Need to replace existing quick connect rear skewer. How do I measure the length to order a replacement skewer?
It is the internal distance between rear dropouts that defines the replacement QR skewer. The existing skewer can be used as a supplementary information. That distance also matches the hub locknut-to-locknut distance, but the latter is harder to measure because it is hard to insert the caliper between spokes.
The image taken from Sheldon Brown's page.
Make sure to read that page as it has tons of useful info. A quote from there:
Typical quick-release axles are 11 or 12 mm longer than the spacing of the hub locknuts. This gives 5.5-6 mm of axle protrusion on each side.
Measure the distance with a caliper up to 1 mm accuracy. The most common modern values for QR-designated rear dropouts are 135 mm for mountainbike and 130 mm for road bikes. Other things I've heard of are 170 mm and 190 mm for fat bikes and 132.5 mm "gnot right" specific to Surly bikes.
For a new QR skewer it is important that its unthreaded length is not too long, otherwise you will not be able to thread the locknut tight on it.