Is 500 ft/mi elevation gain 15% grade?

[JJHACK]

I was thinking about this while in a conversation today. I did not do the math, but seem to remember some standard numbers sticking in my mind

 

[Darren Best]

A 500 feet elevation change in one mile is roughly 9.5 % grade, (rounded to the nearest tenth).

Take the elevation change in feet and divide it by the distance in feet, then multiply that by 100.

 

[Darren Best]

For a 15% grade, you need 800 feet gain in 1 mile.

 

[JJHACK]

Thanks, I had some numbers in my head from memory. Don't recall where from and clearly incorrect.

I know 1000 ft/mile is pretty steep for state land hiking trails. It just does not sound steep when you hear 15-18% grade.