Calculating your margin of error is straightforward once you know the Margin of Error formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Margin of Error Calculator.
What is Margin of Error?
The Margin of Error calculation tells you your margin of error from a few simple inputs. The figure you are solving for here is the margin of error, expressed in percent.
The Margin of Error formula
The core formula is:
Margin of error = Confidence level × √(Proportion × (1 - Proportion) ÷ Sample size) × 100Here is what each input means:
- Sample size — a number. Example: 1,000.
- Proportion — a number. Example: 0.5.
- Confidence level — one of: 90% (z = 1.645), 95% (z = 1.96), 99% (z = 2.576). Example: 95% (z = 1.96).
How to calculate it step by step
- Write down the sample size (for example, 1,000).
- Write down the proportion (for example, 0.5).
- Choose the confidence level (for example, 95% (z = 1.96)).
- Apply the formula above to get your margin of error.
- Double-check the result with the Margin of Error Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Sample size | 1,000 |
| Proportion | 0.5 |
| Confidence level | 95% (z = 1.96) |
| Margin of error | 3.10% |
With sample size of 1,000, proportion of 0.5 and confidence level of 95% (z = 1.96), the margin of error works out to 3.10%.
Example 2
With sample size of 2,000, proportion of 0.5 and confidence level of 95% (z = 1.96), the margin of error works out to 2.19%.
| Result | Value |
|---|---|
| Margin of error | 2.19% |
Example 3
With sample size of 500, proportion of 0.5 and confidence level of 95% (z = 1.96), the margin of error works out to 4.38%.
| Result | Value |
|---|---|
| Margin of error | 4.38% |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Margin of Error Calculator does it instantly, for free, with the formula and a worked example built in.
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