Approximating Your Dogs Measurements
If you can't get all the measurements needed you can approximate your dogs measurements using the one or two you were able to get. This can be used for length/width/height, open circumference and height.
Profile Pics + Length, Width & Closed Height
Starting with the easier measurements to approximate, you start by getting profile pics of your dog, which are closed mouth, taken from above your dogs snout and side on. By getting these pictures and for example only length you can quite easily approximate the missing measurements (width and closed height.
The pictures with no measurements are your dogs profile pics.
You can see below how you can approximate these measurements. Length can approximate width and closed height, Closed height can approximate length, which can then give you the approximate width, as well as width can approximate length, which can then approximate closed height. As you can see though, it would be more useful to get length, rather than width or closed height.
First Photo: Yellow tape measure
The dogs width is 2.7", you can instantly see in this photo that the dogs length is longer than their width, you could make a rough guess or you can edit the photo and draw a line up the length of the nose, then drag it around to over the width/tape measure, thus giving an approximate length. Based on this picture I would put length as approximately 3.5-3.75".
Second Photo: White tape measure
The dogs length is 2.75", based on the pic you can see the dogs width is fairly similar to its length but maybe a bit less. To then approximate the closed height from length you look at their profile pic (side on) and do the same thing of their closed height vs the approx length you have got.
Third Photo: Green tape measure
Using this dogs closed height of 3.5", we can see length is very similar to their closed height measurement but with the curved nose it could be slightly more. I'd approximate this dog as 3.5"-3.75" length. This dogs length is actually confirmed as 3.75". After this you can then approximate the dogs width by looking at the profile picture from above.
Approximating Open Height
You can approximate open height by measuring closed height and then compare that measurement/picture to the dog full/regular panting and find a rough open height measurement as shown in the picture. You can also see that full pant looks like it is more than the 5" shown on the closed height so you would also have to add some more to the measurement too.
You can also add to approximate open height:
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Small Dogs: 1"-2" height added
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Medium dogs: 1.5"-3" height added
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Large dogs: 2"-4" height added
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Remember this a guide; their full pant size will also change how much is added.
Approximating Open Circumference
You can think of open circumference as 2x height. For example if my dogs open height is approx. 4" bigger than closed height then open circumference would be approximately 8" more than closed circumference.
You can also add up closed height vs open height to approximate open circumference:
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Small Dogs: 2"-4" circumference added
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Medium dogs: 3"-6" circumference added
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Large dogs: 4"-8" circumference added
Doing it like above is approximate and not recommended if you can help it as how big your dogs pant is will decide how much to add too. For example if you have a medium dog with a large pant you may need to add 6", where as a medium with a small pant may only need 3".