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Superconducting racetrack coils are used for magnetic levitation, magnetic resonance imaging, etc. When using racetrack coils, it is important to determine the coil characteristics (the resistance, self-inductance, mutual inductance, and distributed capacity of the coil). It is difficult to analyze the racetrack coil that has straight and semicircle parts. Therefore, the analytical solution of this coil has not been obtained yet. In this paper, we derive the analytical solution of the magnetic field of a single-layer racetrack coil based on the magnetic field of the one-turn racetrack coil. In addition, the analytical solution of the self-inductance is derived on the basis of this theory. The validity of this theory is confirmed by comparing measured self-inductance values with the calculated values.