If you open the Calculator app on your iPhone, you'll face a basic calculator. But to get and open scientific calculator on iPhone with no 3rd party apps, you need to do as follows:
1. Make sure the Screen Rotation feature is not locked.
** To turn off screen rotation lock (portrait lock), simply open up the control center and touch the Portrait Orientation Lock button
2. Open the Calculator app on your iPhone
3. Rotate your phone to the Landscape mode and the scientific calculator should appear.