GeometryFormula

Virginia SOL Geometry Formula Sheet

Aligned to the standard reference (draft — verify with your official source)

The Virginia Standards of Learning (SOL) Geometry test provides students with an official VDOE Geometry Formula Sheet during the exam. This preset is aligned to that sheet, collecting the same families of formulas — area, surface area and volume of solids, the Pythagorean theorem, coordinate-geometry formulas, and the basic trigonometric ratios — into a printable, interactive study copy.

The two-dimensional formulas here cover triangles, rectangles, trapezoids, and circles; the three-dimensional formulas cover prisms, cylinders, cones, spheres, and pyramids, with both surface area and volume. Coordinate geometry contributes the distance, midpoint, and slope formulas, and the right-triangle section supplies the Pythagorean theorem, the 45-45-90 and 30-60-90 ratios, and SOH-CAH-TOA. The bonus set adds the rhombus, sectors, equations of a line, and the laws of sines and cosines for deeper review.

Virginia’s SOL geometry questions are strongly standards-referenced, so the highest-value preparation is matching each formula to the specific reporting category it serves — reasoning and proof, lines and angles, triangles, polygons and circles, or three-dimensional figures. Working through the interactive explorer behind each formula, with its live substitution, is an efficient way to connect a formula to the kind of question that uses it.

This preset is marked DRAFT: the formula families are correct, but you should confirm the exact presentation against the current official VDOE Geometry Formula Sheet, which Virginia educators may reproduce for non-commercial classroom use. Once confirmed, choose A4 or US Letter, trim to your unit, and print a clean two-column sheet for focused SOL review.

Virginia has moved its SOL tests to a computer-based, and in many cases computer-adaptive, format, so a smart part of preparation is rehearsing with the formula sheet as an on-screen tool rather than a paper handout — knowing where each formula lives on it saves time under the clock. Print this version to study from at home, then practice locating the same formulas quickly in the digital reference so nothing about the interface slows you down on test day.

Official source: https://www.doe.virginia.gov/teaching-learning-assessment/student-assessment/virginia-sol-assessment-program/sol-test-administration-development/ancillary-test-materials — always confirm formulas against the current official document.

1 · Choose a preset

2 · Pick your formulas

2D shapes
3D solids
Coordinate geometry
Right triangles & trig

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Virginia SOL Geometry — 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}
Rhombus
AreaA=12d1d2A = \tfrac{1}{2} d_1 d_2
Sides=(d1/2)2+(d2/2)2s = \sqrt{(d_1/2)^2 + (d_2/2)^2}
PerimeterP=4sP = 4s
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
General prism
VolumeV=BhV = B h
Surface areaSA=2B+PhSA = 2B + Ph
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
Pyramid
Slant heightℓ=(b/2)2+h2\ell = \sqrt{(b/2)^2 + h^2}
VolumeV=13b2hV = \tfrac{1}{3} b^2 h
Lateral surfaceLSA=2bℓLSA = 2 b \ell
Surface areaSA=b2+2bℓSA = b^2 + 2 b \ell
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 Virginia SOL sheet?

Aligned to the standard VDOE Geometry Formula Sheet. DRAFT — verify against the current Virginia Department of Education document before classroom use. Use the builder to see every formula, add bonus formulas, and print a clean A4 or US Letter copy.

Is this Virginia SOL 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.