The two scales
The PSAT/NMSQT runs from 320 to 1520, made of a Reading and Writing section and a Math section each scored 160 to 760. The SAT runs from 400 to 1600, with each section scored 200 to 800.
The scales are built to line up, which means a 600 on PSAT Math is meant to represent about the same level of ability as a 600 on SAT Math. The difference is at the extremes, where the PSAT simply stops at 760 per section because it does not contain questions hard enough to distinguish above that.
So the honest translation is: your PSAT section score is a reasonable estimate of the SAT section score you would earn right now, with no additional studying, except near the top where the PSAT runs out of room.
The graph of the quadratic function f is shown in the xy-plane. What is the y-coordinate of the vertex of the graph?
Why students often score lower than expected
Two reasons. The first is the ceiling. If you scored near 740 or 760 on a PSAT section, the test did not measure the top of your range, and the equivalent SAT score could be anywhere from around there to 800. The prediction is weakest exactly where students care most about it.
The second is that the PSAT's hardest questions are easier than the SAT's hardest. A student who was comfortable across a PSAT module can meet genuinely harder material on an SAT harder Module 2.
There is also the plain fact that one test on one morning is a noisy measurement. Treat any single score as having real error around it, in both directions.
What the PSAT is actually good for
The domain breakdown, not the total. Your score report splits performance across Craft and Structure, Information and Ideas, Standard English Conventions, and Expression of Ideas on the verbal side, and Algebra, Advanced Math, Problem Solving and Data Analysis, and Geometry and Trigonometry on the math side.
Weight what you find by how much of the test each domain is. Algebra and Advanced Math are each about 35 percent of the Math section, while Geometry and Trigonometry is about 15 percent. A weak Advanced Math showing is worth more than twice the study time of a weak Geometry showing.
The PSAT also gives you a real run at the format: Bluebook, module timing, the break, adaptive routing, the Desmos calculator. That experience transfers directly, and it is free.
Setting an SAT target from a PSAT score
Start from your PSAT total, add nothing for optimism, and then set a target based on the middle 50 percent ranges of the colleges on your list. Those ranges are published by each school in section C9 of its Common Data Set.
The gap between the two numbers is your study plan. A gap of 100 points is a habits and execution problem you can usually close in six to eight weeks. A gap of 250 points is a content problem and needs a longer runway.
Do not set your target off a percentile table. There are several different SAT percentile tables and they change each year, so a number from a blog post is unreliable. Use the college ranges instead, which come from the schools themselves.
National Merit is a separate question
Only the PSAT/NMSQT taken in junior year can qualify you for National Merit. Qualification runs off a Selection Index derived from your section scores, and cutoffs are set by state and change every year, so any fixed cutoff number you see quoted is a guess. National Merit Scholarship Corporation publishes the details each cycle.
That competition has nothing to do with what your PSAT score predicts about your SAT. Keep the two uses of the score separate in your head.