Geometry Guide: Area, Volume & Surface Area Formulas for Every Shape (2026)

The six most common 2D area formulas: Rectangle: A = length × width (l × w). Triangle: A = ½ × base × height (½bh). Circle: A = πr² (radius squared times pi). Trapezoid: A = ½(a+b) × h, where a and b are the parallel sides and h is the perpendicular height. Parallelogram: A = base × height (not side length — the height must be perpendicular). Ellipse: A = π × a × b, where a and b are the semi-major and semi-minor axes. Regular polygon: A = (½) × perimeter × apothem. Sector (pizza-slice): A = (θ/360) × πr², where θ is the angle in degrees. For composite shapes, decompose into basic shapes and sum the areas. For cutouts (e.g., a window in a wall), subtract. NIST reference: NIST SI unit standards. Use our area calculator for instant 2D shape results.

Surface area is the total area of all outer faces of a 3D object — imagine flattening the shape into a net. Rectangular box: SA = 2(lw + lh + wh). Cube: SA = 6s². Cylinder: SA = 2πr² + 2πrh (two circular caps + lateral). Sphere: SA = 4πr². Cone (including base): SA = πr² + πrl, where l = √(r² + h²) is the slant height. Cone lateral only: SA = πrl. Square pyramid: SA = b² + 2bl₁, where b is the base side and l₁ is the slant height of each triangular face. Triangular prism: SA = 2 × (triangle base area) + 3 × (rectangle side areas). Practical applications: how much paint covers a wall, how much foil wraps a cylinder, how much concrete forms a retaining wall. Try our surface area calculator for instant results.

Circle fundamentals: Radius (r), Diameter (d = 2r), Circumference (C = 2πr = πd), Area (A = πr²). Arc length: L = (θ/360) × 2πr, where θ is the central angle in degrees. Sector area: A = (θ/360) × πr². Chord length: c = 2r·sin(θ/2). Segment area (region between chord and arc): Aₛₑₜ = sector area − triangle area. Annulus (ring): A = π(R² − r²), where R = outer radius, r = inner radius. Circle equation (coordinate geometry): (x−h)² + (y−k)² = r², centred at (h,k). Practical uses: circular planting beds, pipe cross-sections, swimming pool areas, tank volumes. Use our area calculator with circle and sector modes.

Real-world geometry problems rarely involve a single perfect shape. The composite method: Step 1 — Identify and outline all basic shapes embedded in the composite figure (rectangles, triangles, circles, semicircles). Step 2 — Assign dimensions to each component from the overall dimensions. Step 3 — Calculate each area or volume separately. Step 4 — Add for combined shapes; subtract for holes or cutouts. Examples: L-shaped room = two rectangles. Circular island in a rectangular yard = rectangle minus circle. Arched doorway = rectangle + semicircle. Hollow cylinder = full cylinder volume minus inner cylinder volume. For land surveys with irregular boundaries, use the trapezoidal rule or divide the polygon into triangles and apply the Shoelace formula. Our area calculator supports composite input.

Length: 1 inch = 2.54 cm; 1 foot = 30.48 cm; 1 yard = 0.9144 m; 1 mile = 1.6093 km; 1 metre = 3.2808 ft. Area: 1 sq ft = 144 sq in = 0.0929 sq m; 1 sq m = 10.764 sq ft; 1 acre = 43,560 sq ft = 4,047 sq m; 1 hectare = 10,000 sq m = 2.471 acres; 1 sq mile = 640 acres = 2.59 sq km. Volume: 1 cubic ft = 1,728 cubic in = 7.481 US gal = 0.0283 cubic m; 1 cubic m = 1,000 L = 264.2 US gal = 35.315 cubic ft; 1 US gallon = 231 cubic in = 3.785 L; 1 UK gallon = 4.546 L; 1 litre = 0.264 US gal = 61.02 cubic in. These conversions are defined by NIST in NIST SP 811. Use our unit converter for all geometry conversions.