The iPhone and iPod touch include a built-in calculator app that's easy to use and handy since it goes where ever you take your pocket-size iOS device. That calculator is pretty basic, but it also hides a full featured scientific calculator, and all it takes to find it is a little twist.
The calculator in iOS 6 is more than it seems...
You can see the standard calculator view when holding your iPhone or iPod touch in portrait mode, meaning holding the device so it's taller than it is wide. To switch to the scientific calculator, just rotate your device into landscape mode so it's wider than it is tall.
...just rotate to see the hidden scientific calculator.
This trick won't work if you have the Rotation Lock on, and it doesn't work for the iPad because in a mystery move Apple decided not to include a calculator app on its tablet device.
For iPad and iPad mini owners that need a calculator app, PCalc from TLA Systems is a nice choice. It's available through Apple's iTunes-based App Store for US$9.99, and a feature-limited free version is available, too.