Six Sigma Calculator (DPMO, Yield & Sigma Level)
By Santaji GadepatilinUpdated November 4, 2026
Six Sigma measures quality by counting defects per million opportunities and converting that rate into a sigma level, where 6σ means just 3.4 defects per million. This six sigma calculator works out DPU, DPMO, yield and the sigma level from your defect count, using the standard 1.5σ long-term shift.
How to use the six sigma calculator
Enter the number of defects found, the number of units inspected and the defect opportunities per unit. The calculator returns defects per unit, DPMO, the yield (first-pass yield per opportunity) and the process sigma level. To find the DPMO for a target sigma level, clear the defects and enter the sigma level.
Six sigma formulas
DPU = D ÷ U · DPMO = D ÷ (U × O) × 10⁶ · Yield = 1 − DPMO ÷ 10⁶
Sigma level = Φ⁻¹(Yield) + 1.5
Example
27 defects found in 1,500 assemblies with 5 opportunities each:
- DPU = 27 ÷ 1,500 = 0.0180
- DPMO = 27 ÷ (1,500 × 5) × 10⁶ = 3,600
- Yield = 1 − 0.0036 = 99.64%
- Sigma level = Φ⁻¹(0.9964) + 1.5 = 2.687 + 1.5 = 4.19σ
Sigma level to DPMO (1.5σ shift)
| Sigma level | DPMO | Yield |
|---|---|---|
| 1σ | 691,462 | 30.8538% |
| 1.5σ | 500,000 | 50.0000% |
| 2σ | 308,538 | 69.1462% |
| 2.5σ | 158,655 | 84.1345% |
| 3σ | 66,807 | 93.3193% |
| 3.5σ | 22,750 | 97.7250% |
| 4σ | 6,210 | 99.3790% |
| 4.5σ | 1,350 | 99.8650% |
| 5σ | 232.6 | 99.9767% |
| 5.5σ | 31.7 | 99.9968% |
| 6σ | 3.4 | 99.9997% |
Notes
- Without the 1.5σ shift (short-term sigma), subtract 1.5 from the sigma levels above.
- For a measured characteristic with specification limits, use the process capability calculator — Cpk × 3 is the short-term sigma level.
Frequently asked questions
How do I calculate DPMO?
DPMO = defects ÷ (units × opportunities per unit) × 1,000,000. With 27 defects in 1,500 units having 5 opportunities each, DPMO = 27 ÷ 7,500 × 10⁶ = 3,600.
How is DPMO converted to a sigma level?
Sigma level = z(1 − DPMO/10⁶) + 1.5, where z is the inverse of the standard normal distribution. The 1.5 is the conventional allowance for the process mean drifting over the long term.
Why is six sigma 3.4 defects per million and not 0.001?
A pure 6σ distance to the limit gives about 0.001 ppm, but Six Sigma assumes the mean shifts 1.5σ in the long run, leaving 4.5σ to the nearest limit — and 4.5σ corresponds to 3.4 ppm.
What is an opportunity?
A distinct chance for a defect that the customer cares about and that you check — for example each solder joint on a board. Define opportunities consistently, because counting more of them lowers DPMO.