GeometryFormula

New York Regents Geometry Formula Sheet

Matched to the official reference sheet

The New York Regents Geometry exam gives every student the same reference sheet: the official NYSED “High School Math Reference Sheet,” shared across Algebra I, Geometry, and Algebra II. Knowing exactly what is — and is not — printed on that sheet is a real advantage, because it tells you which formulas you can look up during the test and which ones you must carry in your head.

This preset mirrors the geometry formulas on that official sheet: the area of a triangle (A = ½bh) and parallelogram (A = bh); the area and circumference of a circle (A = πr², C = πd = 2πr); the volume of general prisms (V = Bh), cylinders (V = πr²h), spheres (V = 4⁄3·πr³), cones (V = ⅓πr²h), and pyramids (V = ⅓Bh); and the Pythagorean theorem (a² + b² = c²). These are the formulas the state guarantees you will have.

Notice what the official sheet leaves out. There is no distance formula, no midpoint formula, no slope formula, and no special-right-triangle ratios — yet Regents Geometry questions lean on all of them, especially in the coordinate-geometry and proof sections. That is why this builder adds them as clearly labeled “bonus” formulas: keep them on your study copy while you practice, then hide them to rehearse under true test conditions.

Use the checklist on the left to tailor the sheet to the topics you are reviewing, switch between A4 and US Letter to match your printer, and print a clean two-column page. Every formula here is computationally verified, and each links back to an interactive explorer where you can drag the shape and watch the numbers change — the fastest way to turn a formula you can look up into one you actually understand before June.

The Regents Geometry exam is offered in January, June, and August, and the same reference sheet appears in every administration and across all four high-school math Regents. That consistency is worth exploiting: because the provided formulas never change, the highest-return study time goes into the coordinate-geometry, transformation, and proof skills the sheet does not cover. Print this preset, keep the provided formulas visible while you learn the method, then hide them to rehearse exactly as the real exam will present them.

Official source: https://www.nysed.gov/state-assessment/geometry

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2 · Pick your formulas

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New York Regents 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
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
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}
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
Free printable geometry formulas · GeometryFormula.com · CC BY-SA 4.0

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Frequently asked questions

What formulas are on the NY Regents sheet?

Matched to the official NYSED “High School Math Reference Sheet” (Algebra I, Geometry, Algebra II). Use the builder to see every formula, add bonus formulas, and print a clean A4 or US Letter copy.

Is this NY Regents 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.