Pina is placed at the most outer part of our body. It is the part of our body that first receives the sound its formation is complex. It is one of its characteristics. They are placed on either side of our head. They are facing the front. Many different curves make up the ears and they are they are three dimensional. This paper shows how the formula was developed based on the spherical coordinate system and directional band. In the spherical coordinate system, it doesn't matter how far the sound is coming from. The result will change based on the direction of the sound. This characteristic of the spherical coordinate system reflects the characteristic of the pina. This paper uses the spherical coordinate system to explain how the pinna works when it receives the vibrations of the sound. The complexity of its structure helps identify all the minute vibrations of the sound. The complex curvatures and the planes of the pinna can be defined as the differences in the arc length of the ear. This paper will use the relationship between the frequencies of the sound and directional band. When a specific point of the pinna receves the sound, the variations in the volume of the pinna plays a role as a receiver. The variation is defined as "the Minute Variation of the Arc of the Outer Ear D". The formula is    sin. The process of developing the formula shows the process of process of pinna receving the sound.