Hmmm. Mathematically, this should work (remember that frequency correlates logarithmically/exponentially with letter names of notes). However, it's not the way that we tend to do it here in the music world. There's an easier way. The process you describe correlates very strongly with what we singers do, but we use letter names instead of frequencies.
First, we find our own range. You mention recording frequencies of your voice? We do that via piano, and this helps us avoid messy hertz calculations: Play a note, sing it, then move that note up or down until you cannot sing the note you're playing. As an example, suppose I'm a female. I'd start with my finger on my piano's middle C (which is always C4). I'd find that my lowest note is G3. Then I'd go back to middle C, and start upwards, finding that I can't sing any higher than D5. So, my range is from G3-D5. Be very careful with your octave numbers; there's a huge difference between G3-D5 and G4-D6.
The second step is generally finding a song and checking its range. It's the same process, but with the singer in the song's voice. To save time, find the highest and lowest note and verify those. Suppose I wanted to sing "White Christmas" by Bing Crosby. If I'm the same female from earlier, I can sing high enough, but I don't suppose I'll be singing down into the second octave like Crosby. I might want to transpose the song higher or find another workaround to avoid that A♭2, or I might not sing the song at all.
You don't actually need a piano - any fixed pitch reference will do-, but it's easier if you have one. Pianos/keyboards will most likely cover the entire range of any particular singer, and also it's tradition :)
Also recognise that range is far from the only factor in singing ability. If you're being asked to sing for a music class, the thing I'd worry more about is pitch and rhythm accuracy, not matching your range to songs. Most music classes (never experienced a counterexample) are fine with singing in transposed keys, and up/down by octaves as needed. Music classes really aren't testing your singing ability, they're testing your musical understanding.
Another thing we singers do is divide the range of frequencies created by the human voice into 4 general ranges to facilitate comparisons: Soprano is the highest (think high female), Alto below that (think low female), Tenor below the Altos (think high male), and Bass as the very lowest notes (think low male). Of course, gender is not a strict requirement for any voice classification, and in fact vocal range is not technically what determines one's type (it's how the voice sounds), but the practicality of the system is apparent. Supposing I'm the same female from earlier in the question, I wouldn't volunteer for the bass section of any arangement. It's just common sense. There are also a bunch of in-between voice classifications.
Range comparisons in general are a very weak predictive tool for most things, and I think too many weigh range too heavily when singing. The best advice I can give you is: Don't worry about it too much, and use common sense.