Confidence Interval Calculator — 95% CI & Margin of Error

Mean

Std dev

Sample size

Confidence

Confidence interval

Margin of error: ± (z = )

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How to use Confidence Interval Calculator

Enter the sample mean — your measured average.
Enter sample size and standard deviation — n and s from your data.
Pick the confidence level — 95% is the convention; 99% widens, 90% narrows the interval.
Report mean ± margin — and if the interval is too wide to be useful, the fix is a (quadratically) larger sample.

What is Confidence Interval Calculator?

A confidence interval calculator turns a sample estimate into an honest range: from your sample mean, sample size and standard deviation, it computes the interval (mean ± margin of error) that quantifies how precisely the sample pins down the true population value. A survey mean of 7.2 with a 95% CI of ±0.4 says the true average plausibly lies between 6.8 and 7.6.

The margin of error is z × (s ÷ √n) — the z-score for your confidence level (1.96 for 95%) times the standard error. The √n in the denominator carries the practical law of sampling: halving the margin requires quadrupling the sample, which is why precision gets expensive fast.

About the Confidence Interval Calculator

Enter your sample mean, sample size and standard deviation, pick a confidence level (90%, 95%, 99%), and read the interval and margin of error instantly.

Where it earns its keep: survey results (a 62% approval from 400 respondents is 62% ± 4.8 — a "lead" inside the margin isn't a lead), A/B tests (two conversion rates whose intervals overlap heavily haven't proven anything yet), quality control (does the batch mean's interval contain the spec?), and any report where a bare average would overstate certainty — attaching the ± is the difference between data and anecdote.

Interpretation, precisely: 95% confidence means the procedure captures the true value in 95% of samples — it's a statement about the method's reliability, not a 95% probability for this one interval. Loose but workable shorthand: "plausible range for the true value."

Frequently Asked Questions

That the method delivers: across repeated samples, 95% of the intervals built this way contain the true value. It is not "95% chance the truth is in this interval" — a subtle but standard distinction; practically, treat it as the plausible range.

z × (s ÷ √n): the confidence z-score (1.645 for 90%, 1.96 for 95%, 2.576 for 99%) times the standard error. n = 100, s = 15, 95%: 1.96 × 1.5 = ±2.94.

Four times bigger — margin shrinks with √n. From ±4 to ±2 means n × 4; to ±1 means n × 16. This square-law is why national polls plateau around 1,000–1,500 respondents (±3%) — further precision costs too much.

Heavy overlap means the difference could be noise — don't ship the "winner" yet. Slight or no overlap suggests a real difference. (The rigorous call is a significance test, but overlap is the honest first read.)

95% is the near-universal default. Use 99% when a wrong conclusion is costly (medical, safety) and accept the wider interval; 90% when you need tighter ranges and can tolerate more risk of missing the truth.