Six Sigma DPMO Calculator
Defects per million opportunities from a sample, the sigma level it corresponds to, and what reaching the next sigma level would mean in defects avoided.
DPMO is defects divided by units times opportunities per unit, scaled to a million.
How the six sigma dpmo calculator works
DPMO is defects divided by units times opportunities per unit, scaled to a million. Sigma level converts that to a position on the normal curve, with the conventional 1.5-sigma shift that six-sigma practice uses for long-term data.
The scale is steep: three sigma is 66,807 DPMO, four is 6,210, five is 233, six is 3.4. Each level is roughly an order of magnitude better than the last, which is why the jump from four to five is worth far more than the jump from three to four.
Formula: DPMO = defects / (units × opportunities) × 10⁶; sigma = Φ⁻¹(1 − DPMO/10⁶) + 1.5
Worked examples
| Inputs | Sigma level | Note |
|---|---|---|
| 92 defects in 40,000 opportunities | 4.334 | 2,300 DPMO — about 4.3 sigma |
| Three-sigma quality | 3 | 66,800 DPMO |
| Six sigma | 6.001 | 3.4 DPMO |
FAQFrequently asked questions
What is DPMO?
Defects per million opportunities — defects divided by the number of chances to make one, scaled to a million. It lets processes of different complexity be compared.
What is a sigma level?
How many standard deviations the process mean sits from the nearest specification limit, plus the conventional 1.5 shift for long-term drift. Six sigma is 3.4 DPMO.
Why the 1.5 shift?
A convention from Motorola: processes drift over time, so short-term capability overstates long-term performance by about 1.5 sigma. Not everyone uses it; this page does.
What is an opportunity?
Any feature that could be wrong — a solder joint, a dimension, a field on a form. Counting them generously flatters the DPMO, which is a known abuse.
What sigma level is normal?
Most manufacturing runs between three and four. Four is good; five is excellent; six is aspirational for all but the simplest processes.
Where these figures come from
- Nakajima (1988) — Introduction to TPM — the origin of Overall Equipment Effectiveness and its six big losses
- OSHA — the US workplace safety administration
Last checked: September 2026. Definitions follow standard operations-management practice; where plants commonly differ, the page says so.