---
title: Sample size calculator: how many responses you need
description: How many responses to target for a given margin of error: the formula, the reference values, and what a small sample can and cannot tell you.
---

# Sample size calculator

How many responses do you need to measure an intention within a few points? This tool gives the sample size for the margin of error and confidence level you choose. No personal data is asked, nothing is stored: the calculation runs on the server, without an account.

The result appears here. Nothing is stored.

## How the calculation is done

The formula is the standard one for a proportion: **n = z² · p(1-p) / e²**. Three choices are made, and you need them to read the result:

- **p = 0.5**, the maximum-variance assumption. It is the cautious choice: it overstates the sample needed as soon as the true proportion moves away from 50 percent.

- **z follows the confidence level**: 1.645 for 90 percent, 1.96 for 95 percent, 2.576 for 99 percent.

- **Finite population correction** when you enter a reference population: if you are interviewing 1,200 customers, there is no reason to target the same size as for the whole US adult population.

The result is rounded up: it is a number of responses to target, never a threshold to approach from below.

## Reference values

| Confidence level | Margin of error | Responses to target |
| --- | --- | --- |
| 90% | 5 points | 271 |
| 95% | 5 points | 385 |
| 99% | 5 points | 664 |
| 95% | 3 points | 1,068 |
| 95% | 5 points, on 1,200 customers | 292 |

## And with a small sample?

The inverse question matters too, and it is usually left out: at 25 responses and 95 percent confidence, the margin of error is plus or minus 19.6 points. At 100 responses it falls to 9.8 points.

In practice: on a small sample, no figure reads as a fine measurement. What remains readable is the sharp gap, a version some people understand and others do not, a price that collapses intent, a ranking of reasons. That is exactly what the free plan settles, with 25 personas per survey and 10 questions.

## Why ask before paying for a field

Sample size is the line that moves a quote from a fielding agency, along with the target and the field duration. Working it out before asking for a quote avoids two symmetrical mistakes: paying for a precision nobody needs, or deciding on a sample too small to read anything but a sharp gap.

A synthetic run does not use this number the same way. It answers on 25, 500 or 5,000 personas, and the margin above still tells you what a figure of that size can support. What a study costs, plan by plan, is on [the cost page](/us/cost-of-market-research).

[Run a synthetic survey](/us/login)

Related: [what a study costs](/us/cost-of-market-research), [how long it takes](/us/how-long-does-market-research-take), and [research without a budget](/us/market-research-without-a-budget).