I give spacings for sowing in rows as that is the simplest way to sow carrot and parsnip. As always the spacings are medium-range suggestions for medium size harvests.
For each way spacing your 3inch idea should give lots of good size roots.
Mostly I sow early carrots in 9inch rows, aiming for two roots per inch, and winter carrots in 12 inch rows, say one per inch.
Parsnips in 12-18 inch rows, and 2-3 inches apart.
