NPS Calculator: Net Promoter Score With Margin of Error

Enter how many people scored 9 or 10, 7 or 8, and 0 to 6, or paste the raw answers, and this returns your Net Promoter Score with the margin of error most dashboards leave out. That margin matters more than people expect: with 100 responses, an NPS of 30 can easily be anything from about 15 to 45, so a five-point move between quarters is usually noise. Add last period's figures and the calculator tells you whether the change is real.

How the Net Promoter Score is calculated

NPS comes from one question: how likely are you to recommend us to a friend or colleague, on a scale of 0 to 10? Anyone answering 9 or 10 is a promoter, 7 or 8 a passive, and 0 to 6 a detractor. The score is the percentage of promoters minus the percentage of detractors, so it runs from −100 (everyone a detractor) to +100 (everyone a promoter). Passives count towards the total but add nothing to either side.

Take 200 responses with 120 promoters, 50 passives and 30 detractors. Promoters are 60%, detractors 15%, so NPS is 60 − 15 = 45. NPS is reported as a plain number, not a percentage.

Why your NPS needs a margin of error

Each response can be treated as +1 (promoter), 0 (passive) or −1 (detractor), and the NPS is 100 times the average. That lets you work out a standard error in the usual way: the variance of one response is the promoter share plus the detractor share minus the square of their difference, divided by the number of responses for the error of the mean. Multiply the standard error by 1.96 for a 95% interval.

In the example above the margin is about ±10.3 points, so the true score is plausibly anywhere from the mid 30s to the mid 50s. Polarised samples, with plenty of both promoters and detractors, carry the widest intervals, because the answers are spread across both ends of the scale.

Comparing two surveys

To test whether a change between two periods is real, the calculator takes the difference between the two scores and divides it by the combined standard error (the square root of the two squared errors added together). That gives a z statistic and a two-sided p-value. It treats the two samples as independent, which holds when the surveys reach different respondents; if the same people answer both times, a paired analysis would be tighter.

A practical rule that falls out of the arithmetic: one detractor converted to a promoter moves the score by 200 divided by the number of responses. On a 50-response survey, that is four points from a single person, which is why small-sample NPS swings so much from month to month.

Getting more out of NPS

• Read the follow-up comments. The score tells you how many are unhappy; the open-text answer from detractors tells you why, and that is what you can actually test changes against.
• Segment before you average. A flat overall score can hide one customer group improving while another slides. Run the calculator per segment, and watch the margin of error grow as each group shrinks.
• Keep the survey consistent. Changing the timing, channel or wording between periods can shift the score on its own, so a significant change may still not mean what it seems to.

For usability rather than loyalty, the SUS score calculator grades a System Usability Scale study, and the conversion rate confidence interval calculator applies the same margin-of-error thinking to conversion rates.