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MATH / INFERENTIAL STATISTICS

Margin of Error Calculator

Estimate a z-based margin of error for a mean from spread, sample size, and critical value. Review the equation, substituted values, result context, and modelling limits in one guided workspace.

  • 01 Calculated in this tab
  • 02 Values stay in this browser tab
  • 03 Use boundary

Conversion input

Known value

Filter by unit name, symbol, or code. Your current selections remain available.

Preparing the calculator...

Use boundary

Calculation path

Estimate a z-based margin of error for a mean from spread, sample size, and critical value. The page evaluates the displayed equation from your supplied values and presents both symbolic and substituted KaTeX working so the arithmetic can be checked.

Calculation path

E = z* sigma/sqrt(n)

What you provide

What you provide

  • Standard deviation, using the same scenario as the other inputs
  • Sample size, using the same scenario as the other inputs
  • Critical value, using the same scenario as the other inputs

What you receive

What you receive

  • Margin of error from the stated equation
  • A symbolic formula plus substituted working with your values
  • Visible assumptions, field guidance, and an authoritative learning reference

Use boundary

Choose the maximum decimal places shown. This does not increase source accuracy.

The selected critical value and standard deviation must match the intended sampling model.

Use internally consistent units and retain extra precision when carrying the result into another calculation.

Reviewed reference factors

Reviewed reference factors