Statistics
Correlation Coefficient Calculator
Quantify the strength and direction of a linear relationship with Pearson’s r plus the supporting covariance and standard deviations.
Quantify linear association between paired lists with Pearson r and R².
Pearson correlation
r = Σ((x − x̄)(y − ȳ)) / [(n − 1) sₓ sᵧ]
Standard deviations sₓ and sᵧ come from the same datasets, so r stays bounded between −1 and 1 and highlights how tightly the paired values move together.
How to use
- Paste X values and Y values in the same order.
- Ensure each list has at least two numeric entries.
- Review r, R², covariance, and each sample standard deviation.
Example
Input: X = 12, 18, 25, 39; Y = 22, 32, 38, 55
Output: r ≈ 0.99, R² ≈ 0.98, Covariance ≈ 107.8
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Correlation Coefficient Calculator: correlation coefficient calculator, pearson r calculator, covariance calculator, correlation calculator online. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic. Each resource is interlinked so crawlers (and readers) can discover the next best action within a couple of clicks—one of the easiest ways to lift topical authority.
Deep dive & study plan
The Correlation Coefficient Calculator is a go-to tool whenever you need to finds pearson r, covariance, and standard deviations for paired samples.. It focuses on correlation, pearson r, covariance, which means searchers often arrive with intent-heavy queries like “how to correlation coefficient calculator quickly” or “correlation coefficient calculator formula explained.” Use this calculator to capture those intents and keep learners on the page long enough to send positive engagement signals.
Under the hood, the calculator leans on standard deviations sₓ and sᵧ come from the same datasets, so r stays bounded between −1 and 1 and highlights how tightly the paired values move together.—that’s why we surface the full expression (“r = Σ((x − x̄)(y − ȳ)) / [(n − 1) sₓ sᵧ]”) directly above the interactive widget. When you embed that formula inside H2s or supporting paragraphs, you help both humans and crawlers understand what entity the page represents.
Execution matters as much as the math. Follow the built-in procedure: Step 1: Paste X values and Y values in the same order. Step 2: Ensure each list has at least two numeric entries. Step 3: Review r, R², covariance, and each sample standard deviation.. Each numbered instruction is short enough to scan on mobile but descriptive enough to satisfy Google’s Helpful Content guidelines. Encourage students to jot down units, double-check signs, and compare answers with the Example card to build confidence.
The Example section itself is packed with semantic clues: “X = 12, 18, 25, 39; Y = 22, 32, 38, 55” leading to “r ≈ 0.99, R² ≈ 0.98, Covariance ≈ 107.8.” Pepper similar narratives throughout your copy (and internal links from related guides) so canonical search intents are answered without pogo-sticking back to Google.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Link out to at least two related calculators to keep readers exploring your topical hub.
FAQ & notes
How does this differ from regression?
Correlation measures strength of association only. If you also need slope and predictions, jump to the linear regression calculator.
Why does r sometimes report 0?
If one list has no variation (all values identical) the standard deviation is zero, so Pearson r cannot be computed and the calculator reports 0 as a neutral result.
What formula does the Correlation Coefficient Calculator use?
Standard deviations sₓ and sᵧ come from the same datasets, so r stays bounded between −1 and 1 and highlights how tightly the paired values move together.
How do I use the Correlation Coefficient Calculator?
Paste X values and Y values in the same order. Ensure each list has at least two numeric entries. Review r, R², covariance, and each sample standard deviation.