How do you calculate long-term sigma from short-term sigma?

Subtract the total sigma shift from short-term sigma. With Zst = 4.5 and a 1.5σ shift, Zlt = 4.5 − 1.5 = 3.0 sigma.

Why is the sigma shift 1.5?

It is an empirical value Motorola derived from observing that processes centered in the short term drift by roughly 1.5σ over the long term. It is a convention, so you can override it with a measured drift.

What is the difference between Zst and Zlt?

Zst (short-term sigma) reflects the process's inherent, best-case capability from a short study; Zlt (long-term sigma) accounts for drift and shift customers see over time. Here 4.5 short-term maps to 3.0 long-term.

Does a 4.5 sigma short-term process equal Six Sigma?

No. A true short-term Six Sigma process is Zst = 6.0, which after the 1.5σ shift yields Zlt = 4.5 (about 3.4 DPMO). A Zst of 4.5 gives Zlt = 3.0, roughly 66,800 DPMO.

Can I use a shift other than 1.5 sigma?

Yes. Enter your own value in the sigma shift field, or add extra drift in the additional and adjustment fields if you have data showing your process moves more than the standard 1.5σ.

What does the utilization percentage mean here?

It shows how much of the short-term sigma survives as long-term capability — 3.0 of 4.5 is 66.7%, so a third of the headline capability is lost to drift.

Quality & Metrology calculator

Sigma Shift Calculator

Sigma shift is the correction Six Sigma practitioners apply when translating a short-term process capability (Zst) into the long-term sigma level (Zlt) a customer actually experiences over weeks and months. The convention, popularized by Motorola, is that a process centered in the short run will drift by about 1.5 sigma over time due to tool wear, batch variation, and operator changes. Quality engineers, Black Belts, and process owners use this metric so a headline 'Six Sigma' short-term capability is honestly reported as roughly 4.5 sigma long-term (3.4 DPMO). It matters because quoting Zst without the shift overstates real-world yield.

What this calculator does

Convert a short-term process sigma to a long-term sigma by subtracting the standard 1.5 sigma shift.
Use it to translate short-term capability into the long-term sigma level used in Six Sigma reporting.
It subtracts a total sigma shift (the 1.5σ convention plus any additional drift you specify) from short-term sigma to give the long-term sigma level Zlt.

Formula used

Total shift = sigma shift + additional drift + further adjustment
Long-term sigma (Zlt) = short-term sigma - total shift

Inputs explained

Short-term sigma (Zst):
Sigma shift (typically 1.5σ):
Additional process drift:
Further sigma adjustment:

How to use the result

Use it when converting a short-term capability study (Zst or Cpk-derived) into the long-term sigma level you report to customers or use for DPMO estimates.
The 1.5σ shift is an empirical rule of thumb, not a law — your actual long-term drift may be larger or smaller and should be verified with a long-term capability study when data allows.

Current U.S. benchmarks

U.S. manufacturing runs at 75.6% of capacity (Federal Reserve, May 2026). New factory orders are up 2.3% year over year (Census).

Common questions

How do you calculate long-term sigma from short-term sigma? Subtract the total sigma shift from short-term sigma. With Zst = 4.5 and a 1.5σ shift, Zlt = 4.5 − 1.5 = 3.0 sigma.
Why is the sigma shift 1.5? It is an empirical value Motorola derived from observing that processes centered in the short term drift by roughly 1.5σ over the long term. It is a convention, so you can override it with a measured drift.
What is the difference between Zst and Zlt? Zst (short-term sigma) reflects the process's inherent, best-case capability from a short study; Zlt (long-term sigma) accounts for drift and shift customers see over time. Here 4.5 short-term maps to 3.0 long-term.
Does a 4.5 sigma short-term process equal Six Sigma? No. A true short-term Six Sigma process is Zst = 6.0, which after the 1.5σ shift yields Zlt = 4.5 (about 3.4 DPMO). A Zst of 4.5 gives Zlt = 3.0, roughly 66,800 DPMO.
Can I use a shift other than 1.5 sigma? Yes. Enter your own value in the sigma shift field, or add extra drift in the additional and adjustment fields if you have data showing your process moves more than the standard 1.5σ.

Last reviewed 2026-05-12.