Can Net Promoter Score be negative?

Yes. NPS scores can range from -100 to +100.

The calculation is to subtract the percentage of detractors from the percentage of promoters (you ignore the passives from this calculation).

So if you have 100 responses and 40 score 0-6 (detractors), 45 score 7-8 (passives), and 15 score 9-10 (promoters) then your NPS score is 15% - 40% = -25

(You might also find our interactive NPS Calculator useful, or read the full background to How the NPS calculation works.)