you delete them from the phone, they will delete from iCloud. Try going to Settings/iCloud and Optimize Storage. This will reduce the space the photos take up.

You are welcome.

It seems that I am having the same type of issue on my iPhone 6; 16GB; and the standard 5GB iCloud account.

This is the first Apple product I've ever owned, and it was purchased in December of 2014. So its been an adjustment to some degree, but my fiancée has had several iPads; which I've used and which ultimately brought me to purchase an iPhone.

I'd like to add that the iPads my fiancée has had, and has today; have all been 16GB, WiFi only, and never purchased additional iCloud storage. She has over 3,000 photos, (2) email addresses with a total of 9,282 emails (as of yesterday), and >15 additional apps; all of which sync to her iCloud account. And she's never had any issues with storage.

I will not pay for additional iCloud storage. (No offense to Apple Inc., because it is a great service)

Some things I've learned about photos and iCloud;

1. Whenever you edit a photo, iCloud saves the original, along with each edit that is done to an individual photo
2. If you also use/have a laptop or desktop (Mac or PC), take advantage of the software that allows you to sync docs and photos that come from your iPhone/iPad/iPod to your iCloud, then to a laptop or desktop. Its helped me tremendously, and I am convinced that it is the only way my fiancée can have all the photos and other junk on her iPad, which she'll probably never look at again.  
3. I tried the whole optimizing of photos whatever setting, and it didn't help me at all. In fact I was able to save the 50 some photos to a SD card by getting on my PC, and going to http://www.iCloud.com. The photos alone were taking up about 2.5GB of storage on my iPhone, and 4.4GB on my iCloud account. Now I have that setting turned off, and have had no problems since.
4. Another useful app, but not necessary to install is Flickr. Create a Flickr account, and then go into your settings and click on the Flickr setting. Add your Flickr username/email and password. Now you have 1,000GB of storage for your photos. Just select the photos you want to save (just not on your iPhone), and tap on the ⬆️ on the bottom of your photos page, and make the selections for a particular album(or no album) and select if you want them to be private or public. 

I have written way more than I had intended, but if it helps at least one person; I'll be   ‼️

Thank you. This was very useful.