Two columns of numbers rising together return a correlation of 0.9995, with 99.9 per cent of the variance explained and a line of best fit of y = 2.011x + 0.1393. That is about as tidy as real data gets.
It still supports no claim about cause, and it would look almost identical for two things that merely happen to grow over the same period.
Straight lines only
The standard correlation coefficient measures how well the points fit a straight line. A relationship that is real but curved can return a value near zero while being perfectly predictable.
The classic case is anything with an optimum in the middle: performance against arousal, yield against fertiliser, speed against fuel economy. Each rises then falls, and a coefficient that only knows about straight lines reports almost nothing. If a rank based measure is a better fit for the question, the Spearman rank correlation calculator is the tool.
The four ways two columns move together
When two variables correlate, the possibilities are: the first causes the second, the second causes the first, both are driven by something else, or it is chance. The coefficient cannot distinguish between them, because it only sees the two columns you handed it.
The third case is the common one in real data. Ice cream sales and drowning deaths correlate because both rise in summer. Nothing about the arithmetic flags the season sitting behind them.
How little it takes to move the number
Correlation is sensitive to outliers in the same way the mean is, and for the same reason: it works with distances rather than ranks. A single point far from the cloud can create a strong correlation where none exists, or destroy a real one.
This is why the first thing to do with a correlation is plot the data. A number cannot show you that the relationship is being carried by one observation, and the outlier fences calculator can tell you which points are unusual enough to be worth that check.
R squared and the trap in the word "explained"
R squared is often described as the proportion of variance explained, which invites reading it as causal. It is a statement about fit: the proportion of variation in one column that is predictable from the other, in that specific sample, assuming a straight line.
A high R squared on a sample of eight points, as above, also says nothing about whether the relationship holds outside the range measured. Extrapolating a fitted line beyond the data is where most confident predictions go wrong.
The correlation calculator returns r, R squared and the line of best fit together, which is the right set of numbers to look at before deciding what, if anything, the relationship means.