GeometryFormula

Complete High-School Geometry Formula Sheet

Curated study set

This is the complete high-school geometry reference — every formula on the site gathered into a single printable, interactive sheet. It is the right choice when you want one comprehensive cheat sheet to cover a full geometry course, prepare for a cumulative final, or keep a master reference on the wall for the whole year.

The sheet spans four areas. In two dimensions you get area and perimeter for squares, rectangles, triangles, parallelograms, trapezoids, rhombuses, circles, sectors, and regular polygons. In three dimensions you get volume and surface area for cubes, prisms, cylinders, cones, spheres, hemispheres, and pyramids. Coordinate geometry contributes distance, midpoint, slope, the section formula, and the equations of a line. Right-triangle work adds the Pythagorean theorem, the special right triangles, SOH-CAH-TOA, and the laws of sines and cosines.

Because it is comprehensive, this sheet is best used with the checklist on the left: start from “everything,” then uncheck the topics you have already mastered so your printed copy focuses on what you still need. Every formula uses consistent variable names and is computationally verified, and each links to an interactive explorer where you can drag the shape and read the full step-by-step substitution — the difference between a formula you can recite and one you can apply under pressure.

For a cumulative review, print the whole thing and work through it group by group. For a targeted session, trim to a single area and print just that. Either way, switch between A4 and US Letter to match your printer, and keep the clean two-column layout that makes the sheet fast to scan the night before a test.

Because it draws every formula from the same verified source that powers the site’s explorers and passes an automated test on each build, this complete sheet is also a dependable teaching artifact: a handout you can trust not to contain the small errors that plague photocopied cheat sheets. Pin it up for the year, hand it out at the start of a course as a roadmap, or use it at the end as a checklist of everything a student should be able to apply — one accurate page covering all of high-school geometry.

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Complete High-School Geometry — Formula Sheet

Verified formulas · GeometryFormula.com

Square
AreaA=s2A = s^2
PerimeterP=4sP = 4s
Diagonald=s2d = s\sqrt{2}
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
Parallelogram
AreaA=bhA = b h
PerimeterP=2(a+b)P = 2(a + b)
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
Regular polygon
PerimeterP=nsP = n s
Apothema=s2tan⁡(180∘/n)a = \dfrac{s}{2\tan(180^\circ/n)}
AreaA=12aPA = \tfrac{1}{2} a P
Interior angle(n−2)⋅180∘n\dfrac{(n-2)\cdot 180^\circ}{n}
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
Cube
VolumeV=s3V = s^3
Surface areaSA=6s2SA = 6s^2
Space diagonald=s3d = s\sqrt{3}
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}
General prism
VolumeV=BhV = B h
Surface areaSA=2B+PhSA = 2B + Ph
Triangular prism
VolumeV=Abase⋅LV = A_{base}\cdot L
Surface areaSA=2Abase+(a+b+c)LSA = 2A_{base} + (a+b+c)L
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
Hemisphere
VolumeV=23πr3V = \tfrac{2}{3}\pi r^3
Curved surface2πr22\pi r^2
Total surface areaSA=3πr2SA = 3\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}
Section formula
Ratio m : nP=(mx2+nx1m+n,my2+ny1m+n)P = \left(\dfrac{m x_2 + n x_1}{m + n}, \dfrac{m y_2 + n y_1}{m + n}\right)
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 Complete (High School) sheet?

The complete high-school geometry reference — every formula on the site. Use the builder to see every formula, add bonus formulas, and print a clean A4 or US Letter copy.

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