Geometry Formulas & Calculators for Students

Geometry Formulas

A simple geometry formulas sheet for the most common 2D and 3D shapes, with examples and calculators for homework checks.

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Direct answer

What are geometry formulas?

Geometry formulas are equations used to calculate measurements such as area, perimeter, circumference, volume, and surface area. Common examples include circle area $A = π r^{2}$ , rectangle area $A = l w$ , cylinder volume $V = π r^{2} h$ , and sphere surface area $S A = 4 π r^{2}$ .

Basic Geometry Formulas

Core measurements

Most geometry problems ask for one of five measurements: area, perimeter, circumference, volume, or surface area.

Measurement	Symbol	Meaning
Area	$A$	Space inside a 2D shape, measured in square units
Perimeter	$P$	Distance around a polygon
Circumference	$C$	Distance around a circle
Volume	$V$	Space inside a 3D solid, measured in cubic units
Surface area	$S A$	Total outside area of a 3D solid

2D Geometry Formulas

Area, perimeter, and circumference formulas

Shape	Formula	Use
Square	$A = s^{2}$	Area from side length s
Square	$P = 4 s$	Perimeter from side length s
Square	$d = s 2$	Diagonal from side length s
Rectangle	$A = l w$	Area from length l and width w
Rectangle	$P = 2 (l + w)$	Perimeter from length and width
Rectangle	$d = l^{2} + w^{2}$	Diagonal from the Pythagorean theorem
Triangle	$A = \frac{1}{2} \times b \times h$	Area from base b and height h
Triangle	$P = a + b + c$	Perimeter from side lengths
Circle	$A = π r^{2}$	Area from radius r
Circle	$C = 2 π r = π d$	Circumference from radius or diameter
Parallelogram	$A = bh$	Area from base b and height h
Parallelogram	$P = 2 (a + b)$	Perimeter from adjacent side lengths
Trapezoid	$A = \frac{1}{2} (a + b) h$	Area from parallel bases a, b and height h
Rhombus	$A = \frac{1}{2} d_{1} d_{2}$	Area from diagonals
Rhombus	$P = 4 s$	Perimeter from side length s

3D Geometry Formulas

Volume and surface area formulas

Shape	Formula	Use
Cube	$V = s^{3}$	Volume from side length s
Cube	$S A = 6 s^{2}$	Surface area from side length s
Rectangular prism	$V = l w h$	Volume from length, width, and height
Rectangular prism	$S A = 2 (l w + l h + w h)$	Surface area
Cylinder	$V = π r^{2} h$	Volume from radius r and height h
Cylinder	$T S A = 2 π r (r + h)$	Total surface area
Cone	$V = \frac{1}{3} π r^{2} h$	Volume from radius and height
Cone	$T S A = π r (r + l)$	Total surface area using slant height l
Sphere	$V = \frac{4}{3} π r^{3}$	Volume from radius r
Sphere	$S A = 4 π r^{2}$	Surface area from radius r

Formula Cards

Copy, save, or print common formulas

Use these cards when you need a formula for notes, class materials, or a quick image export.

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Circle Formulas

Area $A = π r^{2}$

Circumference $C = 2 π r = π d$

Diameter $d = 2 r$

Radius $r = \frac{d}{2}$

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Triangle Formulas

Area $A = \frac{1}{2} bh$

Perimeter $P = a + b + c$

Right triangle $a^{2} + b^{2} = c^{2}$

Heron's formula $A = s (s - a) (s - b) (s - c)$

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Cylinder Formulas

Volume $V = π r^{2} h$

Lateral surface area $L S A = 2 π r h$

Total surface area $T S A = 2 π r (r + h)$

Base area $B = π r^{2}$

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Cone Formulas

Volume $V = \frac{1}{3} π r^{2} h$

Lateral surface area $L S A = π r l$

Total surface area $T S A = π r (r + l)$

Slant height $l = r^{2} + h^{2}$

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Sphere Formulas

Volume $V = \frac{4}{3} π r^{3}$

Surface area $S A = 4 π r^{2}$

Diameter $d = 2 r$

Radius $r = \frac{d}{2}$

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Rectangular Prism Formulas

Volume $V = l w h$

Surface area $S A = 2 (l w + l h + w h)$

Base area $B = l w$

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Geometry Formula Examples

Worked examples

Area of a circle

Given r = 5 cm.
Use $A = π r^{2}$ .
$A = π \times 5^{2} = 25 π \approx 78.54 c m^{2}$ .

Volume of a cylinder

Given r = 3 m and h = 10 m.
Use $V = π r^{2} h$ .
$V = π \times 3^{2} \times 10 = 90 π \approx 282.74 m^{3}$ .

Surface area of a sphere

Given r = 6 in.
Use $S A = 4 π r^{2}$ .
$S A = 4 π \times 6^{2} = 144 π \approx 452.39 i n^{2}$ .

Geometry Calculators

Popular geometry calculators

Use the calculators after reading a formula to check the result, unit, formula, and calculation steps.

Formula Pages

Common shapes

FAQ

Geometry formulas FAQ

What are the most important geometry formulas to memorize?

Start with area, perimeter, circumference, volume, and surface area formulas for square, rectangle, triangle, circle, cylinder, cone, and sphere.

Is this page a geometry formulas sheet?

Yes. It is designed as a geometry formulas sheet for quick reference, with tables, diagrams, examples, and calculators.

What is the difference between perimeter and area?

Perimeter measures distance around a 2D shape. Area measures the amount of flat space inside the shape.

What is the difference between volume and surface area?

Volume measures the space inside a 3D object. Surface area measures the total area of its outside faces or curved surfaces.