With 400 responses at 95% confidence, your true value is within +/- 4.9 percentage points of what you measured.
You need 385 responses for a +/- 5% margin of error at 95% confidence.
Built by Rankite, the SEO team behind Swordfish AI's +400% revenue and Zluri's +45% organic growth. See the case studies
Margin of error is the plus-or-minus number that tells you how far your survey result can stray from the truth. If 60% of 400 respondents prefer your new landing page and your margin of error is +/- 4.9%, the real figure for your whole audience is very likely somewhere between 55.1% and 64.9%. The smaller the margin, the more precise your result, and the only reliable way to shrink it is to collect more responses. The calculator above gives you the number in both directions: the margin of error for a sample you already have, or the sample size you need to hit a target margin.
The standard formula is MoE = z x sqrt(p(1-p)/n). Three ingredients do all the work. The z-score comes from your confidence level: 1.645 for 90%, 1.96 for 95%, 2.576 for 99%. Higher confidence means a wider margin, because you are asking for a stronger guarantee. The proportion p is the percentage you expect to measure; if you have no idea, use 50%, because p(1-p) is largest at 50% and gives you the most conservative (widest) margin. The sample size n sits under a square root, which is why precision gets expensive: cutting your margin of error in half requires four times as many responses, not twice as many.
If you survey a small, known population, the finite population correction tightens the margin. It barely matters until your sample is a meaningful slice of the whole group, which is why the population field is optional.
At 95% confidence with p = 50%, the workhorse settings for most surveys, the numbers look like this:
| Sample size | Margin of error |
|---|---|
| 100 | +/- 9.8% |
| 200 | +/- 6.9% |
| 400 | +/- 4.9% |
| 1,000 | +/- 3.1% |
| 2,000 | +/- 2.2% |
Notice the diminishing returns: going from 100 to 400 responses buys you 4.9 points of precision, but going from 1,000 to 2,000 buys you less than one. For most marketing surveys, 400 to 1,000 responses is the sweet spot between cost and credibility.
The same statistics decide whether an A/B test winner or a month-over-month change in your conversion rate calculator numbers is a real difference or just noise. Before you act on any percentage, check that the gap between two results is bigger than their margins of error. And if you want to know which numbers on your own site are worth acting on, request a free SEO audit and we will walk you through them with real data.
Project the traffic, leads and revenue SEO can add, and the ROI on your investment.
Find your conversion rate, compare it to benchmarks, and see how much traffic your goals require.
Work out your click-through rate and CPC, then benchmark them against search, display and organic averages.
Get a free, no-obligation SEO audit and a 30-minute strategy session. We'll show you exactly where the growth is hiding.
Fill out the form and we'll get back to you within one business day. Prefer email? Write to us directly at contact@rankite.com.