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Sample size at 95% confidence

The 95% confidence level is the dominant convention in market research, social science and opinion polling. Concretely: if you repeated the same survey 100 times, the confidence interval would contain the true value in ~95 of them. The associated z-score is 1.96 — that's what enters the formula n = z²·p·(1−p)/e².

At 95%, the orders of magnitude to remember: 385 respondents for ±5%, 1,068 for ±3%, 9,604 for ±1% (large population). The calculator below is locked on 95% — just vary the margin of error and the population size to watch the required sample adjust live.

Confidence level

95% is the market research standard. Z-scores: 1.645 · 1.96 · 2.576 (NIST statistical tables).

The acceptable gap between your sample and reality. ±5% is the most common choice.

If unsure, leave 50%: it's the worst case, requiring the largest sample.

The total number of people in your target. Above ~100,000 the impact is negligible: leave empty.

Respondents needed

385

You need 385 respondents for a 95% confidence level with a ±5% margin of error.

Export:

How many respondents per precision level?

Precision is expensive: going from ±5% to ±2% multiplies the sample by 6.

101001,00010,0001%3%5%8%10%Margin of error

Summary table

Sample size for the most common combinations.

Summary table
Confidence± 3%± 5%± 10%
90%75227168
95%1,06838597
99%1,844664166

Sample size: done. Now, the fieldwork…

Traditional fieldwork takes 6 weeks and $10,000. Panelia simulates 300+ calibrated respondents in 10 minutes.

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Frequently asked questions

What does '95% confidence' exactly mean?
That the method captures the true value in 95% of repeated samplings. It is NOT '95% probability that the true value lies in this specific interval' — a subtle but classic frequentist nuance.
Where does z = 1.96 come from?
From the normal distribution: 95% of the mass lies within ±1.96 standard deviations of the mean. For 90% it's 1.645, for 99% it's 2.576 (standard statistical tables, e.g. NIST).
When should I prefer 90% or 99%?
90% for fast iterations where an error is cheap; 99% when the decision is hard to reverse. At equal margin, moving from 95% to 99% increases the sample by about 73%.
Does 95% confidence mean 95% accurate answers?
No, no connection. Confidence concerns the estimation procedure, not the truthfulness of individual answers. Social desirability bias, for instance, isn't corrected by the confidence level.