Geometry Formulas — 2D & 3D Shapes Reference
Area, perimeter, volume, and surface area formulas for every common shape. Variables are defined inline — no flipping between pages.
2D Shapes
Circle
Circle Calculator →A perfectly round plane figure with every point equidistant from the center.
A = πr²C = 2πrd = 2rTriangle
Triangle Calculator →A polygon with three sides and three interior angles that sum to 180°.
A = ½bhA = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2P = a + b + cRectangle
A four-sided polygon with four right angles and opposite sides equal.
A = l × wP = 2(l + w)d = √(l² + w²)Square
A rectangle with all four sides equal.
A = s²P = 4sd = s√2Trapezoid
A quadrilateral with exactly one pair of parallel sides (the bases).
A = ½(b₁ + b₂) × hP = a + b₁ + c + b₂Parallelogram
A quadrilateral with both pairs of opposite sides parallel and equal.
A = b × hP = 2(a + b)Ellipse
An oval shape defined by two focal points; a circle is a special case where both foci coincide.
A = πabP ≈ 2π√((a² + b²)/2)Regular Hexagon
A six-sided polygon with all sides and angles equal, common in nature and engineering.
A = (3√3/2)s²P = 6s3D Shapes
Sphere
A perfectly round three-dimensional object where every surface point is equidistant from the center.
V = (4/3)πr³SA = 4πr²Cylinder
A solid with two parallel circular bases connected by a curved lateral surface.
V = πr²hLSA = 2πrhSA = 2πr(r + h)Cone
A solid with a circular base tapering to a single apex point directly above the center.
V = (1/3)πr²hl = √(r² + h²)LSA = πrlSA = πr(r + l)Cube
A rectangular prism with all six faces being equal squares.
V = s³SA = 6s²d = s√3Rectangular Prism (Cuboid)
Volume Calculator →A box-shaped solid with six rectangular faces.
V = l × w × hSA = 2(lw + lh + wh)d = √(l² + w² + h²)Square Pyramid
A pyramid with a square base and four triangular faces meeting at an apex.
V = (1/3)s²hl = √(h² + (s/2)²)SA = s² + 2slTorus
A donut-shaped surface of revolution generated by revolving a circle in 3D space.
V = 2π²Rr²SA = 4π²RrVariable Key
rradiusddiameterhheightbbase lengthsside lengthllength or slant heightwwidtha, b, cside lengths (triangle)Rmajor radius (torus)π≈ 3.14159AareaVvolumeSAsurface areaPperimeterCcircumferenceCalculate areas and volumes instantly
Our math and construction calculators handle the arithmetic for you — just enter your measurements.