NPS calculator with the margin of error

Enter counts or paste a list of scores. The score, the margin of error and the sample size needed update as the numbers change.

How is the score worked out?

Each respondent answers one question, how likely they are to recommend the product, from zero to ten. Nine or ten is a promoter, seven or eight is a passive, zero to six is a detractor.

NPS = (promoters / respondents − detractors / respondents) × 100

Passives sit in the respondent count and nowhere else in the formula.

What does the margin of error mean?

A survey reaches a sample of customers, so its score carries a margin either side of the number shown.

With p the promoter share, d the detractor share and n the respondent count, the 95% margin is:

var = (p + d − (p − d)²) / n
margin = 1.96 × √var × 100

Fifty promoters, thirty passives and twenty detractors, a hundred respondents, score an NPS of 30 with a margin of about ±15.3 points: the true score could sit anywhere from about 15 to 45. Forty promoters, thirty passives and thirty detractors score 10, with a margin of about ±16.3.

At forty replies and the first example's shares, the margin is about ±24.2 points. It shrinks with the square root of the respondent count, so going from 40 replies to 160 only halves it.

How many replies does a team need?

For a margin of plus or minus 5 or plus or minus 10 points, at a spread of answers close to the worked example above, fifty per cent promoters and twenty per cent detractors:

Halving the margin takes roughly four times the respondents, because the margin shrinks with the square root of the count. The calculator above recomputes both figures from whatever shares are currently entered.

When is a change between two surveys real?

Two surveys each carry their own margin, so a score that moved also carries a combined margin, wider than the margin on either survey alone.

With var1 and var2 the variance from each survey, the standard error of the change is √(var1 + var2) × 100, and the change is larger than chance at 95% when it exceeds 1.96 times that standard error. On two surveys of 300 replies each, at fifty per cent promoters and twenty per cent detractors, a change has to pass about 12.5 points to be larger than chance. The second survey fields in the calculator run this test on the counts entered.

What NPS cannot tell you

A score says how many people lean positive or negative. It does not say what they want built, and it does not say which requests sit behind a falling score.

Asking the same people to name a specific request, and letting others add their name to it, keeps the detail a single score throws away. What NPS measures, and what it misses. VoteFirst is a feature voting board, a public roadmap and a changelog, with no survey and no score of its own; a request on it carries its title, its vote count and its comments.

A team tracking satisfaction with individual interactions rather than overall loyalty wants the CSAT calculator instead, which runs the same kind of interval and sample size arithmetic on a different question.