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Confidence interval calculator

Compute a confidence interval for a mean from its standard deviation and sample size.

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Need Lower bound, Upper bound, Margin of error? The Confidence interval calculator derives it from Sample mean, Standard deviation, Sample size, Confidence level in one step. For instance, with Sample mean = 100, Standard deviation = 15, Sample size = 30 and Confidence level = 90% it returns Lower bound = 95.495, Upper bound = 104.505 and Margin of error = 4.505.

How to use it

  1. Enter your values: Sample mean, Standard deviation, Sample size, Confidence level.
  2. Read the result instantly: Lower bound, Upper bound, Margin of error.

Frequently asked questions

What does the Confidence interval calculator actually compute?

It takes Sample mean, Standard deviation, Sample size and Confidence level and derives Lower bound, Upper bound and Margin of error from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

4 values: Sample mean, Standard deviation, Sample size and Confidence level. Nothing else is required — no account, no file upload.

Can you show a worked example?

With Sample mean = 100, Standard deviation = 15, Sample size = 30 and Confidence level = 90%, the calculator returns Lower bound = 95.495, Upper bound = 104.505 and Margin of error = 4.505. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

What happens if I enter larger values?

It moves a lot. Using Sample mean = 200, Standard deviation = 30, Sample size = 60 and Confidence level = 95% instead, Lower bound goes from 95.495 to 192.409 — which is why it is worth testing a few scenarios rather than trusting a single figure.

Which “Confidence level” option should I choose?

You can pick between « 90% », « 95% » and « 99% ». Each one changes what the calculator works out, so switch and compare — the default is « 90% ».

What does it give for smaller values?

Scaled down to Sample mean = 50, Standard deviation = 8, Sample size = 15 and Confidence level = 90%, Lower bound comes out at 46.602. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Summarising a dataset before drawing conclusions from it, checking whether a difference between two groups is real, and putting an interval around an estimate.

What is the most common mistake?

Reading a p-value as the probability that the hypothesis is wrong. It is the probability of seeing data at least this extreme if the null were true — a different statement, and a much weaker one.

What is the difference between the Confidence interval calculator and the Confidence interval for a proportion?

This one returns Lower bound and Upper bound; the Confidence interval for a proportion returns Sample proportion and Wald lower. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Coefficient of variation calculator is the closest one after this: Compute the coefficient of variation (CV) of a dataset — its relative variability.

Further reading

All guides →
ExplainerQuadruple the Sample to Halve the IntervalA mean of 100 with a standard deviation of 15 over 30 observations gives 100 ± 5.37 at 95 %. Going to 120 observations gives ± 2.68 — exactly half, because the sample size enters under a square root.ExplainerAn Error Bar That Shrinks Is Not the Standard DeviationFor 10, 12, 15, 11, 13, 14 the standard deviation is 1.87 and the standard error is 0.76. They answer different questions, and only one of them gets smaller as you collect more data.ExplainerA Country of 68 Million Needs Fifteen More People Than a Town of 10,000The population barely enters the sample size formula. What does enter it is the margin of error, and halving that margin quadruples the survey — from 385 people to 1,537.ExplainerIf the Variance Is Not the Mean, It Is Not PoissonWith an average of five events per interval, exactly three occur 14.0 % of the time, none at all 0.7 %, and ten or more 3.2 % — about once every 31 intervals. The distribution has one parameter, and it sets both the mean and the variance.ExplainerThe Same Three Temperatures Give Three Different Coefficients of VariationFor 2, 4, 4, 4, 5, 5, 7, 9 the coefficient of variation is 42.76 %. It is the right tool for comparing spread across different scales — and completely wrong for any scale whose zero was chosen by convention.How-toHow to Calculate Standard Deviation (Step by Step)Standard deviation measures how spread out your data is. Here's the formula, a worked example, and the difference between population and sample.