How to detect total available/free disk space on the iPhone/iPad device?

I'm looking for a better way to detect available/free disk space on the iPhone/iPad device programmatically.
Currently I'm using the NSFileManager to detect the disk space. Following is the snippet of the code which does the job for me:

-(unsigned)getFreeDiskspacePrivate {
NSDictionary *atDict = [[NSFileManager defaultManager] attributesOfFileSystemForPath:@"/" error:NULL];
unsigned freeSpace = [[atDict objectForKey:NSFileSystemFreeSize] unsignedIntValue];
NSLog(@"%s - Free Diskspace: %u bytes - %u MiB", __PRETTY_FUNCTION__, freeSpace, (freeSpace/1024)/1024);

return freeSpace;
}

Am I correct with the above snippet? or is there any better way to know total available/free disk space.
I've to detect total free disk space, since we've to prevent our application to perform sync in the low disk space scenario.

UPDATE: Since a lot of time has passed after this answer and new methods/APIs have been added, please check the updated answers below for Swift etc; Since I've not used them myself, I can't vouch for them.

Original answer: I found the following solution working for me:

-(uint64_t)getFreeDiskspace {
    uint64_t totalSpace = 0;
    uint64_t totalFreeSpace = 0;
    NSError *error = nil;  
    NSArray *paths = NSSearchPathForDirectoriesInDomains(NSDocumentDirectory, NSUserDomainMask, YES);  
    NSDictionary *dictionary = [[NSFileManager defaultManager] attributesOfFileSystemForPath:[paths lastObject] error: &error];  

    if (dictionary) {  
        NSNumber *fileSystemSizeInBytes = [dictionary objectForKey: NSFileSystemSize];  
        NSNumber *freeFileSystemSizeInBytes = [dictionary objectForKey:NSFileSystemFreeSize];
        totalSpace = [fileSystemSizeInBytes unsignedLongLongValue];
        totalFreeSpace = [freeFileSystemSizeInBytes unsignedLongLongValue];
        NSLog(@"Memory Capacity of %llu MiB with %llu MiB Free memory available.", ((totalSpace/1024ll)/1024ll), ((totalFreeSpace/1024ll)/1024ll));
    } else {  
        NSLog(@"Error Obtaining System Memory Info: Domain = %@, Code = %ld", [error domain], (long)[error code]);
    }  

    return totalFreeSpace;
}

It returns me exactly the size that iTunes displays when device is connected to machine.