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Formula verified · Deterministic calculation

Confidence Interval Calculator

Enter an estimate, its standard error and a supported confidence level to calculate the margin of error and interval bounds.

Confidence interval90.20018008 to 109.79981992
Estimate
100
Margin of error
9.8
Critical value
1.96
Methodology

Normal-based two-sided interval using the selected z critical value and supplied standard error.

Sources
  • CalcuMint deterministic statistics engine
Solution steps
  1. z* = 1.95996398454
  2. Margin of error = z* × SE = 9.799819922700001
  3. Interval = 90.2001800773 to 109.7998199227

How this calculator works

The interval is estimate ± z* × standard error, using the critical value for the selected confidence level.

Formula

estimate ± z* × SE

Computes a two-sided normal-based confidence interval from an estimate and its supplied standard error.

Worked example

95% interval is a verified test case used by the calculation engine.

Assumptions and limitations

  • The supplied standard error is positive.
  • The calculation uses a normal critical value rather than a t distribution.
  • Supported confidence levels are 80%, 90%, 95%, 98% and 99%.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint. Technical calculation version: 1.

  • CalcuMint deterministic statistics engine

Frequently asked questions

Does this calculate the standard error from raw data?

No. Enter the standard error directly.

Does this use a t distribution?

No. This certified version uses normal z critical values.

Related calculators

Sample Size CalculatorEstimate sample size for a proportion from confidence level, margin of error and expected proportion.Z-Score CalculatorStandardize a value using a supplied mean and positive standard deviation.
Confidence Interval Calculator | CalcuMint