PaneliaTools

Sample size for 100,000 people

A mid-size city, a media audience, a national marketing file: at 100,000 people, population size has practically no influence left on the calculation. You need 383 respondents for ±5% at 95% confidence — two fewer than the 385 of an infinite population. This plateau often surprises: no, polling a whole country doesn't require more respondents than polling a large city.

The reason lies in the nature of sampling error: it depends on answer variability and the absolute number of respondents, not on the sample-to-population ratio. Past a few tens of thousands of individuals, each additional person in the population adds no measurable uncertainty. The calculator below, preset to N = 100,000, lets you verify it by varying N.

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

383

You need 383 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%74727068
95%1,05638396
99%1,810660166

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

Why 383 and not much less than 385?
Because the FPC equals n₀/(1+(n₀−1)/N): with n₀ = 385 and N = 100,000, the reduction factor is only 0.4%. The gain only becomes visible when N gets close to n₀.
So polling the whole of France takes ~400 people?
For ONE national proportion at ±5%, yes. Institutes survey 1,000+ people to tighten the margin (±3%) and above all enable readings by region, age or occupation — each subgroup carrying its own margin.
My exact N is 87,000 or 250,000: should I enter it?
It hardly matters: between 50,000 and infinity, the result varies by just a few respondents. Enter it for rigor, or leave it empty — the difference is negligible.
How do I make the most of 383 respondents?
Invest in random recruitment and representativeness (age, gender, region quotas) rather than volume: at this scale, 383 well-drawn respondents beat 2,000 self-selected ones.