Math

Confidence Interval Calculator

Compute a confidence interval for a sample mean using the z-distribution.

Inputs

Sample mean

Standard deviation

Sample size

Confidence level

Result

95% CI

[94.6323, 105.3677]

How it's calculated

CI = x̄ ± z·(s/√n).

x̄ = 100, s = 15, n = 30, 95% → 100 ± 1.96·(15/√30) ≈ 100 ± 5.37.

Should I use z or t?

For large samples (n ≥ 30) or known population σ, z is standard. Small samples with unknown σ should use a t-interval.

What does 95% confidence mean?

If we repeated the sampling many times, ~95% of computed intervals would contain the true mean.

Math

Sample Size Calculator

Find the sample size needed for a survey given confidence, margin of error, and expected proportion.

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P-value Calculator

Convert a z-score to a p-value for one- or two-tailed tests with significance verdict.

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Standard Deviation Calculator

Mean, variance, and standard deviation (sample or population) of a dataset.

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Percentage Calculator

What is X% of Y, X is what % of Y, and percentage change — all in one place.