Sample Size Calculator

1. Pick a confidence level: 90, 95 or 99 percent.
2. Enter the margin of error you can accept, and the expected proportion if you have one.
3. Add the population size if it is small or known; the sample size updates live.

Each output guides your survey plan:

Sample size is the number of people or items you need to survey so that your results represent a larger group within a stated accuracy. Survey too few and the findings are unreliable; survey far more than needed and you waste time and money. The right sample balances precision against cost.

Two choices set it. Confidence level is how sure you want to be that the true value lies within your range, commonly 95 percent. Margin of error is how wide that range is, such as plus or minus 5 percent. Higher confidence and a tighter margin both demand a larger sample.

It applies the standard formula for estimating a proportion, then adjusts for a finite population if you enter one.

The base sample size is n0 = z^2 * p(1-p) / e^2 where z comes from the confidence level, p is the expected proportion and e the margin of error. For a known population N, it shrinks to n = n0 / (1 + (n0 - 1)/N).

1. Turn the confidence level into a z-score.
2. Compute the base sample size from z, the proportion and the margin.
3. Adjust down for a finite population if one is given.

Using a proportion of 50 percent gives the largest, safest sample when you cannot estimate it in advance.

For 95 percent confidence, the z-score is 1.96. With a 5 percent margin and an unknown proportion set to 50 percent, the base sample is 1.96^2 * 0.25 / 0.05^2 = 384.16, which rounds up to 385.

Tighten the margin to 3 percent and the requirement jumps to about 1,068, because halving the margin roughly quadruples the sample. That trade-off is why 5 percent is such a common choice.

If your population is only 10,000, the finite-population adjustment brings the 385 down to about 370, a small saving that grows as the population shrinks toward the sample size.

These settings drive the sample size, and their costs are worth seeing side by side.

A tighter margin costs far more than a higher confidence level, because the margin sits squared in the denominator. To read any of these as a plain percentage, the percentage calculator helps.

Four inputs move the requirement, some far more than others.

Margin of Error

Because it is squared in the formula, halving the margin roughly quadruples the sample, the strongest lever of all.

Confidence Level

Raising confidence from 95 to 99 percent lifts the sample by about 70 percent, since the z-score grows.

Expected Proportion

The sample peaks at a 50 percent proportion; a more lopsided expected response lowers it.

Population Size

For very large populations the size barely matters, but for small ones the finite-population adjustment cuts the sample noticeably.

Planning a Survey

Decide how many responses to collect before you launch, so the results are trustworthy.

Designing a Study

Set a defensible sample for research where precision and confidence must be stated.

Checking a Poll

See whether a published poll surveyed enough people for its claimed margin of error.

1. Confusing Confidence with Margin

Confidence is how sure you are; margin is how wide the range is. They are different settings.

2. Forgetting the Response Rate

The sample is completed responses. Invite more people to allow for those who do not reply.

3. Assuming a Lopsided Proportion

When unsure, use 50 percent. It gives the largest, safest sample.

4. Ignoring the Population for Small Groups

For a small, known population, the finite-population adjustment can reduce the sample meaningfully.

5. Chasing a Tiny Margin

A very small margin demands a huge sample; weigh the precision against the cost.

The formula is exact for a simple random sample estimating a proportion, but real surveys add complications.

Use n = z^2 x p(1-p) / e^2, where z comes from the confidence level, p is the expected proportion and e the margin of error. This calculator applies it and adjusts for your population.

With a 5 percent margin and an unknown proportion, about 385 responses. A tighter 3 percent margin needs about 1,068.

It is how close your survey result is expected to be to the true value, such as plus or minus 5 percent. A smaller margin needs a much larger sample.

It is how sure you want to be that the true value falls within your margin of error. Common choices are 90, 95 and 99 percent.

Use 50 percent. It produces the largest, safest sample, so you are covered whatever the true proportion turns out to be.

For very large populations, barely. For small, known populations, the finite-population adjustment can reduce the required sample noticeably.

Because the margin is squared in the formula. Halving the margin roughly quadruples the sample needed.

Yes. The sample is completed responses, so invite more to allow for non-response and incomplete answers.

No. The calculation runs in your browser, and nothing you enter is sent anywhere unless you Save a result, which stays on this device only.

• Sample size determination (Wikipedia).
• Margin of error (Wikipedia).
• Confidence intervals (Maths Is Fun).