# Sample size calculator

> Plan estimation precision with explicit population and confidence inputs.

[Open tool](https://www.toolcabana.com/cu/sample-size-calculator) · [Statistics and analysis](https://www.toolcabana.com/cu/category/statistics-and-analysis)

Tool ID: sample-size-calculator. Requested language: cu. Description language: en. Complete guide translation: no; untranslated sections use English.

## Overview (en)

The Sample size calculator returns the number of responses needed to estimate a single proportion with a chosen confidence level, margin of error and expected proportion. It uses n = z² × p(1 − p) / e² and applies a finite population correction when you enter a population size. The result is rounded up to a whole respondent and assumes random sampling.

## Supported tasks (en)

Plan estimation precision with explicit population and confidence inputs.

## Steps (en)

1. Enter the requested values in the settings panel.
2. Adjust the basic settings, then open Advanced mode for export and fine-tuning options. Custom settings stay active when the panel is closed.
3. Run sample size calculator, review the output, then use the available copy or download controls.

## Settings

- Confidence (%) (en; key: confidence; type: number); minimum: 50; maximum: 99.99
- Absolute proportion margin (%) (en; key: margin; type: number); minimum: 0.01; maximum: 49
- Expected proportion (%) (en; key: proportion; type: number); minimum: 0.01; maximum: 99.99
- Population (0 = unbounded) (en; key: population; type: number); minimum: 0; maximum: 1000000000000

## Limitations (en)

Local bounded calculations. Numeric inputs must be finite and within the visible ranges. Lists and tables have operation-specific limits. Models, estimates and supplied rates must be checked against your intended use.

## Privacy and connections (en)

This operation processes its source in your browser. Copy and download are explicit actions; source input is not saved in an account or history.

## Questions (en)

### How is sample size calculated for a survey?

The base size is n0 = z² × p × (1 − p) / e², where z comes from the confidence level, p is the expected proportion and e is the margin. At 95% confidence, a 5% margin and p = 50%, n0 is about 384.1, which rounds up to 385.

### How does population size affect the required sample?

With Population set to 0, the population is treated as unbounded. Entering a population size N applies the correction n0 / (1 + (n0 − 1) / N), which lowers the required sample for small populations. A population of 1 is rejected.

### Why use 50% as the expected proportion?

p × (1 − p) is largest at 50%, so it gives the most conservative, largest sample size when you do not know the likely result. If earlier data suggests a proportion such as 10%, entering it produces a smaller required sample.

### Where is my input processed?

This operation processes its source in your browser. Copy and download are explicit actions; source input is not saved in an account or history.

### What are the input limits?

Local bounded calculations. Numeric inputs must be finite and within the visible ranges. Lists and tables have operation-specific limits. Models, estimates and supplied rates must be checked against your intended use.

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