Teams & projects
Sigma level calculator
Enter defects, units and opportunities per unit to get DPMO and the process sigma level that Six Sigma teams use to benchmark quality.
Opportunities per unit is how many distinct ways one unit can fail; it sets how DPMO and the sigma level are scaled.
How the sigma level is calculated
The process sigma level turns a defect count into a single quality grade. First work out defects per million opportunities: DPMO = defects ÷ (units × opportunities) × 1,000,000. With 12 defects across 1,000 units that each have 3 opportunities, that is 12 ÷ 3,000 × 1,000,000 = 4,000 DPMO, a yield of 99.6%. Then convert the yield to a z-score from the normal distribution and add the standard 1.5 sigma shift, which accounts for long-term drift. A yield of 99.6% gives about 4.15 sigma.
The 1.5 shift is a Six Sigma convention introduced by Motorola: a process that looks like 6 sigma in the short term is assumed to wander by up to 1.5 sigma over time, so the headline figure builds that allowance in. This is why a true 6 sigma process is quoted as 3.4 DPMO rather than the 0.002 DPMO a pure normal curve would give.
| Sigma | DPMO | Yield |
|---|---|---|
| 2σ | 308,537 | 69.1% |
| 3σ | 66,807 | 93.32% |
| 4σ | 6,210 | 99.379% |
| 5σ | 233 | 99.977% |
| 6σ | 3.4 | 99.99966% |
Reading the sigma level
Most established processes sit between 3 and 4 sigma, which is roughly a 93–99% yield. Each step up is far harder than the last: moving from 3 to 4 sigma cuts defects about tenfold, and 4 to 5 another tenfold. That is why the sigma level is a benchmark for comparison and goal-setting rather than a daily control metric; a control chart is better for spotting a process going out of control in real time.
The figure is only as honest as your definition of a defect and an opportunity. Inflating opportunities makes the same process look better, so agree the counting rules before comparing teams or products. Treat the result as approximate: the conversion assumes defects follow a normal distribution, which holds well enough for benchmarking but not for safety-critical certification.
Frequently asked questions
Why add a 1.5 sigma shift?
It is a Six Sigma convention that allows for a process drifting over the long term. Without it, a short-term 6 sigma process would be quoted at 0.002 DPMO instead of the familiar 3.4 DPMO.
What sigma level is good?
Many stable processes run at 3 to 4 sigma. Five sigma and above is excellent, and 6 sigma means 3.4 defects per million opportunities. The right target depends on the cost and risk of a defect.
Can the sigma level be more than six?
Mathematically yes, when defects are extremely rare, but the data needed to prove it is huge. Beyond about 6 sigma the number is more marketing than measurement for most processes.