Trader Toolkit · Calculator

Correlation

Pearson’s coefficient of two series you paste or type, with the working.

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Two that rise and fall as one:a measure made, a cause not shown.

Two series of the same length

Result

Series A

6 values. Invented numbers until you paste yours: separate them with spaces, new lines, commas or semicolons.

Series B

6 values, paired in order with series A. Decimals take a point.

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Correlation coefficient (r)

+0.8286

strong, positive, by the usual convention

Pairs compared

values in each series

Mean of A’s values: 3.5
Mean of B’s values: 3.5
r squared: 0.6865
Direction: they tended to move the same way

Each point is one pair: A’s value across, B’s up. The closer the points lie to one straight line, the nearer the coefficient is to +1 or −1. Here it is 0.8286.

The working, pair by pair
#	a	b	a − ā	b − b̄	product	(a − ā)²	(b − b̄)²
1	1	2	−2.5	−1.5	3.75	6.25	2.25
2	2	1	−1.5	−2.5	3.75	2.25	6.25
3	3	4	−0.5	0.5	−0.25	0.25	0.25
4	4	3	0.5	−0.5	−0.25	0.25	0.25
5	5	6	1.5	2.5	3.75	2.25	6.25
6	6	5	2.5	1.5	3.75	6.25	2.25
Sums, over all 6 pairs					14.5	17.5	17.5

SimulationA calculation on the figures you entered. A measure of the numbers you typed, for the period they cover. It is not a forecast, and a correlation is not a cause. Educational information, not investment advice or a recommendation to trade.

How it works

Formula

r = Σ (a − ā)(b − b̄) ÷ √( Σ (a − ā)² × Σ (b − b̄)² )

With your numbers

1Mean of A (sum ÷ count)21 ÷ 6 = 3.5
2Mean of B (sum ÷ count)21 ÷ 6 = 3.5
3Sum of the products of the two distances from the meanΣ (a − ā)(b − b̄) = 14.5
4Sum of the squared distances of A from its meanΣ (a − ā)² = 17.5
5Sum of the squared distances of B from its meanΣ (b − b̄)² = 17.5
6Coefficient: the first sum ÷ the square root of the other two multiplied14.5 ÷ √(17.5 × 17.5) = 14.5 ÷ 17.5 = 0.8286
7Squared: the share of one series’ variation that a straight line on the other accounts for0.8286² = 0.6865

Assumptions

The numbers are the ones you typed or pasted. This page fetches no market data and supplies none: the two starting series are invented, and are there only so that the working can be seen.
The two series are paired in order: the first value of A with the first of B, and so on. If they are not for the same dates in the same order, the coefficient means nothing.
Pearson’s coefficient measures how closely the pairs follow a straight line. Two series can be tightly related in another shape and still give a figure near zero.
Two prices that both drift upwards over time correlate strongly whether or not they have anything to do with each other. That is why “the change from one value to the next” is offered: it is the usual way to compare how two markets move from day to day.
A correlation describes the period typed and nothing else. It changes over time, often sharply in a crisis, and it does not say that one series moves the other.
Words such as weak, moderate and strong are a common convention for the size of the figure (under 0.3, under 0.7, and above), not a rule.

Terms used

In plain language

One number for how closely two series have moved together.

Pearson’s coefficient runs from −1 to +1. At +1 every pair of values lies on one rising straight line; at −1 on a falling one; near zero there is no straight-line relationship to speak of. It is worked out from distances: how far each value sits from its own series’ average, multiplied pair by pair, added up, and scaled so that the units cancel.

The numbers are yours. This page fetches no prices and supplies none: paste two columns from your own records, in the same order and for the same dates. The starting figures are invented, and are there only so that every step of the working has something in it.

What is compared matters more than the formula. Two prices that both drifted upwards over a year correlate strongly even if they are unrelated, because both simply rose. Comparing the change from each value to the next removes that shared drift, and is the usual way to ask whether two markets move together from day to day. The page offers both and says which it used.

A coefficient describes the period it was measured over. It changes, sometimes quickly, and relationships that held for years have broken in a week. It says nothing about why two series moved together, and it is not a forecast that they will.

Continue

Fetching the page

The working, pair by pair

a − ā

b − b̄

product

(a − ā)²

(b − b̄)²

−2.5

−1.5

3.75

6.25

2.25

−1.5

−2.5

3.75

2.25

6.25

−0.5

0.5

−0.25

0.25

0.5

−0.5

−0.25

0.25

1.5

2.5

3.75

2.25

6.25

2.5

1.5

3.75

6.25

2.25

Sums, over all 6 pairs

14.5

17.5

How it works

Formula

r = Σ (a − ā)(b − b̄) ÷ √( Σ (a − ā)² × Σ (b − b̄)² )

With your numbers

1Mean of A (sum ÷ count)21 ÷ 6 = 3.5

2Mean of B (sum ÷ count)21 ÷ 6 = 3.5

3Sum of the products of the two distances from the meanΣ (a − ā)(b − b̄) = 14.5

4Sum of the squared distances of A from its meanΣ (a − ā)² = 17.5

5Sum of the squared distances of B from its meanΣ (b − b̄)² = 17.5

6Coefficient: the first sum ÷ the square root of the other two multiplied14.5 ÷ √(17.5 × 17.5) = 14.5 ÷ 17.5 = 0.8286

7Squared: the share of one series’ variation that a straight line on the other accounts for0.8286² = 0.6865

Assumptions

The numbers are the ones you typed or pasted. This page fetches no market data and supplies none: the two starting series are invented, and are there only so that the working can be seen.

The two series are paired in order: the first value of A with the first of B, and so on. If they are not for the same dates in the same order, the coefficient means nothing.

Pearson’s coefficient measures how closely the pairs follow a straight line. Two series can be tightly related in another shape and still give a figure near zero.

Two prices that both drift upwards over time correlate strongly whether or not they have anything to do with each other. That is why “the change from one value to the next” is offered: it is the usual way to compare how two markets move from day to day.

A correlation describes the period typed and nothing else. It changes over time, often sharply in a crisis, and it does not say that one series moves the other.

Words such as weak, moderate and strong are a common convention for the size of the figure (under 0.3, under 0.7, and above), not a rule.

Terms used