Free calculator
Margin of error calculator
For one survey proportion under a simple random sample story: pick a two-sided confidence level, your completed n, and the observed p as a percent—or turn on conservative p = 50% when you only need a worst-case band. Optionally enter a finite population N for the usual correction. This is survey statistics, not gross margin on a price (use the margin and markup calculator for pricing margin). Google Sheets and Excel can rebuild the same z with NORM.S.INV(1 − α/2).
When to use this calculator
Quick SRS margin checks after fieldwork—or a conservative planning band—without a full statistics suite.
- Read ±% precision for a reported percent from n completes at 90%, 95%, or 99% confidence.
- Turn on p = 50% when you want a worst-case Wald band before you know the outcome split.
- Apply a finite population correction when the audience is a known small N.
We use the common Wald half-width for a single proportion p̂ under a simple random sample: MOE ≈ z √( p(1−p) / n ) for a very large population. With a finite population N, we multiply the variance factor by (N−n)/(N−1) inside the square root—the same family as our sample size calculator.
Confidence → z
For two-sided level (1 − α), z solves Φ(z) = 1 − α/2 using the same normalCdf bisection as the sample size tool.
Half-width
MOE = z × √( p(1−p) / n ) when N is omitted; with N, use MOE = z × √( p(1−p)/n × (N−n)/(N−1) ).
This page does not implement two-sample difference margins, Wilson/exact intervals, cluster design effects, or mean margins with σ—use full statistics software when you need those extensions.
To plan minimum n from a target margin instead, open the sample size calculator.
For two-sided Wald intervals on proportions or mean z/t intervals, use the confidence interval calculator.
For unit pricing margin % on revenue, open margin and markup—same word **margin**, different meaning.
FAQs spell out CONFIDENCE.NORM, two-sample limits, and NPS context.
Google Sheets & Excel
The critical z for a two-sided (1 − α) confidence level satisfies Φ(z) = 1 − α/2. In English function names, =NORM.S.INV(1-α/2) returns z when α = 1 − confidence (store α as a decimal). Combine with SQRT on p(1−p)/n (and the FPC factor if needed) to rebuild the Wald half-width in a sheet.
=NORM.S.INV(0.975)Replace 0.975 with 1 − α/2 for other confidence levels.
=B2*SQRT(B3*(1-B3)/B4)B2 = z, B3 = p (decimal), B4 = n. Multiply by 100 for percent points. Add ×SQRT((N−n)/(N−1)) when N is finite.
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Frequently asked questions
What does this margin of error calculator show?
An approximate ±% half-width for a single sample proportion p̂ at your chosen two-sided confidence, using the Wald / normal shortcut and the same optional finite population factor as our sample size tool. It is not a full design or weighting engine.
Is this the same “margin” as pricing or trading?
No. Margin and markup on this site mean profit vs price or cost for a unit—a pricing concept. Margin of error here is survey statistics vocabulary for precision of a percent estimate.
Why is there a p = 50% toggle?
The factor p(1−p) is largest at 0.5, so assuming 50% gives a conservative (wider) margin when you do not want to trust an early p yet.
When should I enter population N?
When your frame is a known finite list (members, employees) and simple random sampling without replacement is the right mental model. Leave N blank when the universe is large relative to n so the correction is negligible.
Why is the margin 0% when p is 0% or 100%?
On the Wald path, p(1−p) is 0, so the standard error is 0 and this calculator reports 0—a limitation of the normal approximation at the boundary, not a claim of infinite precision.
Can I compare two proportions?
Not in v1. Two-proportion comparisons need different standard errors (and often continuity corrections). Use dedicated stats software or extend your sheet carefully when you need that test.
Should I use CONFIDENCE.NORM in Excel?
CONFIDENCE.NORM / CONFIDENCE.T target mean margins with a supplied σ or s—not this binomial √(p(1−p)/n) story. Prefer NORM.S.INV for z and build √(p(1−p)/n) explicitly for proportions.
I have NPS counts—how does that relate?
The Net Promoter Score tool turns 0–10 buckets into an NPS index. If you want a margin on a single percent (for example % promoters), enter that percent as p with the same n here—this page does not recompute NPS for you.
What assumptions are baked in?
Simple random sample, Wald normal approximation, and optional finite population correction—good for quick checks, not stratified or cluster designs without extra factors.
Which spreadsheet function matches z here?
In English Excel and Google Sheets, NORM.S.INV(1-α/2) with α = 1 − confidence as a decimal. Localized names differ by language pack—use Insert function to find the inverse normal in your install.
Is this professional survey advice?
No—results are educational and depend on the inputs you choose. Weighting, mode, nonresponse, and legal constraints can all change what “enough precision” means in practice.