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Math Calculators

Confidence Interval Calculator

Verified formula Updated Jun 2026 Private — runs on your device

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Verified formula Private

Margin of error

5.368

Lower bound
94.632
Upper bound
105.368

For general information only — not financial, tax, legal or medical advice. Verify before you rely on it.

How to use the Confidence Interval Calculator

The Confidence Interval Calculator works out your margin of error, along with 2 related figures in an instant. Enter sample mean, standard deviation and sample size and the result updates as you type — it is free, needs no sign-up, and runs entirely in your browser so your figures stay private.

  1. Enter the sample mean.
  2. Enter the standard deviation.
  3. Enter the sample size.
  4. Choose the confidence level.
  5. Read off your margin of error, together with lower bound and upper bound — the calculator updates automatically, with no button to press.

Formula

The Confidence Interval Calculator uses the formula:

Margin of error = Confidence level × Standard deviation ÷ √(Sample size)

Worked example

For example, with sample mean of 100, standard deviation of 15, sample size of 30 and confidence level of 95% (z = 1.96), the margin of error is 5.368.

Inputs used
Sample mean 100
Standard deviation 15
Sample size 30
Confidence level 95% (z = 1.96)
Results
Margin of error 5.368
Lower bound 94.632
Upper bound 105.368

Results are estimates for educational use, not professional advice.

Key terms explained

Standard deviation
A measure of how spread out a set of values is around their mean.
Mean
The average of a set of numbers — their sum divided by how many there are.

Frequently asked questions

The margin is z × standard deviation ÷ √n, and the interval is the mean plus or minus that margin. For mean 100, SD 15, n 30 at 95%, it is about 100 ± 5.37.

It is a range that is likely to contain the true population mean, at the chosen confidence level.

For small samples where the population standard deviation is unknown, a t-value is more accurate. This tool uses z for simplicity and larger samples.

Increase the sample size or accept a lower confidence level. A larger sample reduces the margin for the same confidence.

Enter the sample mean. Enter the standard deviation. Enter the sample size. Choose the confidence level. Read off your margin of error, together with lower bound and upper bound — the calculator updates automatically, with no button to press.

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