The gear you mentioned upstairs is not a sprocket. The relationship between the diameter Dp of the sprocket’s indexing circle and the pitch P is Dp=P/sin(180/Z). Z is the number of teeth. The value of the index circle is between the tooth top circle and the tooth root circle, and is generally greater than half of the sum of the tooth top circle and the tooth root circle. The value of the pitch P is converted from inches, and is generally the value of the article number multiplied by one. Divide inches by 16. This is what I know. I hope it will be useful to you.