Confidence Level Calculator
Convert between confidence level, critical value and margin of error.
About Confidence Level Calculator
Raising confidence widens the interval because a larger critical value is required. Moving from 95 to 99 per cent confidence widens the interval by about 31 per cent for the same data. There is no free lunch: greater confidence always means a less precise interval unless the sample grows.
Formula
Confidence Level
Critical value is the standard normal z for the two-tailed area; margin of error = z × SE
- alpha
- One minus the confidence level, split across both tails
Worked example
With the default values below, Confidence Level Calculator returns Critical Value of 1.96039. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Confidence levelaccepts 50–99.99 %
- 95 %
- Standard errorminimum 0
- 2.5
- Point estimate
- 50
Results
- Critical Value
- 1.96039
- Margin of Error
- 4.90099
- Lower Bound
- 45.09901
- Upper Bound
- 54.90099
- Significance Level
- 0.05000
Step by step
- 1Values used
- 2Confidence Level
- 3Critical Value= 1.96039
- 4Margin of Error= 4.90099
- 5Lower Bound= 45.09901
- 6Upper Bound= 54.90099
- 7Significance Level= 0.05000
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How is Confidence Level calculated?
Critical value is the standard normal z for the two-tailed area; margin of error = z × SE Raising confidence widens the interval because a larger critical value is required. Moving from 95 to 99 per cent confidence widens the interval by about 31 per cent for the same data.
Why does Confidence Level matter?
There is no free lunch: greater confidence always means a less precise interval unless the sample grows.
What values do I need to enter?
This calculator takes 3 inputs: Confidence level, Standard error, Point estimate. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.