Indentation
Much about indentation is a style issue. Best to follow your group's style guide. That said I would align comment with code.
//check letter count
if (check == 'l')
to
// check letter count
if (check == 'l')
Spell check
Spelling errors are a distraction and a confusion.
double vs. float
In C, double is the default type for floating point constants like 0.0588. Code is going through lots of gyrations converting form int to float to double and back to float. I suggest using double unless required to use float or code has lots of FP.
// float gradeLevel = (0.0588 * (100 * (float) length(input, 'l') / (float) length(input, 'w')) - 0.296 * (100 * (float) length(input, 's') / (float) length(input, 'w'))) - 15.8;
double gradeLevel = 0.0588 * (100.0 * length(input, 'l') / length(input, 'w'))
- 0.296 * (100.0 * length(input, 's') / length(input, 'w')) - 15.8;
If staying with float, use float constants: 0.0588 --> 0.0588f
Rounding (advanced)
round()returns a double. C provides a nice way to round to a floating point to an integer type in one step
long gradeLevel = lround(0.0588 * (100.0 * length(input, 'l') / length(input, 'w'))
- 0.296 * (100.0 * length(input, 's') / length(input, 'w')) - 15.8);
...
printf("Grade %ld\n", gradeLevel);