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Digital SAT Math Formulas: The 20 You Need, and 12 You Don't

GuidesRivie Prep Team9 min read

Most 'SAT formula lists' online are bloated with 40 or more formulas, half of which are already on the Bluebook reference sheet or rarely tested. Here's what you actually need, and what you can stop studying.

In short

  • The Bluebook reference sheet gives you 12 formulas for free on every math question. Stop memorizing those.
  • 20 formulas show up often enough on the Digital SAT to justify memorization.
  • A handful more are nice-to-haves: probability, sequences, complex numbers.
  • The formulas students most often over-study (Heron's, law of cosines, trapezoid midsegment) almost never appear.

The Digital SAT's Bluebook app includes a reference sheet visible on every math question. A lot of 'must-memorize' lists still circulating online were written for the paper SAT, back when no reference sheet existed. For the test you're actually taking, memorizing what's already on the reference sheet is wasted effort.

This article sorts every formula you might encounter into three groups: already on the reference sheet (don't memorize), worth memorizing (do memorize), and over-studied (skip).

On the Bluebook reference sheet: don't memorize

These 12 formulas are always visible during the test. Know what they mean and when to reach for them, but don't burn flashcard time on them.

TopicFormula (as shown on the reference sheet)
Area of a circleA = πr²
Circumference of a circleC = 2πr
Area of a rectangleA = ℓw
Area of a triangleA = ½bh
Pythagorean theorema² + b² = c²
Volume of a rectangular boxV = ℓwh
Volume of a cylinderV = πr²h
Volume of a sphereV = (4/3)πr³
Volume of a coneV = (1/3)πr²h
Volume of a pyramidV = (1/3)ℓwh
30-60-90 right trianglesides in ratio 1 : √3 : 2
45-45-90 right trianglesides in ratio 1 : 1 : √2
All twelve are on every math question's reference panel. You can't 'forget' them under pressure.

The 20 formulas worth memorizing

These aren't on the reference sheet, and they come up often enough that reaching for them fluently is a meaningful speed advantage.

Algebra (6)

  • Slope from two points: m = (y₂ − y₁) / (x₂ − x₁).
  • Point-slope form: y − y₁ = m(x − x₁). Faster than slope-intercept for building a line through a known point.
  • Parallel lines share the same slope. Perpendicular lines have slopes that are negative reciprocals.
  • Distance between two points: d = √((x₂ − x₁)² + (y₂ − y₁)²). A Pythagorean application, worth having as a one-step memory.
  • Midpoint: ((x₁ + x₂)/2, (y₁ + y₂)/2).
  • For a system of two linear equations to have no solution, the lines are parallel (same slope, different intercepts). For infinitely many solutions, they're identical (one equation is a scalar multiple of the other).

Advanced math (7)

  • Quadratic formula: x = (−b ± √(b² − 4ac)) / (2a).
  • Discriminant: b² − 4ac. Positive means two real solutions, zero means one repeated solution, negative means no real solutions.
  • Vertex form: a(x − h)² + k has vertex (h, k). Positive a opens up (min at k), negative a opens down (max at k).
  • Sum and product of roots (Vieta's): for ax² + bx + c = 0, sum = −b/a, product = c/a.
  • Factor theorem: (x − r) is a factor of p(x) if and only if p(r) = 0.
  • Difference of squares: a² − b² = (a + b)(a − b).
  • Exponential growth or decay: y = a · b^x. When b > 1 it's growth; when 0 < b < 1 it's decay. Growth rate r as a percent: multiplier is 1 + r.

Problem-solving and data (4)

  • Percent change: (new − old) / old × 100%. Always divide by the original value, never the new one.
  • Mean from sum: mean × count = sum. Most 'find the missing value' mean problems resolve to this one line.
  • Probability: favorable outcomes / total outcomes. For conditional probability P(A|B), the denominator is total(B), not total overall.
  • Margin of error interpretation: the confidence interval applies to the population parameter, not the sample. 'We are 95% confident the true percentage is in [X, Y].'

Geometry and trig (3)

  • SOH-CAH-TOA: sin = opposite / hypotenuse, cos = adjacent / hypotenuse, tan = opposite / adjacent. Complements: sin(x) = cos(90° − x).
  • Arc length: s = (θ/360°) × 2πr. Sector area: A = (θ/360°) × πr². Both are the whole-circle formula scaled by the angle fraction.
  • Circle equation: (x − h)² + (y − k)² = r², with center (h, k) and radius r. Watch the sign of h and k. An equation written with (x + 3)² has center x = −3, not x = 3.

The highest-leverage memorization

If you memorize only three of these: the quadratic formula, percent change (watch the base), and vertex form. Those three appear on every Digital SAT Math section in some form.

The 12 formulas you can skip

These appear so rarely on the Digital SAT that memorizing them is poor return on study time. If one shows up, you can derive it or flag and skip.

  • Heron's formula for triangle area.
  • Law of cosines and law of sines. Non-right-triangle problems are almost never set up requiring these.
  • Arithmetic-sequence sum formulas. SAT-style sequences are short enough to add by hand.
  • Compound interest in full form. It's almost always a plain exponential problem in disguise.
  • Most matrix operations.
  • Volume of any regular polyhedron beyond the standard shapes on the reference sheet.
  • Trapezoid area via midsegment.
  • Polar coordinates.
  • Binomial expansion beyond (a ± b)².
  • The standard-deviation formula. You need to understand what SD measures, not compute it.
  • Z-scores.
  • Log change-of-base. If it shows up, use Desmos.

When Desmos replaces memorization

Bluebook includes a graphing Desmos calculator on every math question. For any equation you can key in (quadratics, systems, trig, log and exponential), Desmos is almost always faster than remembering the formula and solving by hand. Use it.

How to memorize formulas that don't stick

Flashcards of the formula alone don't work. What actually works: write each formula on a sticky note, then solve two problems that use it. One where the formula is the direct tool, one where it's applied inside a word problem. The problem-solving step is what forms the retrievable memory.

If a formula hasn't stuck after a week of doing that, it almost certainly means you don't yet have the conceptual hook for it. Slope through two points, for example, clicks once you see it as rise-over-run on a specific graph. It never clicks as a symbolic rule.


Rivie's practice tests tag every missed math item with its trap pattern (slope_inversion_or_sign, percent_change_base, vertex_x_vs_y_coordinate, and so on). When you review, you find out not just that you missed a formula question, but which specific formula trap keeps catching you. Those names match the ones in the reference sheets above.

SAT math formulasDigital SAT mathBluebook reference sheetformulas to memorize

Frequently asked questions

Still stuck? Write to help@rivie.org. Prices are on the pricing page.

What math formulas are on the Digital SAT reference sheet?

The Bluebook reference sheet shows 12 formulas on every math question: areas of circles, rectangles, and triangles; circle circumference; the Pythagorean theorem; volumes of rectangular boxes, cylinders, spheres, cones, and pyramids; and the side ratios for 30-60-90 and 45-45-90 triangles. These are visible live during the test, so memorizing them is low-value.

Do I really not need to memorize the Pythagorean theorem?

Correct. The Pythagorean theorem is on the reference sheet. You should absolutely understand when to reach for it (any right-triangle side problem, any distance-formula-style coordinate problem), but you don't need to memorize the equation itself.

How many formulas actually come up on the Digital SAT Math section?

Around 20 off-reference formulas are worth memorizing because they appear often enough to justify the study time. Another dozen or so appear in advanced practice materials but almost never on the real test. Memorizing those is a poor use of preparation time.

Should I use Desmos or memorize formulas?

Both. Memorize the core 20 formulas listed above so that recognizing which tool to reach for is automatic. But Desmos, available on every math question, is faster than pen-and-paper for graphing, solving systems, checking factoring, and exploring functions. Use it aggressively for setup and verification, not as a replacement for understanding.

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