GeometryFormula

Basic Middle-School Geometry Formula Sheet

Curated study set

This basic preset is built for middle-school geometry, roughly grades 6 through 8, where the goal is confidence with the essential shapes before high-school geometry raises the stakes. It focuses on the formulas that show up again and again: the area and perimeter of flat shapes and the volume of the most common solids, with nothing that would overwhelm a student meeting these ideas for the first time.

The core set covers squares, rectangles, triangles, parallelograms, trapezoids, and circles in two dimensions, and cubes, rectangular prisms, and cylinders in three. These nine shapes carry the vast majority of middle-school geometry problems — from finding the area of a garden to the volume of a fish tank. Each formula uses the same clear variable names throughout the site, so students never have to relearn notation as they move from one shape to the next.

The bonus section introduces three ideas that bridge into high school: the Pythagorean theorem, and the volumes of spheres and cones. Adding them is a gentle way to stretch a strong student without changing the friendly scope of the core sheet. Because every formula links to an interactive explorer, a curious student can drag a rectangle wider or a cylinder taller and see the area or volume respond — which turns an abstract formula into something concrete and memorable.

For teachers, this makes a clean handout for a unit review or a take-home reference; for parents, it is a simple, correct sheet to support homework. Choose A4 or US Letter, keep or trim the shapes to match the current unit, and print a tidy two-column page that a middle-schooler can actually read and use.

These formulas line up with the Common Core middle-school geometry expectations: finding area, surface area, and volume in grade 6; working with scale, angles, and circles in grade 7; and applying the Pythagorean theorem and volume of cones, cylinders, and spheres in grade 8. Building the sheet alongside the current unit — checking on new shapes as the class reaches them — turns it into a running record of what a student has learned, which is far more motivating than handing over every formula at once.

1 · Choose a preset

2 · Pick your formulas

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

3 · Print or share

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Basic Middle-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}
Circle
AreaA=πr2A = \pi r^2
CircumferenceC=2πrC = 2\pi r
Diameterd=2rd = 2r
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}
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
Pythagorean theorem
Right trianglea2+b2=c2a^2 + b^2 = c^2
Free printable geometry formulas · GeometryFormula.com · CC BY-SA 4.0

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Frequently asked questions

What formulas are on the Basic (Middle School) sheet?

A curated starter set for middle-school geometry (grades 6–8). Use the builder to see every formula, add bonus formulas, and print a clean A4 or US Letter copy.

Is this Basic (Middle School) 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.