# Margin of Error Calculator

Free margin of error calculator. Calculate the margin of error for surveys and polls based on sample size, confidence level, and observed proportion.

## What this calculates

Calculate the margin of error for your survey or poll. Enter the sample size, observed proportion, and confidence level to determine how precise your results are.

## Inputs

- **Sample Size (n)** — min 2 — The number of respondents or observations.
- **Sample Proportion (%)** — min 0, max 100 — The observed proportion (use 50% if unknown for maximum margin of error).
- **Confidence Level** — options: 90%, 95%, 99% — The desired confidence level.
- **Population Size (optional)** — min 0 — Total population. Leave 0 for infinite population.

## Outputs

- **Margin of Error** — formatted as percentage — The margin of error as a percentage.
- **Lower Bound** — formatted as percentage — Proportion minus margin of error.
- **Upper Bound** — formatted as percentage — Proportion plus margin of error.
- **Standard Error** — The standard error of the proportion.
- **Interpretation** — formatted as text — How to interpret the margin of error.

## Details

The margin of error indicates the range within which the true population value likely falls.

Formula:
MoE = z × √(p(1-p)/n)

Where:

- z = z-score for confidence level

- p = sample proportion

- n = sample size

With Finite Population Correction:
MoE = z × √(p(1-p)/n) × √((N-n)/(N-1))

A smaller margin of error means more precise results. To reduce it: increase sample size or lower confidence level.

## Frequently Asked Questions

**Q: What does ±3% margin of error mean?**

A: A ±3% margin of error at a 95% confidence level means that if you repeated the survey 100 times, about 95 of those surveys would produce results within 3 percentage points of the true population value. For example, if 52% of respondents said yes, the true value is likely between 49% and 55%.

**Q: Why do polls use ±3% to ±5% margin of error?**

A: This range represents a balance between precision and cost. A ±3% margin requires about 1,067 respondents while ±5% needs only 385 respondents (at 95% confidence). Going below ±2% becomes very expensive as it requires thousands of respondents.

**Q: How does sample size affect margin of error?**

A: Margin of error decreases as sample size increases, but with diminishing returns. Doubling the sample size only reduces the margin of error by about 29% (divides by √2). Going from n=100 to n=400 halves the margin of error.

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Source: https://vastcalc.com/calculators/statistics/margin-of-error
Category: Statistics
Last updated: 2026-04-21