Choose the denominator
Select metric conversion, defective units or individual defects per opportunity.
Inputs
Direct conversion between defective-unit PPM and DPMO assumes one defect opportunity per unit.
Direct conversion between defective-unit PPM and DPMO assumes one defect opportunity per unit.
Enter a number, e.g. 250 or 0.025.
Count each defective unit once, even if it has multiple defects.
Use nonnegative whole counts.
Use nonnegative whole counts.
Count individual defects and define opportunities per unit consistently.
Use nonnegative whole counts.
Use nonnegative whole counts.
A positive whole number.
One-sided normal conversion; not a measurement of process capability.
Result
- Defective units per million (PPM)
- Defect percentage (%)
- DPMO
- Sigma level
The metrics describe your inputs. Binding targets depend on your inspection definition.
PPM and DPMO are numerically equal here assuming one defect opportunity per unit. Sigma level is a one-sided model conversion.
A calculator by SYMESTIC.
How the calculator works
A short guide in three steps
Define the denominator, enter the data and read the metrics.
Enter your data
Use one consistent inspection period. Set the sigma shift to match your convention.
Check the result
Read the definitions and assumptions. Multiple defects in one unit do not mean multiple defective units.
Formulas
PPM = defective units ÷ inspected units × 1,000,000
Defect percentage (%) = PPM ÷ 10,000
DPMO = defects ÷ (units × opportunities per unit) × 1,000,000
Sigma = Φ⁻¹(1 − DPMO ÷ 1,000,000) + shift
DPMO = [1 − Φ(Sigma − shift)] × 1,000,000
Frequently asked questions
PPM, DPMO and sigma explained
Definitions and limits of conversion.
What does defective-unit PPM mean?
Defective-unit PPM counts defective units per million inspected units. One percent equals 10,000 PPM.
When are PPM and DPMO equal?
When there is exactly one defect opportunity per unit and the same defect definition. With multiple opportunities, distinguish defective units from individual defects.
How is sigma level calculated?
The calculator uses the one-sided inverse standard normal distribution of the defect-free proportion and optionally adds 1.5. This is a convention, not directly measured process capability.
What do zero defects mean?
Zero observed defects yield zero PPM or DPMO and mathematically unbounded sigma. A finite sample does not prove the population is defect free.
Which inputs are allowed?
Nonnegative whole counts, positive units and opportunities. Defects cannot exceed the total number of opportunities.