Visualisation means to see any object or any thing,and calculation means to doing some calculation or mathematical operations.
what is the difference of VISUALIZATION and CALCULATION??

I've always assumed in chess that visualisation is more of a positional thing whereas calculation was tactical.
Although with the way you're defining them it seems like they are just the same thing with a slightly different mental approach.

Theres a lot of overlap, you use visualization to calculate. If youre calculating say 6 moves ahead to see where the pieces will be, you are 'visualizing' the position 6 moves down the track.

Other then puzzles - which do seem to strengthen visualization capacity - are there ways to increase our ability to visualize positions, and as a result calculation facility?
That people can visualize/calculate out a knights tour blows my mind.

its not so difficult, just find the square you want a knight to go, and find the quickest way there.
Some ways you could try
>Puzzles for calculation
>blind chess, (theres an app for training)
>simply play long games and calculate variations

Don't take a board. Imagine the sequence of moves : 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Bxc6 bxc6 5.d4
What are black candidate moves here ? You need to visualize the position in your head to answer the question.
Now, in a given position, like the daily puzzle, to find the best move, you try to look ahead : "if I play this, he plays that, then I do this, he does that..." - that's calculating in chess

>blind chess, (theres an app for training)
How do people do this? All I see when I close my eyes is darkness. That overlaid with sporadically playing soundtrack of space music.

For me, calculation is working out what moves need to be made, visualization is the ability to accurately see the resulting positions. Without strong visualization skills, you can't make sound judgements based on your calculations. You won't know when to stop your calculations!
I agree that the two go hand-in-hand. Taken together, they are the most important skill in chess. There are many, many methods to improve both.

Don't take a board. Imagine the sequence of moves : 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Bxc6 bxc6 5.d4
What are black candidate moves here ? You need to visualize the position in your head to answer the question.
Now, in a given position, like the daily puzzle, to find the best move, you try to look ahead : "if I play this, he plays that, then I do this, he does that..." - that's calculating in chess
Yeah that's how I seperate them. If you hold a future position in your head and "look around" for an evaluation and candidate moves from there, then you're visualizing.
If you do "counting" like he takes, I take, he takes, I have a check, and then I take, and he can fork me so I can't do that... there's no need to visualize anything. Or in other words, whenever you don't hold the final position in your mind's eye and really consider it, you're not really visualizing anything.
That's my definition, but it's also true that you can't completely separate them.

Every time you calculate a move, you are visualizing a position that is a certain amount of ply changed from the original. So if I'm calculating a capture and my opponent's response, I am also visualizing a position that is the same as the one I am currently in, except with that change.
By the way, after calculating a sequence of moves, it's always good to take a deliberate look (in your head) at the position that arises afterwards. A lot of times there are subtle touches after the fireworks clear, such as getting that fork you want (many might stop their calculation there if they didn't see any more forcing moves from the opponent, but...), but finding out that by the time your opponent moves one of his pieces away, and you take the other, the piece that captured it can suddenly be trapped and have its escape squares cut off (this is the kind of position I'm saying you should visualize). Hopefully that piece won't be your queen!
For me, it's like how a square is a rectangle but a rectangle is not a square. One form of calculation could be thought of as a rapid change in visualization (starting from position x, then looking at x + 1 ply, x + 2 ply, and so on), but obviously there are other forms of calculation too.

its not so difficult, just find the square you want a knight to go, and find the quickest way there.
Except that, in this case, it's the longest way...!

Actually, I guess a rectangle could be a square, but only if the rectangle you are talking about also happens to be a square .
In other words, you can find rectangles that aren't squares, but you can't find squares that aren't rectangles

It is possible to calculate without visualizing the position.
Here's a simple example: 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6
Can White win the e-pawn?
Yes. There's one attacker and one defender. White can remove the defender with 4.Bxc6 dxc6 5.Nxe5, winning the e-pawn.
BUT, if you visualize the position, you will see that Black can regain the pawn with 5...Qd4! 6.Nf3 Qxe4+!
If you're really good at visualizing, you will see that after 7.Qe2 Black has a structurally compromised Q-side, but his pieces have easier development after the Queen trade. The position is objectively about equal, but Black's easier development gives him good practical chances.
Just about every series of exchanges can be calculated without visualizing the position. Here's another simple example. Simple question, Can Black win the d-pawn? To answer it, one only needs to calculate without visualizing the final position.

Great post smyslov fan, just a little nitpick: Is it not true that, even to determine superficially that you will "win a pawn" with Bxc6, wouldn't you still have to at least visualize the knight on c6 leaving the board? Again, it's perhaps a more superficial visualization, but without thinking about what will happen to the e5 pawn without a knight on c6, I don't see how anyone would say "I'm winning a pawn."
I know white doesn't actually win a pawn, but the reason why someone may think it does is still due, in some part, to visualization, isn't it?
Again though I fully advocate the point you are making. I think some people might visualize the position after 4 Bxc6 bxc6, but not visualize the position after 5 Nxe5, figuring they don't have to.
In your diagram, although it's true that here counting the amount of times the square is defended would lead you to the right path, I honestly still think it's a good habit to visualize the position anyway. For example, visualize the position after 6...cxd4 7 cxd4 Nxd4?? 8 Nxd4 -- I know, it seems crazy to visualize the position here because it's "obviously fine for white," but it's good to do it anyway, because in some positions there might be some random tactics black would have. Indeed, I would even say visualize the position after 8...Qxd4?? 9 Qxd4, simply because it would only take a millisecond to check. Here there is obviously no tactic black can use but sometimes there are -- it's good to make sure, and takes virtually no time. Sometimes you might find that after you move one of your pieces to capture another piece, it ends up leaving control of something else, such as the back rank.

I say doing lots of puzzles at once every day and tactics on HARRRRRD setting makes your visuocalculations better the fastest so it comes to you like instinct almost, I mean, mrrrm, intuition :3
Essentially they're the same thing.
To calculate, you need to visualise what happens next.
Words can share similar meanings. Words aren't black and white. It seems to me that you're just categorising the two words as opposites.

Visualization is the ability to see the position that will be reached if certain moves were to be made - and specifically to be aware of the consequences of those moves.
Visualwize gives training exercises that focus on visualizing a certain amount of moves and the exercises simulates the reality http://chessfox.com/visualwize-3-0/
Calculation skill is the abilty to recognize and calculate mainly all te forced moves. If moves aren't forced then it is almost impossible to calculate and it will be far more effective to depend on your positional understanding when you consider moves that aren't forced.
what is the difference of VISUALIZATION and CALCULATION??
visualization is forming a picture in your mind, so that u can see what happens next, so u can decide what to do....
while
calculation?? like in an endgame, we calculate whether our king can reach the pawn or not before the enemy could reach, this is calculation, but we have to VISUALIZE also right??? visualize the king stepping forward.....
so WHAT the difference?? to improve tactics, we need visualization skill or calculation skill???