CALCULATE WITH CONFIDENCE

Statistics · Sampling & confidence

Margin of Error Calculator

Calculate a normal-approximation margin of error for a mean or proportion.

Statistics · Sampling & confidence

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Private in-browser calculation · explicit assumptions
A confidence interval pairs a point estimate with model-based uncertainty. Repeated samples produce different intervals.
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Statistics result

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Understand sampling uncertainty

How confidence intervals express uncertainty

Margin of Error. A confidence procedure adds model-based uncertainty around an estimate. Wider confidence levels and noisier or smaller samples generally produce wider intervals.

Method used

Margin of error = critical z × standard error.

The margin describes sampling uncertainty under the selected method, not every possible source of error.

What the result cannot establish

A 95% confidence interval does not mean there is a 95% probability that a fixed parameter lies inside this realized interval. The 95% describes long-run coverage of the procedure under its assumptions.

Assumption: Coverage depends on randomization, independence, an appropriate standard error, and a justified approximation.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.

Calculation method

How the margin of error calculator works

Margin of error = critical z × standard error.

The margin describes sampling uncertainty under the selected method, not every possible source of error.

Worked example

Margin of Error example

At 95% confidence, standard error 2 gives a margin of error about 3.92.

Margin of error = critical z × standard error.

Supported inputs

Precision and limits

Model and design

Coverage depends on randomization, independence, an appropriate standard error, and a justified approximation.

Numerical scope

Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.

Interpretation

The margin describes sampling uncertainty under the selected method, not every possible source of error.

Decision boundary

The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.

Privacy

Entered values and calculated results stay in this browser and are not sent to an analytics service.

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