@ddafoe +1 on the Reed Instruments. Is $180 "expensive"? Not if you care about your hearing. That’s cheaper than many spend on a decent set of RCA interconnects.
The problem with many of these phone apps is that you have no way of knowing if they were matched to the microphones and preamps in these devices. That one guy above, Jon, says the one for his specific iPhone is "close" to a calibrated SPL was fortunate. Good for him. Perhaps Apple commands such a market share that the developers could spend the time getting it right.
I doubt all these developers take the time to get real data on the myriad of phones out there, especially Android except for certain Samsung phones. And then, where do they get this information?
How do we even know the frequency range and response of these microphones and preamps in our cell phones. I mean they are mainly designed (and perhaps even intentionally limited) to pick up and amplify human speech (85Hz to 255Hz), not music. In telephony, the usable voice frequency band ranges from approximately 300 to 3400 Hz. Note that 300Hz is indeed above the fundamentals, but they say, "However, enough of the harmonic series will be present for the missing fundamental to create the impression of hearing the fundamental tone."
So, your phone likely has a sampling frequency of 8000Hz in order to cover decently up to 4000Hz, and whether the microphone goes any higher (or lower than 300Hz) with a decent linear response is open to question and experimental tests.
At least if you buy a legit SPL meter (a good one) they let you know the frequency range it covers (31.5 Hz to 8 kHz in the case of the Reed Instruments) and its accuracy (±1.4 dB - which isn’t that good but "decent").