iphone 6s battery only 81% maximum. Need a new battery?

Possibly.

Apple would consider premature battery failure if your iPhone has less than 80% capacity with less than 500 recharge cycles.

• Maximizing Battery Life and Lifespan - Apple
• iPhone Battery and Performance - Apple Support
• iPhone Battery & Power Repair - Apple Support

Oliver@Leo1 wrote:

My iPhone 6s Maximum Battery Percentage is 81% and it won't stay charged for 1 entire day. Do I need a new battery?

It's kind of on the edge. Apple will replace the battery through the end of the year for $29. I would go for it if it was my phone. Make a genius bar appointment if you want to go this way: Genius Bar Reservation and Apple Support Options - Apple. They can usually do it while you wait.