What are the distinctions between 大概 and 大约？
大概 is more general 

大約 is more narrow. Specifically be used to express estimation of numbers

Both 大概 and 大約 can mean "approximately" 

"There are approximately fifty people" can be translated as "大概有五十人" or "大約有五十人"

More example:

大概二十英尺 / 大約二十英尺 (about 20 feet)

大概四十岁 / 大約四十岁 (about 40 years old)

大概三年/ 大約三年 (about 3 years)

However, 大概 also means "probably" and "roughly"

You can say 他大概不会来了 (He probably won't come), but you cannot say 他大約不会来了 (He approximately won't come)

You can also say "大概說明一下" (roughly explain a little), but you cannot say "大約說明一下" (approximately explain a little)


  Whenever numbers are involved, you can safely use either 大約 or 大概 for "approximately"