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Correlation Calculator

Math Calculators

Pearson r · R² · significance t-test

Quick Answer

Correlation Calculator: Pearson r · R² · significance t-test. Correlation Calculator uses standard math formulas to compute accurate results instantly.

Pearson correlation coefficient
0.9955
Very strong positive correlation · n=9
r0.9955
R² (determination)0.9909
DirectionPositive
StrengthVery strong
t=27.65 > 2.262 → significant at α=0.05
R² is the share of variance in y explained by x. Correlation ≠ causation — a hidden third variable (e.g. temperature driving both ice-cream sales and drowning) can create strong but meaningless correlations.

Strength reference

|r|StrengthTypical scenario
0.8 – 1.0Very strongHeight vs weight
0.6 – 0.8StrongStudy time vs score
0.4 – 0.6ModerateExercise vs resting HR
0.2 – 0.4WeakShoe size vs income
0.0 – 0.2Very weakBirthday month vs IQ

Critical t values (α=0.05, two-tailed)

nCritical |t|
52.776
82.365
102.262
152.145
202.101
302.048
502.009
1001.984

Calculation steps

  1. 1n = 9, x̄ = 6.0000, ȳ = 76.1111
  2. 2Σ(x−x̄)(y−ȳ) = 306.0000
  3. 3Σ(x−x̄)² = 60.0000，Σ(y−ȳ)² = 1574.8889
  4. 4r = 306.0000 / √(60.0000×1574.8889) = 0.9955
  5. 5t = r·√((n−2)/(1−r²)) = 27.650, df = 7

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How to Use

  1. Enter values or expressions: type directly into the Correlation Calculator — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Correlation Calculator is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: Pearson r · R² · significance t-test.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Correlation Calculator formula

Correlation Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Correlation Calculator?
Open the page and fill in the input fields — results update automatically. Pearson r · R² · significance t-test.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

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Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.

Cite this page: YiJianSuan. Correlation Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/correlation

Results provided by this tool are for reference only and do not constitute professional advice.