Six Sigma Calculator

This Six Sigma calculator turns defect counts into the standard Six Sigma measures: sigma level, DPMO and yield. Enter the units you inspected, the opportunities for a defect on each unit and the defects you found.

Units inspectedunitsOpportunities per unitDistinct chances for a defect that mattersper unitDefects founddefectsApply the conventional 1.5 sigma shift

Process sigma level

4.39

DPMO: 1,900
Yield: 99.810%

Your process against the spec limitLong-term spread of the process. The orange tail is the share that falls outside.

The limit sits 2.89 standard deviations from the mean of the long-term data; the orange tail is the share outside it. The sigma level above adds the 1.5 shift when it is ticked.

Example values are filled in. Replace them with your own; nothing you type leaves your browser.

Worked example

The example values, step by step

Step 1 · Opportunities
5,000 units × 4 per unit
= 20,000
Step 2 · DPMO
38 defects ÷ 20,000 × 1,000,000
= 1,900
Step 3 · Yield
1 − 1,900 ÷ 1,000,000
= 99.81%
Step 4 · Long-term sigma
Inverse normal of 0.9981
= 2.89
Step 5 · Process sigma
2.89 + 1.5 shift
= 4.39

Reading the result

In the example, 1,900 defects per million opportunities works out to about 4.4 sigma with the conventional shift, or 2.9 without it.

Always say whether a sigma level includes the 1.5 shift. Two teams can report different numbers for the same data otherwise.

DPMO at whole sigma levels (with the 1.5 shift)

Sigma level	DPMO
2	308,538
3	66,807
4	6,210
5	233
6	3.4

Computed from the normal distribution with a 1.5 sigma shift, the same way as the calculator.

Common data mistakes

Counting trivial opportunities, which inflates the sigma level without any improvement.
Mixing defects and defective units. One unit can have several defects.
Reporting a sigma level from data that has not passed a measurement system check.

The methods behind the number

The formula

How it's calculated

DPMO: Defects ÷ (Units × Opportunities per unit) × 1,000,000
Yield: 1 − (DPMO ÷ 1,000,000)
Sigma level: Inverse normal of yield + 1.5 shift

Define opportunities carefully

An opportunity is a chance for a defect that matters to the customer. Counting trivial opportunities inflates the sigma level without improving anything.

About the 1.5 sigma shift

By convention, sigma tables add a 1.5 sigma shift to allow for drift over time. This calculator follows that convention; turn it off to see the long-term figure.

Check the measurement first

Sigma levels are only as good as the defect data. A measurement system analysis is worth doing before you report results.

Frequently asked questions

What does Six Sigma mean in numbers?

With the conventional 1.5 shift, a six sigma process produces about 3.4 defects per million opportunities.

Should I use defects or defective units?

DPMO counts defects, and a single unit can have several. If you only know defective units, set opportunities per unit to one.

Can sigma level be negative?

Mathematically, yes, for extremely poor yields. In practice, it signals that the process needs basic stabilization before Six Sigma metrics are useful.

How do you calculate sigma level?

Work out DPMO from defects, units and opportunities, convert it to yield, then take the inverse normal of the yield. Add 1.5 if you follow the conventional shift.

Why add a 1.5 sigma shift?

It is a convention from Motorola's Six Sigma program, meant to allow for drift over time. Some statisticians question it, so state whether your figure includes it.

What is the difference between DPMO and PPM?

DPMO counts defects per million opportunities. PPM usually counts defective parts per million units. One part can hold several defect opportunities.

Sources and further reading

For vendors

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