- z · confidence level
- How much certainty you want: 1.645 for 90%, 1.96 for 95% and 2.576 for 99%.
- e · margin of error
- How much the result may vary up or down. ±3 points is written as 0.03.
- p · expected proportion
- We use 50% (0.5), the scenario that requires the largest sample. That way, no answer will have a margin larger than the one calculated.
- N · population
- How many people make up the audience you’re studying. It only matters when the number is small.
Free tool
Sample size and margin of error calculator
How many interviews does your survey need? Get the answer in seconds, then see how the number is calculated, with the help of a soup spoon.
Estimate for simple random sampling, assuming a 50% proportion (the most conservative scenario). Each study’s sampling plan also accounts for quotas, stratification and analysis groups.
Step 1 · What a sample is
One spoonful tells you how it tastes
You don’t have to eat the whole pot to know if the soup needs salt. One spoonful is enough, as long as the soup is well stirred.
The sample is that spoonful: a group of people chosen to represent the entire audience, which researchers call the population. If the sample is well chosen, what it tells you applies to everyone, within a known margin of error.
Here’s the part that surprises most people: the spoon you use to taste soup at home is the same one you’d use for a cafeteria’s giant stockpot. A bigger pot doesn’t call for a bigger spoon.
Step 2 · Population size
Why the cafeteria needs the same size spoon
A survey’s precision depends on the sample size and barely at all on the size of the population. A city of 100,000 people and a country of 200 million need practically the same sample for the same margin of error.
Population size only matters when it’s small: if the pot holds very little soup, one spoonful is already a big share of it. The formula handles this with the finite population correction.
| Population | Sample | Proportion |
|---|---|---|
| 1.000 | 517 | |
| 10.000 | 965 | |
| 100.000 | 1.056 | |
| 1.000.000 | 1.066 | |
| 2,800,000 (Federal District) | 1.067 | |
| very large | 1.068 |
Step 3 · Stir before tasting
The spoon only works if the soup is stirred
A large, poorly chosen sample gets it more wrong than a smaller, well-chosen one. Stirring the soup means giving everyone a chance to end up in the spoon, through random selection, quotas and stratification. Here are three kitchen mistakes good research avoids:
- Tasting only the surface
Grabbing whoever is easiest to reach: only people who answer online, or only people who walk past one spot. That’s a convenience sample: quick, but not representative.
- The spoon that only scoops broth
Leaving out part of the audience: people without internet, people who don’t answer the phone, people who live far away. The chunks stay at the bottom and never make it into the taste.
- Always tasting from the same side
Picking the same kind of person every time, even unintentionally. Quotas by region, sex, age and class, plus random selection, fix this. That’s what stirring before tasting means.
Step 4 · How the calculation works
Ingredients
Step 1 · Sample for a large population
Step 2 · Finite population correction
Step 3 · Round up
Working backward · margin from sample size
The recipe, ingredient by ingredient
n₀ = z² × p × (1 − p) ÷ e²
At 95% confidence and ±3 points: 1.96² × 0.5 × 0.5 ÷ 0.03² = 1,067.1.
n = n₀ × N ÷ (n₀ + N − 1)
With the Federal District’s population (2,800,000): 1,067.1 × 2,800,000 ÷ (1,067.1 + 2,800,000 − 1) = 1,066.7.
1,066.7 → 1,067 interviews
Always round up: with 1,066 interviews, the margin would already be slightly over ±3 points. Without the correction (very large population), you’d need 1,068.
e = z × √(p × (1 − p) ÷ n) × √((N − n) ÷ (N − 1))
With 1,225 interviews at 95% confidence: 1.96 × √(0.25 ÷ 1,225) = ±2.8 points. That’s what the calculator’s “Margin of error” tab does.
Step 5 · More interviews, diminishing returns
The second spoonful tells you less than the first
The first spoonful tells you almost everything about the flavor. The second confirms it. The tenth adds almost nothing. Samples work the same way: the margin of error drops quickly at first, then more slowly.
The rule of thumb: to cut the margin in half, you need four times the sample. Going from 400 to 1,600 interviews takes the margin from ±4.9 to ±2.5 points. That’s why the right sample size balances precision and budget.
Step 6 · Subgroups
Want to taste each ingredient? Each one needs its own spoonful
One spoonful tells you how the whole soup tastes. But if you want to know how the carrots, the potatoes and the beans taste, each ingredient needs its own spoonful.
In research, that’s the case when you want to reliably compare regions, age groups or customer types. Each group you analyze separately needs its own sample.
- Region 1384
- Region 2384
- Region 3384
- Region 4384
- Region 5384
5 × 384 = 1,920 interviews
Step 7 · What the spoon doesn’t tell you
The margin of error doesn’t fix a bad recipe
The margin of error only measures the uncertainty of tasting a spoonful instead of the whole pot, known as sampling error. It won’t fix a badly worded question, people who refuse to answer, a poorly trained interviewer or poorly processed data.
That’s why, beyond calculating the sample, Checon follows the ISO 20252 standard, with external audits, at every stage, from questionnaire and fieldwork to quality checks and analysis.
Learn about Quantitative Research →Read the guide on margin of error →See the research glossary →
Frequently asked questions
Questions about sample size and margin of error
Question 01
What is the minimum sample size for a survey?
There’s no single minimum. It depends on the margin of error you can accept and the groups you need to analyze. As a reference, 400 interviews give you about ±4.9 points and 1,000 interviews about ±3.1 points, at 95% confidence.
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Question 02
Why does the calculator use a 50% proportion?
Because 50% is the scenario that requires the largest sample. When you don’t know the expected result, using 50% ensures that no answer will have a larger margin of error than the one calculated.
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Question 03
Is it better to use 95% or 99% confidence?
95% is the standard in market and opinion research. 99% gives you more certainty but requires about 70% more interviews for the same margin of error.
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Question 04
Does the sample size change if the population is small?
Yes, it gets smaller. For populations of a few thousand people, the finite population correction reduces the required sample considerably. For large populations, the effect is negligible.
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Question 05
Does the margin of error apply to every question?
The calculated margin applies to the total sample and to results around 50%. For results closer to 10% or 90%, the real margin is smaller. For subsets of the sample, such as a single region, it’s larger.
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Question 06
How do I calculate the sample when I want to analyze subgroups?
Each group you analyze separately needs its own sample. Enter the number of groups in the calculator’s optional field, and it will calculate the sample for each group and add up the total.
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Contact
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Tell us what decision you need to make. A specialist will get back to you within 1 business day with an initial approach.
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