Short, less than 160 character SMS being split I'm receiving SMS messages that are being split into multiple messages. These messages are well below the 160 character limit. For example, I checked three at random that were split and they only had 82, 91, and 79 characters.

The messages aren't split after the same number of characters.

I'm see this problem with a sender who has an iPhone 6 on sprint, and I have a Samsung Galaxy S5 on MetroPCS (T-mobile). I've tried different SMS apps on my phone.

What might the problem be?
One possibility is that "characters" is not what you think. SMS was originally designed for single-byte languages, so in languages that use non-Latin characters, one "character" in that language counts as 2 or 4 characters in the  SMS message. The problem is particularly noticeable in Chinese. Emoji also count as multiple characters for this purpose.

If your correspondent is writing in Chinese or other non-Latin languages, or makes heavy use of emoji, they won't be able to write 160 characters.