I don’t think that there is a “perfect†size for visiting cards. The usual size for visiting cards is 92mm/54mm. Are you looking to print them for business or personal?
All of the visiting cards I have dealt with have been around 3.5 x 2 inches or so. That being said I don’t think there’s any set size, just whatever you feel works for you.
The standard dimensions for a printed business card are 3.5 x 2 inches. That's the finished card size. Many printed designs include bleed. The "bleed area" is an extra 1/8 inch of space for design elements or backgrounds that extend beyond the finished size of your piece. A business card design with bleed is printed slightly oversized and then cut down to size, giving the appearance that the printing "bleeds" off the edge of the card, rather than having white borders.
Your business card should have attraction for your potential customers and employees. You can use also it as an advertising tool because leaves the impression in the mind of people so use compelling image that reflects your business, include logo, font should be large enough that is easy to read, keep it simple, do not use outdated information and the width of card should be 3.6 and height 2.1 inches.