It isn't very efficient to try to memorize "equations" for the lung capacities. Remember that a Capacity is made up of two or more Volumes. I find it easiest to start from Tidal Volume and work from there. Tidal Volume is a volume, so it doesn't have an "equation." It's the amount you take in and out with normal breathing. Now if you think of your own breathing, there's always some more you could take in by force. That's your Inspiratory Reserve Volume. Remember, it's a volume, so there isn't an "equation" for it. It's simply the extra air you can take in after you've taken in your normal Tidal Volume. Now go back to Tidal breathing, and there's some extra air there that you can push out beyond normal breathing. That's your Expiratory Reserve Volume (again, a volume and not a capacity). That's just defined as what you can blow out beyond what your normal-breathing baseline air out is. Lastly, after you've blown out all the air you can, your lungs still aren't empty and totally collapsed. There's a last volume there, the Residual Volume.
Now take those 4 volumes, and there are only 4, and combine them in different ways that make sense given their names.If I ask you for Total Lung Capacity, that should be simple. It's all the Volumes added up. If I ask you for Vital Capacity, you know that it's a Capacity, so you know you're gonna have to add two or more Volumes. Vital Capacity should make you think of everything you as a person can do with your lungs. That should mean to you "as deflated as I can go to as inflated as I can go." This means you should sum all your Volumes except Residual Volume, since you can't move that no matter how hard you try. It's not part of your Vital ability, so to speak.
With those two Capacities out of the way, there's just two left. There's an Inspiratory Capacity and a Functional Residual (expiratory) Capacity. These do not overlap. Go to the bottom of your normal tidal expiration, then breathe in normally, then breath in fully. That's your Tidal Volume, then your Inspiratory Reserve Volume. Those two combined make your Inspiratory Capacity. Your Functional Residual Capacity is the opposite. Go to the bottom of your Tidal Volume and think about all the volume left in your lungs. It's your Expiratory Reserve Volume plus the air you can't breathe out, the Residual Volume. Those two together are your Functional Residual Capacity.
That's it, all four Volumes and all four Capacities. Once you memorize the meaning of the Volumes, just take the time to consider which combinations make sense and play a matching game with the Capacities. I think you'll see it comes pretty easily after that, with no need for equations.
