Margin of Error Calculator
Calculate the margin of error for a survey proportion. Enter the sample proportion, the sample size, and a confidence level of 90, 95, or 99 percent, and the tool returns the margin of error in percentage points.
What this calculator does
The Margin of Error Calculator estimates your result instantly from the values you enter, using standard statistics formulas. Calculate the margin of error for a survey proportion. Enter the sample proportion, the sample size, and a confidence level of 90, 95, or 99 percent, and the tool returns the margin of error in percentage points. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About Margin of Error Calculator
This calculator returns the margin of error for an estimated proportion. Choose a confidence level and the tool uses its z-score (1.645 for 90%, 1.96 for 95%, 2.576 for 99%), then applies MOE = z × √(p(1 − p) / n) using your sample proportion p and sample size n.
The proportion must be between 0 and 1 and the sample size at least 1. The result is shown as a ± value in percentage points, rounded to three decimals.
Formula & Mathematical Calculation
Margin of Error = f(Sample proportion (0–1), Sample size (n), Confidence level)
Calculated according to standard stats formulas implemented in the calculator core.
Calculation Example
With sample proportion p = 0.5, sample size n = 500, and confidence level 95% (z = 1.96):
- p(1 − p) / n = 0.25 / 500 = 0.0005
- MOE = 1.96 × √0.0005 = 1.96 × 0.0223607 = 0.0438269
The Margin of Error box shows ± 4.383%.
Key Benefits
- Converts a confidence level of 90%, 95%, or 99% to the matching z-score automatically
- Applies the standard proportion margin-of-error formula z times sqrt(p(1-p)/n)
- Reports the result directly in percentage points as a plus-or-minus band, to three decimals
- Validates that the proportion is between 0 and 1 and the sample size is at least 1; free and in-browser
How to Use this Calculator
-
Enter the sample proportion
Type the observed proportion between 0 and 1 into Sample proportion, for example 0.5 for 50 percent. -
Enter the sample size
Type the number of respondents into Sample size (n); it must be at least 1. -
Choose the confidence level
Select 95%, 90%, or 99% from the Confidence level menu. -
Calculate
Press Calculate to read the Margin of Error in percentage points.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- Margin of Error Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.