How it works
Four steps, in the order the page asks for them.
What the calculator provides
What you can estimate
Choose the quantity you intend to report, and the inputs adjust to what that estimate needs.
Single-group estimates
- Population Mean (μ)
- Needs the margin of error you will accept and an estimate of the standard deviation.
- Population Proportion (p)
- Needs the margin of error and a planning value for the proportion.
Two-group comparisons
- Difference of Means (μ₁ - μ₂)
- Plans the precision of a difference rather than of a single mean.
- Difference of Proportions (p₁ - p₂)
- Plans the precision of a risk or rate difference between two groups.
Both directions
- Sample Size
- Give the margin of error you need and read the sample size that delivers it.
- Margin of Error
- Give the sample size you already have and read the precision it can support.
How the estimate is formed
The assumptions are worth stating plainly.
- Intervals are built from normal critical values, so the result is a large-sample approximation; the critical value in use is displayed with every answer.
- When planning a difference of proportions, the second proportion is held at the conservative value of 0.5, which is the choice that maximises the required sample size rather than the one that flatters it.
- This is interval precision, not hypothesis-test power. A study sized for a narrow interval is not automatically powered to detect a particular effect, and the reverse is equally true.
- The precision curve shows the trade-off directly, which is the fastest way to see that halving a margin of error costs roughly four times the sample.
Common questions
How is this different from a power calculator?
A power calculation asks how many observations you need to detect an effect of a given size. A precision calculation asks how many you need for a confidence interval of a given width. Studies that report an estimate rather than test a hypothesis are planned this way.
Can I work backwards from a sample I already collected?
Yes. Switch the direction to margin of error, enter the sample size, and the calculator returns the precision that sample supports at your chosen confidence level.
Which confidence levels are available?
90%, 95%, 99% and 99.9%, with 95% as the default.
What if I have no idea what the proportion will be?
Use 0.5, which produces the largest sample size and therefore the safest plan. The calculator already applies that convention to the second group when you plan a difference of proportions.