How to get better at calculation?

For a long time I wondered why strong chess players were often good at maths, because beyond basic arithmetic there is not very much maths involved in chess. People who are good at maths tend to be especially good at solving chess puzzles.

Only recently I realized that it is because people who are good at maths are much stronger than the average person at calculation.

What is the best way to get better at doing chess calculations? Is there a good way to directly measure your calculation strength? Or is it best to just keep practicing puzzles? Is stronger calculation a byproduct of doing puzzles, or is it a separate skill?

I like to winning games.

Both are essential.

I think doing puzzles helps your calculation at first, but then it slowly becomes pattern recognition.

Yes. Pattern recognition comes with doing puzzles. After doing over a thousand of them, my pattern recognition has gotten quite a lot better but my calculation strength is still quite weak.

It is better than it was when I first started, but when there are six or more pieces that could all trade, I find it quite confusing and difficult to determine which captures to make in what order to make the captures in so that I come off best no matter how the opponent responds. In the slow games I am sometimes able to eventually work it out, but in the fast games I have no chance.

Explain "calculation"? 

Logical evaluation of candidate moves, coming to conclusions based on determinations rather than relying on general principles or pattern recognition.

Working out the best move by calculating the variations.

What you're asking about is way above your head at your level.  General principles are exactly what you need right now.

Chess is pattern recognition.

I can calculate many moves ahead but I can't always calculate the best move or evaluate the position and the end of the line. I suggest you to just grind puzzles but only play the move if you see all the lines till black doesn't have any more tricks. It's fine if you even take 10 minutes on one puzzle.

Take a position like this.  White to move.  How would you evaluate the position?

Chess is more than just pattern recognition. It's a thinking man's (or woman's) game.

Of course.  So what is your current thinking process?

I would look at the threats that each side has. Look at the imbalances. Try to come up with a plan. White has a space advantage and a castled King. Black's pieces are not well coordinated.

The d4 pawn is clearly the center of attention with two attackers and two defenders.

General chess principles would definitely be a consideration for me there. I would probably move the bishop on c1 out.

alculation is situation-based, there are positions that require calculation but before you reach such positions in the middle game you first need to get a good feel of positions, look at a position and at one go ask yourself "which side is better in this position and why is that", that's fundamental positional understanding and only after you get good positional understanding should you move to calculation and visualisation, calculations come from very tactical positions, but you need to have good positional play to know that you're in a better position than your opponent at the given time and then proceed to calculate tactics that could lead you to a favourable endgame or a checkmating attack. Get "a good move guide" by Bent Larsen, I think that would take your general positional assessment to the next level and then calculation, visualisation and advanced tactics would be the next focus, hope that helps.

What threats are on the board?

What are the imbalances?

What makes the d-pawn so important?

What advantages does white have?

Where would you place the DSB?

”The most important attribute for any chess player is the ability to calculate variations quickly and accurately. ... Visualization skills ... should be developed as far as possible via tactical and blindfold exercises. This should be the first port of call for anyone who wishes to improve their chess.”

- GM Nigel Davies

Endgame exercises develop calculation skills.

I think the disconnect was with the terms "evaluation" and "candidate moves".

Solving puzzles does include calculating tactics and pattern recognition. A puzzle itself provides you with information that there is a tactical solution, unlike each position in a game.

You might perform a pre-move tactical assessment (a threat analysis) and not need to do anything more based on the immediate threats and the urgency required to answer them.

You might perform a tactical evaluation after a positional evaluation (mentioned in post #16). All depends on your process as a whole, but this is where candidate moves would come into play.

Chess calculation has nothing to do with math calculation. The same word is used ("calculation"), but you should regard the word calculation as a homonym. Also, being good at doing math calculations (adding, subtracting, multiplying, dividing numbers) has very little to do with being good at mathematics. Being exceptionally good at calculating is like being exceptionally good at writting letters fast. Being able to write letters fast doesn't have a lot to do with being a good novel writer, by the same token, being able to calculate fast doesn't have a lot to do with being good at mathematics. Calculation is the alphabet of mathematics. The average calculation ability is enough to be good at math (obviously you will have to practice math a lot so that you don't make silly calculation errors, but everyone can do this and also  practicing calculation is analogous to practicing writting letters. No matter how well and fast you calculate, or how well and fast you write letters, that has very little to do with your ability to solve math problems or write novels).
As far as I know, most chess GMs hated mathematics in school and they weren't good at it. You are focusing on those which were good at both but they are in the minority. Math calculation has little to do with chess calculation and math has very little to do with chess. 
Sorry if the tone of this comment appears to be rude, that was not my intention.