The scoring system in DDR 4th Mix/Plus is considerably simple (compared to the 3rd Mix). Note: this scoring system is also featured in DDR Gameboy 3.
For each step:

A "Perfect" is worth 777 points
A "Great" is worth 555 points
A "Good" is worth 0 points (stops the combo)
A "Boo" is worth 0 points (stops the combo)
A "Miss" is worth 0 points (stops the combo)

(333 * your current combo count) points

To illustrate (we don't need the number of steps in the song since the scoring system does not base itself on that):

Step 1 (Perfect): 777 + (333 * 1) = 1110
Step 2 (Perfect): Previous Score + 777 + (333 * 2)
= 1110 + 777 + 666
= 2553
Step 3 (Great): Previous Score + 555 + (333 * 3)
= 2553 + 555 + 999
= 4107
Step 4 (Good): Previous Score + 0
= 4107 + 0
= 4107
Step 5 (Perfect): Previous Score + 777 + (333 * 1)
= 4107 + 777 + 333
= 5217

Your stage Grade is calculated as follows:

Each step has a value of two "Dance Points" assigned to it. When you add them all up, you get the maximum number of possible "Dance Points". (Equal to 2 * N)

Your earned "Dance Points" are calculated as follows:

A "Perfect" is worth 2 points
A "Great" is worth 1 points
A "Good" is worth 0 points
A "Boo" will subtract 4 points
A "Miss" will subtract 5 points


AA = All Perfect
A = All Perfect and Great
B = At least 64% of maximum Dance Points
C = Less than 64% of maximum Dance Points
D = Failed
*Note: A grade of AA or A overrides any other grade. If you have less than 80% of maximum Dance Points, but a Full Combo, the A grade overrides the B. Likewise, if you do not have a Full Combo, the highest grade you can get is an B.

Grading system derived by Taren N.

Let C = your combo after stepping.
Let S = your current stage number.

If you are on stage 6 or above,
A Perfect is worth [int(C/4) * (S-5)] ^ 2 + 301 points, and
A Greatis worth = Perfect - 200 points.

Example:
Suppose I have a 41 combo on Stage 125. I get a Perfect for my 42nd combo. I receive...

C = 42, so int(C/4) = 10
S - 5 = 125 - 5 = 120
(10 * 120)^2 + 301 = 1440301 points.

Point of Interest: In regular/nonstop mode, a string of 2447 perfects in a row will overflow the score counter. When you exceed 1,000,000,000 points, the counter only registers 999,999,999.

Note to self: Endless scoring needs revision. My example doesn't come out right according to this picture. In the picture, the rolling digits mean that the step was worth between 11,100,000,000 and 99,900,000,000 points.

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