iOS get physical screen size programmatically?

There isn't an API that will give you this. Your best bet is to look at the device's screen size (in points) and from that surmise if it's an iPad or iPhone etc., and then use hard-coded values for the screen sizes.

Here's some code to get the screen size:

CGRect screenRect = [[UIScreen mainScreen] bounds];
CGFloat screenWidth = screenRect.size.width;
CGFloat screenHeight = screenRect.size.height;

Be aware that width and height might be swapped, depending on device orientation.

Here's a short method that estimates the device screen size. It's updated as to the latest devices, but may fail on future ones (as all methods of guessing might). It will also get confused if the device is being mirrored (returns the device's screen size, not the mirrored screen size)

#define SCREEN_SIZE_IPHONE_CLASSIC 3.5
#define SCREEN_SIZE_IPHONE_TALL 4.0
#define SCREEN_SIZE_IPAD_CLASSIC 9.7

+ (CGFloat)screenPhysicalSize
{
    if(UI_USER_INTERFACE_IDIOM() == UIUserInterfaceIdiomPhone)
    {
        CGSize result = [[UIScreen mainScreen] bounds].size;
        if (result.height < 500)
            return SCREEN_SIZE_IPHONE_CLASSIC;  // iPhone 4S / 4th Gen iPod Touch or earlier
        else
            return SCREEN_SIZE_IPHONE_TALL;  // iPhone 5
    }
    else
    {
        return SCREEN_SIZE_IPAD_CLASSIC; // iPad
    }
} 

If it were available it would be in UIScreen or UIDevice but it is not there.

You can infer it from info in Erica's UIDevice-extension and the specs for each device listed here on Wikipedia.