GeometryFormula

ACT Math Formula Sheet

Curated study set

Unlike the SAT, the ACT provides no formula sheet at all. On test day you are expected to know every area, volume, coordinate, and trigonometry formula from memory. That makes a well-organized study set more valuable for the ACT than for any other exam — and that is exactly what this preset is: a curated “must-memorize” list, not a reproduction of an official sheet (because none exists).

The ACT math section rewards breadth and speed. This set collects the formulas that appear most often: area of rectangles, triangles, trapezoids, and circles; the Pythagorean theorem and the two special right triangles; SOH-CAH-TOA for the trigonometry questions that the SAT largely avoids; the distance, midpoint, and slope formulas for coordinate geometry; and the volumes of boxes, cylinders, spheres, and cones. The bonus section adds the laws of sines and cosines and the equations of a line for the plane-geometry and trig questions that separate top scorers.

A practical tip: the ACT leans harder into trigonometry than the SAT, so do not skip the trig items. Knowing SOH-CAH-TOA cold, plus when to reach for the law of sines versus the law of cosines, can be the difference of several points. Every formula here links to an interactive explorer, which is a faster way to burn the relationships into memory than re-reading a static list.

Print this as your master memorization checklist, then quiz yourself by hiding groups one at a time. Switch between A4 and US Letter to match your printer, trim the list to the topics you still find shaky, and keep the clean two-column layout for quick daily review in the weeks before your test date.

The ACT math section gives you 60 questions in 60 minutes — one minute each — so recall has to be instant; there is no time to derive a formula you half-remember. That time pressure is the real reason the memorization matters more here than on any other exam. Work this sheet in short, frequent sessions rather than one long cram: a few minutes of self-quizzing every day fixes the formulas in long-term memory far better than a single marathon the night before.

Official source: https://www.act.org/

1 · Choose a preset

2 · Pick your formulas

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ACT Math — Formula Sheet

Verified formulas · GeometryFormula.com

Rectangle
AreaA=l⋅wA = l \cdot w
PerimeterP=2(l+w)P = 2(l + w)
Diagonald=l2+w2d = \sqrt{l^2 + w^2}
Triangle
Area (base & height)A=12bhA = \tfrac{1}{2} b h
Area (Heron’s)A=s(s−a)(s−b)(s−c)A = \sqrt{s(s-a)(s-b)(s-c)}
Semiperimeters=a+b+c2s = \dfrac{a+b+c}{2}
PerimeterP=a+b+cP = a + b + c
Trapezoid
AreaA=12(a+b)hA = \tfrac{1}{2}(a + b)h
Medianm=a+b2m = \dfrac{a + b}{2}
Circle
AreaA=πr2A = \pi r^2
CircumferenceC=2πrC = 2\pi r
Diameterd=2rd = 2r
Sector & arc
Sector area (degrees)A=θ360⋅πr2A = \dfrac{\theta}{360}\cdot \pi r^2
Sector area (radians)A=12r2θA = \tfrac{1}{2} r^2 \theta
Arc lengthL=θ360⋅2πrL = \dfrac{\theta}{360}\cdot 2\pi r
Rectangular prism
VolumeV=lwhV = l w h
Surface areaSA=2(lw+lh+wh)SA = 2(lw + lh + wh)
Space diagonald=l2+w2+h2d = \sqrt{l^2 + w^2 + h^2}
Cylinder
VolumeV=πr2hV = \pi r^2 h
Lateral surfaceLSA=2πrhLSA = 2\pi r h
Surface areaSA=2πr(r+h)SA = 2\pi r(r + h)
Cone
Slant heightℓ=r2+h2\ell = \sqrt{r^2 + h^2}
VolumeV=13πr2hV = \tfrac{1}{3}\pi r^2 h
Lateral surfaceLSA=πrℓLSA = \pi r \ell
Surface areaSA=πr(r+ℓ)SA = \pi r(r + \ell)
Sphere
VolumeV=43πr3V = \tfrac{4}{3}\pi r^3
Surface areaSA=4πr2SA = 4\pi r^2
Distance formula
Distanced=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
Midpoint formula
MidpointM=(x1+x22,y1+y22)M = \left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right)
Slope
Slopem=y2−y1x2−x1m = \dfrac{y_2 - y_1}{x_2 - x_1}
Equations of a line
Slope-intercepty=mx+by = mx + b
Point-slopey−y1=m(x−x1)y - y_1 = m(x - x_1)
StandardAx+By=CAx + By = C
Pythagorean theorem
Right trianglea2+b2=c2a^2 + b^2 = c^2
Special right triangles
45–45–90x:x:x2x : x : x\sqrt{2}
30–60–90x:x3:2xx : x\sqrt{3} : 2x
Trig ratios (SOH-CAH-TOA)
Sinesin⁡θ=opphyp\sin\theta = \dfrac{\text{opp}}{\text{hyp}}
Cosinecos⁡θ=adjhyp\cos\theta = \dfrac{\text{adj}}{\text{hyp}}
Tangenttan⁡θ=oppadj\tan\theta = \dfrac{\text{opp}}{\text{adj}}
Law of sines
Law of sinesasin⁡A=bsin⁡B=csin⁡C\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}
Law of cosines
Law of cosinesc2=a2+b2−2abcos⁡Cc^2 = a^2 + b^2 - 2ab\cos C
Free printable geometry formulas · GeometryFormula.com · CC BY-SA 4.0

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Frequently asked questions

What formulas are on the ACT sheet?

The ACT does NOT provide a formula sheet. This is a curated “must-memorize” study set of the formulas the test assumes you know. Use the builder to see every formula, add bonus formulas, and print a clean A4 or US Letter copy.

Is this ACT formula sheet free to print?

Yes — no sign-up, no watermark, no cost. Print it or save it as a PDF from your browser as often as you like.

Can I customize the sheet?

Yes. The preset pre-checks the aligned formulas; you can add or remove any formula, switch paper size, and copy a shareable link to your exact sheet.