normally, they are not interchangeable. 描述：describe simply 形容：describe with some rhetoric. for example, there is a man who runs very fast. A: he runs very fast. then you can say A uses his sentense to 描述 this man runs very fast. B: he runs like a rabbit. then you can say B uses his sentense to 形容 this man runs very fast.

I'm Sorry but I have different opinions. Just for reference. 1. Normally, they ARE interchangeable, though technically, “描述“ includes ”形容“。”形容“ is one kind of ”描述“. 你怎么描述他跑步？ 他跑的很快/他快得像只兔子。 you can answer this question in either way. only the former answer is a narrative description while the latter one is described to use a metaphor, but both of them belong to "descriptions". 你怎么形容他跑步？ 他跑得像只兔子。（more suitable）/他跑得很快（too plain, but not a wrong answer!）。 normally, as I have said, they are mutually alternative. 你怎么形容这个人？= 你怎么描述这个人？ Exceptions are as follows: 2. In ancient times, "形容" can be used as a noun (an appearance of one person or a shape of one object) (It is not modern Chinese, while it can be still used in written Chinese, but this usage is not suitable in conversations. Otherwise, it sounds quaint or mushy.) 3. “形容” is more suitable in a formal way and a poetical way. The corresponding examples have been given by other kind answerers here. Please allow me to interpret one of them. "非笔墨所能形容"=“不是语言所可以描述的” （非=不是；笔墨=语言；所能=可以……的； 形容=描述；） The former word is more rhetorical, poetical, and archaic than the latter one respectively. Despite it, you could also say "非笔墨所能描述". That is also absolutely correct and has a native flavor. Maybe some individuals think the former expression is more polishing. But they are not set phrases. 4. adjective = 形容词 rather than 描述词。 This is a set phrase. After the reform in 100 year ago, modern Chinese has became very random. the written one and spoken one have tended to be mixed up. There are too many ambiguous rules now, which could be carved yesterday and can become old-fashioned tomorrow. I don't think we need to pay much attention to them. We have to learn it intuitively. Anyway, personal views only.

描述 = describe giving your opinion 形容 = describe naming the features

描述：描写叙述，运用各种修辞手法对事物进行形象化的阐述 例子1：他生动地“描述”了那件事的经过。 例子2： 作品朴实地“描述”了农民的生活。 形容：这个意思可就多了 1、指外貌，摸样 例：形容憔悴 2、指表情，神态 例：她听了这话，又深深的看了我一眼，作了一种不了解的形容，依旧的走到她的房里去了。 3、指事物的外部形状 例：按其形容，皆刀斧凿削而成者 4、同描述 例：非笔墨所能形容的 主要就那么几种意思，希望能帮的上，呵呵