Point Estimate & Margin of Error Calculator
Turn a sample mean, standard deviation and size into a point estimate, margin of error and confidence interval using the Student-t distribution.
How it works
SE = s ÷ √n · Margin of error = t* · SE · CI = x̄ ± margin of error · df = n − 1
A point estimate is a single best guess for a population value — here the sample mean. Because a single sample never lands exactly on the true value, the margin of error puts a ± band around it: the critical t value times the standard error. The point estimate plus and minus that margin gives the confidence interval, the range that would capture the true mean in the stated percentage of repeated samples.
Worked example
A sample of 40 has mean 68.5 and SD 5.2. The standard error is 5.2 ÷ √40 ≈ 0.822; for 95% confidence with 39 df, t* ≈ 2.02, so the margin of error is about ± 1.66. The interval is 68.5 ± 1.66 → 66.84 to 70.16.
Sources: Margin of error — Wikipedia
Frequently asked questions
What is the difference between a point estimate and an interval estimate?
A point estimate is one number (the sample mean). An interval estimate is a range around it — the confidence interval — that reflects the uncertainty from sampling. The margin of error is the half-width of that interval.
How can I shrink the margin of error?
The margin scales with 1 ÷ √n, so quadrupling the sample size roughly halves it. A lower confidence level or less variable data (smaller SD) also narrows it.
Should I use t* or z*?
Use t* when the population standard deviation is unknown and estimated from the sample, which is almost always the case. This calculator uses t*; for large n it is nearly identical to z* (1.96 at 95%).
Related calculators
For education — confirm the test assumptions (independence, sample size, roughly normal data) before drawing conclusions from a p-value.