The approximate frequency of middle C (C4) under standard tuning is 261.626 Hz.
This value comes from equal temperament with the A above middle C fixed at 440 Hz, the international A440 reference. In that system, each semitone is separated by a frequency ratio of the twelfth root of two. C4 lies nine semitones below A4, producing approximately 261.626 Hz.
Middle C is written C4 in scientific pitch notation and is near the center of an 88-key piano. A common mix-up is 523.251 Hz, which is C5—one octave above middle C. Another is 440 Hz, which identifies A4, not C4. The exact sound of an acoustic piano can vary slightly because real instruments are tuned with practical adjustments, but 261.626 Hz is the standard theoretical value.