While the iPhone has Apple's built-in calculator app, the iPad doesn't. I looked on the App Store, but the apps either didn't support the iPad's screen well or lacked the calculation functions I wanted...
So I decided to make my own app!
It's called PaletteCalculator! You can use it not only on the iPad but also on iPhone and Android.
What can it do?
It can do basic arithmetic, trigonometric functions, exponents, and more. It should have the basic functions you'd expect from a scientific calculator. As a bonus, I've also added hyperbolic functions and combinatorics functions for permutations and combinations.
Formula Display

It can display the calculation expression you're currently entering. It also has an autocomplete feature for things like * and ).
Parentheses are color-coded to match, like in programming editors. You can turn this off in the settings if you prefer.
History

It shows your past calculation expressions and results.
Long-pressing gives you detailed information, and tapping lets you input the result into your current expression.
Memory

It has the standard memory functions found on scientific calculators.
GT returns the sum of the results in your history.
Multiple Input Methods
You can choose between two modes, Hld and UnHld, using buttons.
Hld behaves similarly to Apple's built-in calculator.
UnHld lets you move the cursor to change the input position. You can also double-tap to select a range.
Using these cleverly makes it easier to input complex expressions!
UnDo
You can undo your actions to revert to the previous state (except for C and AC).
Split View Support

Of course an iPad app needs to support Split View!
It also supports portrait orientation.
Very handy for taking notes while calculating.
Customizable Appearance
There are 19 regular themes and 2 image-based themes to choose from.
I'm sure you'll find a theme you like!
Regular Themes
From left to right: White Blue Green Red
Purple Orange Pink Silver
Black Navy Moss WineRed
Wine Pastel Fruit Ocean
Forest Flower Cherry.
My personal favorite is Ocean. Using it in summer gives a refreshing feel.
Image Themes
The left one is ImgDark and the right one is ImgLight.
Setting a photo of your child, grandchild, pet, or memorable moment as the background can be heartwarming.
Thoughtful Design
The functions are organized into categories on separate pages, making it easier to find what you need.
Separating functions by category also makes it easier to use different functions in portrait mode. For phones, portrait with larger buttons may be easier to operate.
Install
You can install it from here. Please give it a try!
