The shape atlas · get to know the shapes
2D & 3D shapes: properties and formulas
Explore their properties, compare formulas, and try a calculation on every page.
2D · quadrilateral
Rectangle
A = w × h
Explore the rectangle ↗2D · curved shapeCircle
A = πr²
Explore the circle ↗2D · polygonTriangle
A = ½bh
Explore the triangle ↗2D · quadrilateralTrapezoid
A = ½(a + b)h
Explore the trapezoid ↗3D · curved solidSphere
V = ⁴⁄₃πr³
Explore the sphere ↗3D · curved solidCylinder
V = πr²h
Explore the cylinder ↗3D · curved solidCone
V = ⅓πr²h
Explore the cone ↗3D · polyhedronRectangular prism (cuboid)
V = w × h × d
Explore the rectangular prism ↗Compare the formulas
Use matching length units throughout. Area and surface area use squared units; volume uses cubed units.
| Shape | Measurement | Formula |
|---|---|---|
| Rectangle | Area | A = wh |
| Rectangle | Perimeter | P = 2(w + h) |
| Circle | Area | A = πr² |
| Circle | Circumference | C = 2πr = πd |
| Triangle | Area | A = bh / 2 |
| Triangle | Area from three sides | A = √[s(s − a)(s − b)(s − c)] |
| Trapezoid | Area | A = (a + b)h / 2 |
| Trapezoid | Perimeter | P = a + b + c + d |
| Sphere | Volume | V = 4πr³ / 3 |
| Sphere | Surface area | S = 4πr² |
| Cylinder | Volume | V = πr²h |
| Cylinder | Total surface area | S = 2πr² + 2πrh = 2πr(r + h) |
| Cone | Volume | V = πr²h / 3 |
| Cone | Total surface area | S = πr(r + ℓ) = πr² + πrℓ |
| Rectangular prism (cuboid) | Volume | V = whd (length × width × height) |
| Rectangular prism (cuboid) | Surface area | S = 2(wh + wd + hd) |