Math / Browser calculator

Confidence Interval Calculator

Confidence Interval Calculator works from the inputs you provide and returns lower bound, upper bound, margin of error. Use the calculation panel to explore a scenario, then check the formula and limitations before applying the result.

Your inputs

Minimum: 0
Minimum: 1 · Maximum: 1000000000 · Whole numbers
Minimum: 1e-06 · Maximum: 10

Your results

Enter your values and calculate to see the result.

Formula and calculation method

Margin = z × population standard deviation / √n. Interval = mean ± margin.

Z interval for a mean with a known population standard deviation. Small samples with an estimated standard deviation generally require a t interval instead.

How to use confidence interval calculator

  1. Set Sample mean. The example below uses 100.
  2. Set Known population standard deviation. The example below uses 15.
  3. Set Sample size. The example below uses 100.
  4. Set Critical z value. The example below uses 1.96.
  5. Select Calculate to update the result. Reset restores the illustrated inputs. Copy, print or download your own result if you need a record.

Worked example

Example inputs
Sample mean
100
Known population standard deviation
15
Sample size
100
Critical z value
1.96
Lower bound
97.06
Upper bound
102.94
Margin of error
2.94

Factors affecting your result

Z interval for a mean with a known population standard deviation. Small samples with an estimated standard deviation generally require a t interval instead.

Changing sample mean changes the scenario being evaluated. Adjust one input at a time when comparing results, keep a copy of the assumptions, and compare values using the same unit and period. A precise arithmetic result does not make an uncertain assumption precise.

Frequently asked questions

How does the confidence interval calculator work?

Margin = z × population standard deviation / √n. Interval = mean ± margin.

What inputs does Confidence Interval Calculator need?

Enter sample mean, known population standard deviation, sample size, critical z value. Choose values that correspond to the same situation and measurement convention.

How should I interpret the confidence interval calculator result?

Z interval for a mean with a known population standard deviation. Small samples with an estimated standard deviation generally require a t interval instead.

Are my confidence interval calculator inputs uploaded?

No. The calculation runs in this browser. Favorites, recent tool names, theme and formatting preferences may be saved locally, but calculation inputs are not sent to a calculation server or stored by this website. Shared links do not include entered values.

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