Confidence interval calculator for a mean or proportion
Choose mean or proportion, enter sample information and confidence level. HitEquals returns lower and upper limits, estimate, standard error, margin and method.
Inputs used by this calculator
Confidence Interval Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| Interval for | Population mean | Population mean · Population proportion | Chooses which Confidence Interval Calculator method or unknown the engine evaluates. |
| Confidence level | 95% | 90% · 95% · 99% | Supplies the confidence level quantity used by the published equation or result breakdown. |
| Sample mean | 50 | Any finite number supported by the formula | Supplies the sample mean quantity used by the published equation or result breakdown. |
| Sample standard deviation | 10 | 0 to 1e+300 | Supplies the sample standard deviation quantity used by the published equation or result breakdown. |
| Sample size | 100 | 2 to 1000000000 | Supplies the sample size quantity used by the published equation or result breakdown. |
| Successes | 60 | 0 to 1000000000 | Supplies the successes quantity used by the published equation or result breakdown. |
What confidence means
Confidence describes the long-run performance of the interval procedure. A 95% method would contain the true parameter in about 95% of repeated samples under its assumptions.
Interval for a mean
When population standard deviation is unknown, use sample standard deviation and a t critical value with n−1 degrees of freedom.
x̄±t*·s/√nInterval for a proportion
The Wilson score interval stays within zero and one and behaves better than the simple p̂±z standard-error interval near boundaries.
Worked mean example
For x̄=50, s=10 and n=100, standard error is 1 and the 95% t multiplier is just under 2, giving limits near 48 and 52.
Width and sample size
Standard error shrinks with √n, so quadrupling sample size roughly halves the random-error component when other inputs remain fixed.
Interpretation limits
The interval does not repair selection bias, measurement error, dependence or an invalid sampling frame. It also does not assign a probability to a fixed parameter after the data are observed.
What changes interval width
| Change | Typical effect |
|---|---|
| Higher confidence | Wider |
| Larger sample | Narrower |
| More variability | Wider |
| Bias | Not repaired by width |
Frequently asked questions
Is there a 95% chance the parameter is inside?
In frequentist terms, 95% describes the long-run success rate of the method, not a probability assigned to the fixed parameter.
Why use t for a mean?
The population standard deviation is usually unknown and estimated from the sample.
Why use Wilson for a proportion?
It behaves better near zero or one than the basic symmetric normal interval.
Can confidence limits exceed the data range?
Mean intervals can; proportion limits are constrained to 0–100%.
Does a narrow interval prove accuracy?
No. Systematic bias can remain.
How does sample size affect width?
The random-error term usually scales approximately with one over the square root of n.
What to keep in mind
The mean interval uses a t critical approximation and assumes independent observations from an approximately normal population or an adequate sample. The proportion interval is Wilson; sampling design and bias are outside scope.
Results are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.