SAT Geometry Formulas You Can’t Miss

Preparing for the U.S. SAT exam can feel like climbing a mountain — especially when it comes to the math section. While the majority of the math questions emphasise algebra and data analysis, the geometry (and trigonometry) portion cannot be ignored. Fortunately, by focusing on the SAT geometry formulas that you can’t miss, you’ll gain confidence, speed and accuracy.

In this article, we’ll cover:

• Why geometry matters on the SAT

• What geometry formulas are provided on the test vs. what you must memorise

• A comprehensive list of the MUST-KNOW geometry formulas (with explanations and tips)

• How to study and apply these formulas effectively on test day

• Common pitfalls and how to avoid them

Why Geometry Formulas Matter on the SAT

Although geometry questions tend to make up a smaller portion of the SAT Math section compared to algebra, they still matter a great deal. According to test-prep experts, geometry represents about 10

Why does that matter? Because:

• A missed geometry question can cost you points you didn’t plan to lose.

• Many geometry problems are formula-based and hence can be solved more quickly if you recognise the pattern.

• Some formulas appear directly on the formula sheet provided during the test — meaning you don’t have to memorise them — but others do not. Knowing which is which is key.

• Geometry questions often combine shapes, volumes, areas, special triangles, circle relationships, etc., so mastering the associated formulas gives you a toolkit for fast problem-solving.

In short: mastering the core SAT geometry formulas gives you one of the highest “return on investment” tasks in your SAT math prep.

What You Get on the SAT Formula Sheet vs What You Must Memorise

One helpful feature of the current SAT (including the digital version) is that you are provided with a formula/reference sheet at the start of the math section.

On the formula/reference sheet

You will find (for geometry/trigonometry) things like:

• Area of a circle: A=πr²

• Circumference of a circle: C=2πr 

• Area of a rectangle: A=ℓ×w 

• Area of a triangle: A=(1/2)bh

• Pythagorean theorem: a² +b² =c²

• Volume of a rectangular solid: V=ℓwh

• Volume of a cylinder: V=πr²h
  These are listed in several guides.

What you must memorise

Even though many geometry formulas are provided, there are several related formulas and conceptual relationships that are not given on the sheet — yet you may still face problems requiring them. These include:

• Special right triangles side‐ratios (45-45-90, 30-60-90)

• Equation of a circle:

  $(x-h)^2 + (y-k)^2 = r^2$ 

• Length of arc and area of sector of a circle:

  $\tfrac{\theta}{360} \times 2\pi r$and

  $\tfrac{\theta}{360} \times \pi r^2$ 

• Angles in parallel lines, sum of triangle angles = 180°, radians ↔ degrees equivalence (2π radians = 360°)
  Thus your strategy: be very familiar with the formulas on the sheet, and ensure you memorise the “outside” ones that aren’t provided.
  

The Comprehensive List: SAT Geometry Formulas You Can’t Miss

Below is a structured breakdown of the most important geometry formulas you should have at your fingertips. Each section includes the formula, a short explanation/when to use it, and a few quick tips.

1. Area & Perimeter of 2-D Shapes

• Area of a circle:

   

  $$A=\pi r^2$$ 

  Use when you know the radius of the circle.

• Circumference of a circle:

   

  $$C=2\pi r\text{or}C=\pi d$$ 

  Use when you’re asked the “around” measurement.

• Area of a rectangle:

   

  $$A=\mathrm{\ell }\times w$$ 

  Length times width.

• Perimeter of a rectangle:

   

  $$P=2\mathrm{\ell }+2w$$ 

  Often implied, good to know even if not explicitly listed.

• Area of a triangle:

   

  $$A=\frac{1}{2}\times b\times h$$ 

  Base times height (height must be perpendicular to base).

• Area of an equilateral triangle:

   

  $$A=\frac{\sqrt{3}}{4}{s}^2$$ 

  Special case when all sides equal.

• Regular polygon interior angle (for an n-sided regular polygon):

   

  $$\text{Each interior angle}=\frac{(n-2)\times 180\mathrm{°}}{\mathrm{n<span\; style="font-size:\; 16px;\; font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"></span>}}$$ 

  Useful when you see a “regular polygon” geometry question.

2. Triangle & Right Triangle Relationships

• Pythagorean Theorem (right triangles):

   

  $$a^2+b^2=c^2$$ 

  c is hypotenuse.

• Special right triangle 45-45-90:
  Sides in ratio:

   

  $$x : x : x\sqrt2$$​

  Angles are 45°, 45°, 90°.

• Special right triangle 30-60-90:
  Sides in ratio:

   

  $$x:x\sqrt{3}:2x$$ 

  Angles: 30°, 60°, 90°. Often helps avoid full Pythagorean arithmetic.

3. Circle & Arc / Sector Relations

• Length of an arc:

   

  $$L_{\text{arc}}=\frac{\theta }{360\mathrm{°}}\times 2\pi r$$ 

  θ is central angle of the arc

• Area of a sector:

   

  $$A_{\text{sector}}=\frac{\theta }{360\mathrm{°}}\times \pi r^2$$ 

  Think “slice of a pizza.”

• Relationship between degrees & radians:

   

  $$360\mathrm{°}=2\pi \text{radians}$$ 

  Good to recall if a problem uses radians.

4. Volume & Surface Area of 3-D Shapes

• Volume of a rectangular solid (box):

   

  $$V = \ell \times w \times h$$ 

• Volume of a cylinder:

   

  $$V=\pi r^{2}h$$ 

• Volume of a sphere:

   

  $$V=\frac{4}{3}\pi r^3$$ 

  You’ll need to know this even though spheres show up less often.

• Volume of a cone:

   

  $$V=\frac{1}{3}\pi r^{2}h$$ 

• Volume of a pyramid:

   

  $$V=\frac{1}{3}\times (\text{base area})\times h$$ 

  Typically base area =

  $\ell \times w$for rectangular base.

5. Coordinate Geometry & Line / Slope Relations

Though more “algebraic/coordinate” in nature, some geometry problems on the SAT will require these.

• Slope of a line through

  $(x_1, y_1)$and

  $(x_2, y_2)$:

   

  $$m=\frac{y_2-y_1}{x_2-x_{\mathrm{1<span\; style="font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;\; font-size:\; 16px;"></span>}}}$$ 

• Equation of a circle (center

  $(h,k)$, radius

  $r$):

   

  $$(x-h{)}^2+(y-k{)}^2=r^2$$ 

• Distance between two points:

   

  $$d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}$$ 

  Although you might indirectly use this via Pythagorean theorem.

6. Angle & Parallel Lines Relationships

Some geometry questions may pivot on understanding angle relationships rather than shape formulas. Good to keep in mind:

• Sum of internal angles of a triangle = 180°
  

• Parallel lines cut by a transversal: alternate interior angles equal, corresponding angles equal, etc.
  Often tested implicitly.

• In a full circle: 360° = total degrees.
  Use when dividing arcs, sectors.

Tips for Using These Formulas on SAT Day

✅ Recognise when a formula applies

When you see keywords like “base,” “height,” “radius,” “volume,” “surface area,” “arc,” “sector,” immediately ask: which shape is this? Which dimension is given or missing? Which formula fits?

✅ Memorise vs verify

Even though many formulas are on the reference sheet, you still need to know how to apply them. Memorising shape‐formula associations and doing quick mental checks (units, reasonable magnitude) will reduce errors.

✅ Practice with variations

Geometry questions on the SAT often combine pieces: e.g., “What is the volume of a cylinder minus the volume of a cone inside it?” or “What fraction of the circle is shaded? Use the arc length or sector area.” Practice combining formulas.

✅ Know your special triangles

When you spot a right triangle with angles or straightforward integer side lengths (e.g., 3-4-5, 5-12-13, 30-60-90, 45-45-90) you can use the ratios rather than full calculations — this saves time.

✅ Watch units and rounding

SAT often uses π or 3.14 — decide when to keep π symbolic vs approximate. Also track units (cm, inches) and whether answer demands exact value vs rounded.

✅ Use the formula sheet smartly

You may glance at the sheet when stuck — but it’s faster to know the formula so you don’t waste time hunting for it. Having speed is a huge advantage.

✅ Review mistakes

When you practice geometry problems, keep track of which formulas you mis‐applied or forgot. Build flash-cards for the ones you consistently miss.

Common Pitfalls & How to Avoid Them