Area Calculator — Complete Guide
Our area calculator covers every type of area calculation — from simple 2D geometric shapes to complex 3D surface area, body surface area, and roof area. Each calculation shows the formula used with your values substituted in, plus step-by-step working, and automatic unit conversions.
Area and surface area calculator — used in construction, architecture, medicine, and everyday geometry
2D Area Formulas
Circle Area Calculator
Formula: A = π × r². If you know the diameter (d), use r = d/2. The area of a circle grows with the square of the radius — doubling the radius quadruples the area.
📘 Example — Pool with 5m radius
A = π × 5² = 3.14159 × 25 = 78.54 m²
For tiling: buy at least 87 m² (add 10% for waste)
How to Find the Area of a Triangle
For a basic triangle: A = ½ × base × height. Height must be perpendicular to the base. For a right triangle: the two legs ARE base and height, so A = ½ × leg₁ × leg₂. For any triangle when 3 sides are known, use Heron's formula: A = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2.
Hexagon and Polygon Area
Regular hexagon: A = (3√3/2) × s² where s is the side length. Regular polygon with n sides: A = (n × s²) / (4 × tan(π/n)). Hexagons appear in honeycombs, floor tiles, and architectural designs.
3D Surface Area Calculator
Cylinder Surface Area Calculator
Total SA = 2πr² + 2πrh (two circles + lateral surface). Lateral only = 2πrh. Used for canning, pipe insulation, and tank lining calculations.
Cone Surface Area Calculator
Total SA = πr² + πrl where l = slant height = √(r²+h²). Lateral only = πrl. Used in ice cream cone design, traffic cones, and funnel dimensions.
How to Find Surface Area of a Triangular Pyramid
A triangular pyramid has 4 triangular faces. Total SA = base area + 3 × lateral face area. For a regular triangular pyramid with equilateral base of side a and slant height l: SA = (√3/4)a² + (3/2)al. Our calculator handles both regular and irregular cases.
Body Surface Area (BSA) Calculator
Body surface area is used in medicine to calculate drug dosages (especially chemotherapy), renal clearance, and burn treatment coverage. The most widely used formula is the Du Bois formula:
BSA = 0.007184 × H^0.725 × W^0.425 (H in cm, W in kg)
Average adult BSA: Male ≈ 1.9 m², Female ≈ 1.6 m². Our BSA calculator also shows the Mosteller formula (simpler, also widely used): BSA = √(H(cm) × W(kg) / 3600).
Roof Area Calculator
Roof area is calculated from the footprint area × pitch factor. The pitch factor accounts for the roof's slope. For a gabled roof: Roof Area = Footprint × Pitch Factor. Common pitch factors: flat (1.00), 4/12 pitch (1.054), 6/12 pitch (1.118), 8/12 pitch (1.202), 12/12 pitch (1.414). Use our roof calculator to find total area for roofing materials.
How to find length and width from area: Rearrange the rectangle formula. If Area = L × W, then Length = Area ÷ Width. Example: a room with 120 ft² area and 10 ft width → Length = 120 ÷ 10 = 12 ft. Enter area and one dimension in our rectangle mode to find the other.
Roof area calculator — find total roof surface area for shingles, tiles, and waterproofing material estimates
