Sample planning
Answer “If 400 people respond, how precise is a 40% result?” before you start fielding.
Tools / Margin of Error Calculator
Margin of Error Calculator
Plan sample size before you field a survey. Enter n, pick a confidence level, and optionally set an expected yes/satisfied share to estimate margin of error.
MOE ≈ z × √(p(1 − p) ÷ n) · Reported as ± percentage points
Enter counts to see the result
- 1
Enter planned sample size
Use the number of completes you expect, not invitations sent.
- 2
Set confidence and proportion
95% is the usual default. Use 50% expected yes rate when you are unsure (widest margin).
- 3
Read ± margin
The result is the half-width around your point estimate in percentage points.
Why plan margin of error
Know how wide your percentage might swing before you launch, so you do not over-read a small sample.
Conservative default
Leave expected proportion at 50% when you do not know the outcome yet. That gives the largest (safest) margin for a given n.
Pairs with CI tool
After fielding, use the [confidence interval calculator](/tools/confidence-interval-calculator) with actual success counts and Wilson intervals.
Useful for
Research proposals
Justify sample size in a brief or class project with a stated confidence level.
CX and product surveys
Check whether your weekly pulse has enough completes to detect a 5-point CSAT move.
Election and class polls
Quick ± band for teaching or internal polls when n is fixed in advance.
The formula
MOE ≈ z × √(p(1 − p) ÷ n)
Reported as ± percentage points around your estimate. Optional finite population correction applies when you sample a large share of a known population N.
Planning vs after fielding
Margin of error (this page)
- You know sample size n upfront
- Assumed proportion p (50% if unknown)
- Wald formula for planning
Confidence interval calculator
- You have actual success counts
- Wilson score interval
- Better for small samples and extremes
Related calculators
Frequently asked questions
How is this different from the confidence interval calculator?
This page is for planning: you enter expected sample size and get ± margin before collecting data.
The confidence interval calculator uses actual results (successes and n) and Wilson score intervals after fielding.
Why default to 50% expected proportion?
When p = 0.5, p(1 − p) is largest, so the margin is widest. Planning with 50% is conservative if you do not know the outcome yet.
What confidence level should I use?
95% is the common default. 90% gives a narrower band; 99% is wider and more cautious.
When should I enter population size?
When you sample without replacement from a known finite group (for example 300 of 800 employees) and the sample is a large fraction of the group.
Are my numbers stored?
No. Everything runs locally in the browser.
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