Prediction Interval Estimator
Estimate a range for one future observation rather than a confidence interval for the population mean. The tool shows the method and key assumptions so you can inspect how the input values lead to the estimate.
How to use this calculator
- Enter sample mean using the unit and definition shown beside the input.
- Enter sample standard deviation using the unit and definition shown beside the input.
- Enter sample size using the unit and definition shown beside the input.
- Check that all values refer to the same time period and scenario.
- Review the outputs alongside the assumptions before using them in a decision.
Formula and assumptions
Prediction margin=t·s·√(1+1/n); interval=mean±margin.
- The t multiplier is an input so you can use the value appropriate to your degrees of freedom and confidence level. The formula assumes an approximately normal population and independent observations.
- The estimate is calculated from values you enter. It does not connect to external accounts, obtain live prices, or validate local regulations or engineering specifications.
Worked examples
Worked example
With mean 82, s=12.7, n=30 and t=2.045, the prediction margin is about 26.6.
Enter the summary statistics and the critical multiplier from your chosen reference.
A prediction interval is usually wider than a confidence interval for the mean.
Understanding the result
The t multiplier is an input so you can use the value appropriate to your degrees of freedom and confidence level. The formula assumes an approximately normal population and independent observations.
Change one input at a time to see how sensitive the output is to that assumption.
Important notes
The t multiplier is an input so you can use the value appropriate to your degrees of freedom and confidence level. The formula assumes an approximately normal population and independent observations.
Frequently asked questions
What formula does the Prediction Interval Estimator use?
Prediction margin=t·s·√(1+1/n); interval=mean±margin.
What should I verify before relying on the result?
The t multiplier is an input so you can use the value appropriate to your degrees of freedom and confidence level. The formula assumes an approximately normal population and independent observations.
Can I compare different scenarios?
Yes. Change one assumption at a time, keep units and definitions consistent, and save the inputs used for each comparison.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.