# Sample size: how many people do you need to survey?

> Why can a poll of 1,000 people describe a country of 100 million? This guide explains margin of error, confidence level and the 385 rule in plain words, with charts that show where adding more respondents stops being worth the cost.

Published 2026-10-09 by Toolcloak. 4 minute read. Original: https://toolcloak.pages.dev/articles/sample-size-how-many-people-to-survey-margin-of-error-and-confidence
Related free tool: [Sample Size Calculator](https://toolcloak.pages.dev/tools/sample-size-calculator)

You almost never need to ask everyone. A well-chosen **sample** of a few hundred or a few thousand people can describe a very large group with a known amount of error. The calculator turns three choices into one number: how precise you want to be, how sure you want to be and how varied you expect the answers to be.

> **In short**
> - For a large population, **385 responses** give a ±5% margin of error at 95% confidence, whether you survey a town or a country.
> - Precision is expensive: halving the margin of error needs **four times** as many responses.
> - Population size barely matters unless the group is small. For under a few thousand people, a correction lowers the number you need.
> - A big sample cannot fix a bad sample. If the wrong people answer, more of them just makes you confidently wrong.

## The three dials

**What each setting means**

| Box | What it means |
| --- | --- |
| Margin of error | How far the result may sit from the truth. ±5% means a measured 60% really lies between 55% and 65%. |
| Confidence level | How often the method gets it right. 95% means 19 out of 20 surveys would land within the margin. |
| Expected proportion | Your guess of the answer split. If unsure, use 50%, the case that needs the most people. |
| Population size | The whole group you care about. It matters only when the group is small. |

*The common formula is n = z² × p × (1 − p) ÷ e², where z is 1.96 for 95% confidence, p is the expected proportion and e is the margin of error.*

Try it: [Sample Size Calculator](https://toolcloak.pages.dev/tools/sample-size-calculator). Set the margin of error, confidence level and population to get the number of responses you need.

## Where 385 comes from

**Sample size for ±5% at 95% confidence, answers split 50-50**

1. **Pick the numbers.** z = 1.96 (95% confidence), p = 0.5, e = 0.05.
2. **Top of the formula.** 1.96² × 0.5 × 0.5 = 3.8416 × 0.25 = 0.9604.
3. **Bottom of the formula.** 0.05² = 0.0025.
4. **Divide and round up.** 0.9604 ÷ 0.0025 = 384.16, so you need **385** responses.

*Always round up. 384 would fall just short of the target.*

## Smaller margin, much bigger sample

Precision follows a square-root law. To cut the margin of error in half you need four times the responses. The curve below is why most surveys settle for ±3% to ±5%.

| Margin of error | Responses needed (95%) | Compared with ±5% |
| --- | --- | --- |
| ±10% | 97 | about a quarter |
| ±5% | **385** | baseline |
| ±3% | 1,068 | 2.8 times |
| ±2% | 2,401 | 6.2 times |
| ±1% | 9,604 | 25 times |

*Going from ±5% to ±1% means asking about 25 times as many people.*

**Responses needed for each margin of error (95% confidence)**

|  | Value |
| --- | --- |
| ±10% | 97 |
| ±5% | 385 |
| ±3% | 1068 |
| ±2% | 2401 |
| ±1% | 9604 |

*The last bar is so tall that the first two look tiny. That is the point: the last bit of precision is the costliest.*

**Margin of error as the sample grows (95%, answers split 50-50)**

| Responses | Margin of error (±%) |
| --- | --- |
| 50 | 13.9 |
| 100 | 9.8 |
| 250 | 6.2 |
| 400 | 4.9 |
| 1000 | 3.1 |
| 2500 | 2 |
| 10000 | 1 |

*The line drops fast at first and then flattens. The jump from 100 to 400 responses roughly halves the error; the jump from 2,500 to 10,000 only takes off one point.*

**Is 385 responses enough? Margin of error for your sample**

| Zone | Range |
| --- | --- |
| Sharp | under 3% |
| Usable | 3–6% |
| Rough | over 6% |

*A rough guide only. Close races and small differences need a sharper margin than a general 'how many people like this' question.*

## How sure do you want to be?

A higher confidence level means you accept fewer surprises, but it costs responses. 95% is the common default; 99% is used when the cost of being wrong is high.

**Responses for ±5% at different confidence levels**

|  | Responses |
| --- | --- |
| 90% (z 1.645) | 271 |
| 95% (z 1.96) | 385 |
| 99% (z 2.576) | 664 |

*Moving from 95% to 99% asks for about 70% more people for the same margin of error.*

## Does population size matter?

For large groups, no. Surveying a town of 100,000 needs about the same 383 responses as a country of 100 million. For small groups there is a **finite population correction**: n = n₀ ÷ (1 + (n₀ − 1) ÷ N), where n₀ is the basic answer (384.16) and N is the population.

**Responses needed for ±5% at 95% confidence, by population size**

|  | Value |
| --- | --- |
| 200 | 132 |
| 500 | 218 |
| 1,000 | 278 |
| 5,000 | 357 |
| 10,000 | 370 |
| 100,000 | 383 |

*For a class or a company of 200 people you need 132 answers (66% of them). For 100,000 people you need 383, which is less than half a percent.*

**A team of 200: how many must answer for ±5%?**

| Group | Count |
| --- | --- |
| Must respond | 132 |
| Can stay silent | 68 |

*Small groups need a high response share. In a tiny group it is often simpler to ask everyone.*

## When you already know the answer will be lopsided

The 50% assumption is the safest, because it gives the largest sample. If you are confident that only about 10% of people will say yes, you need fewer. Do not use this shortcut unless you really have evidence.

| Expected share | Responses for ±5% (95%) |
| --- | --- |
| 50% (unknown, safest) | 385 |
| 30% | 323 |
| 20% | 246 |
| 10% | 139 |
| 5% | 73 |

*The formula uses p × (1 − p), which is biggest at 50%.*

> **Sample size is not the same as sample quality:** The formula assumes everyone in the group had an equal chance of being asked. An online poll that only reaches people who are already fans, or a form that most people ignore, can have thousands of answers and still be badly wrong. A smaller random sample usually beats a bigger self-selected one.

> **Plan for people who do not reply:** If you expect only 25% of invited people to respond and you need 385 answers, invite about 1,540 (385 ÷ 0.25). Response rate is often the real limit, not the formula.

## A short checklist

1. **Decide the margin of error** you can live with, such as ±5%.
2. **Choose the confidence level.** Use 95% unless there is a reason not to.
3. **Use 50%** for the expected share if you have no good estimate.
4. **Enter your population,** especially if it is under a few thousand people.
5. **Divide by your expected response rate** to know how many invitations to send.

## Frequently asked questions

### What sample size do I need for a survey?

For a large population, 385 responses give a ±5% margin of error at 95% confidence. For ±3% you need about 1,068, and for ±1% about 9,604.

### Why is 385 so common?

It comes from the formula n = z² × p × (1 − p) ÷ e² with 95% confidence (z = 1.96), a 50% expected split and a 5% margin of error, which gives 384.16, rounded up to 385.

### Does population size matter for sample size?

Only for small groups. Beyond a few thousand people the required sample barely changes. For small populations a finite population correction reduces the number you need.

### What is margin of error?

It is the range around your result in which the true value is expected to lie at your chosen confidence level. A result of 60% with ±5% means the real figure is likely between 55% and 65%.

### What confidence level should I use?

95% is standard. Use 90% for quick, low-stakes checks and 99% when a wrong conclusion would be costly, remembering that higher confidence needs more responses.

### Can a large sample still be wrong?

Yes. If the people who answer are not representative of the group, for example only volunteers or only one region, a large sample gives a precise but biased result.