Enter your confidence level, margin of error and population size to get the sample size your survey needs.
What Is a Sample Size Calculator?
A sample size calculator tells you how many responses a survey needs: 95% confidence, ±5% margin → 385 respondents (for an unknown population). It uses p = 0.5 (the most conservative proportion) and the finite-population correction when you enter a population. Halving the margin quadruples the sample — precision is expensive.
How to Use
- Pick the confidence level.
- Enter the margin of error %.
- Enter the population (0 if unknown).
- Click “Calculate Sample Size”.
Formula
n₀ = z² × 0.25 ÷ E². With population P: n = n₀ ÷ (1 + (n₀−1) ÷ P).
Worked Example
95%, ±5%, unknown population: n₀ = 1.96² × 0.25 ÷ 0.05² = 384.16 → 385.
How It Works, In Plain Words
The tool works backwards from how precise you need to be. The confidence level sets the z-value: 95% uses 1.96, 99% uses 2.576 and 90% uses 1.645 — higher confidence demands a bigger sample. The margin of error E is the wobble you will tolerate around your result, entered as a percentage. The proportion is fixed at p = 0.5, because 0.5 × 0.5 = 0.25 is the largest the proportion term can be — the cautious choice when you do not yet know the answer, which is the whole point of surveying.
Those pieces combine as n₀ = z² × 0.25 ÷ E². For the worked example: 1.96² × 0.25 ÷ 0.05² = 384.16, and because you cannot interview a fraction of a person, the tool rounds up — 385. If you enter a population, the finite-population correction then shrinks the requirement, since sampling a large share of a small group is more informative. Leave the population at 0 and the unadjusted figure stands; the tool shows both so you can see the correction’s effect.
Real-World Uses
A market researcher sizing a customer survey starts here to cost the fieldwork before promising a client ±5% accuracy. A student planning a dissertation survey uses it to justify the number in the methodology chapter — and to discover early whether the target is realistic. An election watcher reads published polls more wisely after seeing why ±1% needs roughly 9,600 respondents, far beyond most budgets. A small club surveying its own members enters the population and finds the correction brings the target down to something achievable. A charity testing a new leaflet on a mailing list does the same sums before printing. In every case the number is a plan, not a guarantee: it assumes the sample is drawn randomly, which the next sections stress.
Benefits
- Conservative p = 0.5 built in;
- Finite-population correction included;
- Both adjusted and unadjusted figures;
- Useful for surveys and polls.
Features of Our Tool
- Instant results in your browser;
- No sign-up, no download, 100% free;
- Works on mobile, tablet and desktop;
- Clear step-by-step explanation below the tool;
- Private — your entries never leave your device.
Common Mistakes
- Wanting ±1% — that needs ~9,600 respondents;
- Ignoring non-response: invite more than the target;
- Forgetting the sample must be random, not just large.
Common Mistakes to Avoid
Chasing tiny margins is the classic budget shock: the mistakes list notes ±1% needs about 9,600 respondents, because the margin shrinks with √n, not with n — the FAQ spells out that halving the error means quadrupling the sample. Second, forgetting non-response: the target is completed responses, so follow the page’s advice and invite 20–50% more. Third, treating size as a substitute for randomness: a huge self-selected sample is still biased — the tool assumes every member of the population had a fair chance of being picked. Fourth, entering the margin as a decimal (0.05) instead of a percentage (5): the box asks for percent, and a decimal entry explodes the result.
FAQ
What sample size for 95% and ±5%?
385 respondents.
Why p = 0.5?
It gives the largest (safest) sample size — the conservative choice when the true proportion is unknown.
Does population size matter?
Only for small populations — above ~20,000 it barely changes the result.
How do I halve the margin of error?
Quadruple the sample — precision scales with √n.
What about non-response?
Invite 20–50% more than the target to cover dropouts.
What does 95% confidence actually mean?
That the method works 95 times out of 100: if the same survey were repeated many times, about 95% of the intervals built this way would contain the true value. It is a claim about the procedure’s reliability, not a guarantee about this one result.
Should I round the sample size up or down?
Always up. The formula’s 384.16 becomes 385 because 384 respondents would fall just short of the precision you asked for — rounding down quietly widens the margin of error beyond your target.
Related Calculators
Confidence Interval Calculator; Z-Score Calculator; P-Value Calculator