Margin of Error Calculator

Margin of Error is evaluated from Sample Size, Confidence Level and Sample Proportion. The calculation reports Margin of Error, Confidence Interval Lower and Confidence Interval Upper.

Results

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About the Margin of Error Calculator

Margin of Error is treated here as a quantitative relation between Sample Size, Confidence Level and Sample Proportion and Margin of Error, Confidence Interval Lower and Confidence Interval Upper.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
MOE = Z x sqrt(p(1-p)/n)
For a two-sided confidence interval: add and subtract MOE from sample proportion.

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

MOE = Z x sqrt(p(1-p)/n)
For a two-sided confidence interval: add and subtract MOE from sample proportion.

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: National poll: n=1000, 95% confidence, 52% support found

Inputs

sample_size: 1000 confidence: 95 proportion: 52
Margin of Error: 3.1%. Confidence Interval Lower: 48.9%. Confidence Interval Upper: 55.1%

With Sample Size = 1,000, Confidence Level = 95 and Sample Proportion = 52 as the stated inputs, the result is Margin of Error = 3.1%, Confidence Interval Lower = 48.9% and Confidence Interval Upper = 55.1%. Each value corresponds to the declared output fields.

Example 2: Larger survey: n=2400, 95% confidence, 65% satisfaction

Inputs

sample_size: 2400 confidence: 95 proportion: 65
Margin of Error: 1.91%. Confidence Interval Lower: 63.09%. Confidence Interval Upper: 66.91%

With Sample Size = 2,400, Confidence Level = 95 and Sample Proportion = 65 as the stated inputs, the result is Margin of Error = 1.91%, Confidence Interval Lower = 63.09% and Confidence Interval Upper = 66.91%. Each value corresponds to the declared output fields.

Example 3: Small sample: n=150, 90% confidence, 40% agree

Inputs

sample_size: 150 confidence: 90 proportion: 40
Margin of Error: 6.58%. Confidence Interval Lower: 33.42%. Confidence Interval Upper: 46.58%

With Sample Size = 150, Confidence Level = 90 and Sample Proportion = 40 as the stated inputs, the result is Margin of Error = 6.58%, Confidence Interval Lower = 33.42% and Confidence Interval Upper = 46.58%. Each value corresponds to the declared output fields.

Example 4: Very small sample: n=50, 95% confidence

Inputs

sample_size: 50 confidence: 95 proportion: 50
Margin of Error: 13.86%. Confidence Interval Lower: 36.14%. Confidence Interval Upper: 63.86%

With Sample Size = 50, Confidence Level = 95 and Sample Proportion = 50 as the stated inputs, the result is Margin of Error = 13.86%, Confidence Interval Lower = 36.14% and Confidence Interval Upper = 63.86%. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate margin of error for a survey
  • Evaluate polling accuracy
  • Assess precision of sample-based estimates