INPUTS
Your sample
Use 50% if you do not know the expected percentage: it gives the largest, safest margin of error.
MARGIN OF ERROR CALCULATOR
Margin of error calculator for surveys and samples.
Find how precise a survey result is from the sample size and confidence level, for a percentage or a mean, with an optional finite population correction when you sample a large share of a known population.z × SE
METHOD
Margin of error formula, worked example, and how to report it
What is the margin of error?
The margin of error is how far a survey result could be from the true population value at a chosen confidence level. If 60% of respondents agree with a ±5% margin at 95% confidence, the true figure is probably between 55% and 65%. Larger samples give smaller margins of error.
Formula
MOE = z × √(p(1 − p) ÷ n) × √((N − n) ÷ (N − 1))z is 1.645 for 90%, 1.960 for 95% and 2.576 for 99% confidence. The last part is the finite population correction; leave it out when the population is large or unknown. For a mean, replace √(p(1 − p) ÷ n) with SD ÷ √n.
Worked example: survey of 385 people
n = 385, 95% confidence, p = 0.5 (unknown proportion).
- Multiply p by (1 − p): 0.5 × 0.5 = 0.25.
- Divide by n: 0.25 ÷ 385 = 0.000649.
- Take the square root: standard error = 0.0255.
- Multiply by z = 1.96: margin of error = 0.0499.
- Report: ±5.0 percentage points at 95% confidence.
How sample size changes the margin of error
- n = 100: ±9.8%
- n = 200: ±6.9%
- n = 385: ±5.0%
- n = 1,000: ±3.1%
- (95% confidence, p = 0.5, large population)
How to write it in your methodology
“With 385 respondents, the survey has a margin of error of ±5.0 percentage points at the 95% confidence level, assuming maximum variability (p = 0.5).”
References
- Cochran, W. G. (1977). Sampling techniques (3rd ed.). Wiley.
- Lohr, S. L. (2021). Sampling: Design and analysis (3rd ed.). CRC Press.
ABOUT THIS TOOL
Margin of Error Calculator
Work out the margin of error of a survey from the sample size and confidence level, for a percentage or a mean, with an optional finite population correction for small populations.
- State the margin of error of a completed survey
- Check whether a sample of 200 is precise enough
- Explain survey precision in your methodology chapter
KEY FUNCTIONS
Margin of error for a proportion or a mean90%, 95%, 99% or custom confidenceFinite population correctionPlain-language result for your methods chapter
USE IN YOUR THESIS
Cite this calculator and export your results
APA 7 reference for software or an online tool. Cite the statistical method in your text as well.
SolveGrid. (2026). Margin of Error Calculator [Online calculator]. https://solvegrid.online/margin-of-error-calculator
LEARN THE METHOD
Guides for this calculator workflow
GUIDESlovin's formula for sample size (with examples)Use n = N ÷ (1 + N·e²) to find a thesis sample size, compare it with Cochran's formula, and write it up correctly.Read →GUIDEStandard deviation formulaCompare sample and population standard deviation, variance, mean deviations, quartiles, and spread.Read →
n→[ ]→1−β→
Sample Size Calculator
Find the minimum sample size for a survey or thesis using Slovin/Yamane or Cochran's formula, with confidence level, margin of error, population size, response-rate adjustment, and a copy-ready methods sentence.
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Power Analysis Calculator
Justify your sample size the way supervisors expect: choose the test, set the expected effect size, alpha, and power, and get the required N, a power curve, and a methodology sentence.