How it works
A planning proportion and sample size give a normal-approximation margin in percentage points. This form solves for critical multiplier; enter the known quantities in Margin of error, Planning success proportion, Sample size.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Margin of error | 10 pp | Formula symbol: error. Required unit: pp. Must be greater than zero. Allowed range: 0.000001–100. |
| Planning success proportion | 50 % | Formula symbol: p. Enter the percentage as a number: for 15%, enter 15. Must be greater than zero. Allowed range: 0.000001–99.999999. |
| Sample size | 100 | Formula symbol: n. Enter a numeric value. Use a whole number. Must be greater than zero. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- Margin of error
- 10 pp
- Planning success proportion
- 50 %
- Sample size
- 100
Complete example results
- Critical multiplier
- 2
Reading the result
The result solves for critical multiplier from the entered quantities. Check the result unit and the formula conditions before using it.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
When can I use the critical multiplier result?
You supply the critical multiplier. The normal approximation can be poor with few expected successes or failures; this is not a Wilson or exact interval. Required n is rounded up.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.
Method sources: itl.nist.gov