Volume of Geometric Solids Calculator
Calculate the volume of geometric solids online: cube, cuboid, sphere, cylinder, cone, square pyramid and triangular prism. Instant results with formulas and examples.
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Area of Geometric Shapes Calculator
The area of geometric shapes calculator lets you compute the surface area and perimeter of any common flat figure in seconds. Simply select the shape — square, rectangle, triangle, circle, trapezoid, rhombus, regular hexagon or ellipse — enter the required dimensions, and the calculator applies the correct mathematical formula instantly, returning results accurate to four decimal places. This tool is useful for students checking geometry homework, interior designers and landscape architects planning surface areas, and anyone who needs a quick area calculation in practical situations — from floor tiles to building plots. All formulas used are standard Euclidean geometry formulas: circle area π·r², triangle area a·h/2, regular hexagon area 3√3·a²/2, and more.
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How we calculate the area
Square: A = a². Rectangle: A = a × b. Triangle: A = (a × h) / 2. Circle: A = π × r². Trapezoid: A = (a + b) × h / 2. Rhombus: A = (d₁ × d₂) / 2. Regular hexagon: A = 3√3 × a² / 2. Ellipse: A = π × a × b. Perimeters are calculated using the respective formulas; the ellipse perimeter uses Ramanujan's approximation.
Example: area of a rectangle 8 m × 5 m
For a rectangle with sides a = 8 m and b = 5 m: area = 8 × 5 = 40 m², perimeter = 2 × (8 + 5) = 26 m. For a circle with radius r = 7 m: area = π × 7² ≈ 153.9380 m², circumference = 2 × π × 7 ≈ 43.9823 m.
Frequently asked questions
What is the formula for the area of a circle?
The area of a circle is A = π × r², where r is the radius (the distance from the centre to the edge). For example, a circle with r = 5 m has area A = π × 25 ≈ 78.5398 m².
How do you calculate the area of a triangle?
The most common formula is A = (base × height) / 2, where the height is perpendicular to the chosen base. Alternatively, use Heron's formula when all three side lengths are known: A = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2.
What is the difference between area and perimeter?
Area measures the surface enclosed by a shape (in square units, e.g. m²), while perimeter measures the total length of the boundary of the shape (in linear units, e.g. m). Both can be calculated for the same figure.
How do you find the area of a trapezoid?
The area of a trapezoid is A = (a + b) × h / 2, where a and b are the lengths of the two parallel sides (bases) and h is the perpendicular height between them.
What is the formula for the area of a rhombus?
The area of a rhombus equals half the product of its diagonals: A = (d₁ × d₂) / 2. Alternatively, A = a² × sin(α), where a is the side length and α is one of the interior angles.
How is the area of a regular hexagon calculated?
For a regular hexagon with side length a, the area is A = (3√3 / 2) × a². A regular hexagon consists of six equilateral triangles, each with area (√3 / 4) × a².
What is the formula for the area of an ellipse?
The area of an ellipse is A = π × a × b, where a is the semi-major axis and b is the semi-minor axis. When a = b = r, the ellipse becomes a circle and the formula reduces to π × r².
How do I convert area from m² to cm²?
1 m² = 10 000 cm². To convert, multiply by 10 000. For example, 2.5 m² = 25 000 cm². Similarly, 1 m² = 1 000 000 mm² and 1 ha = 10 000 m².
Can I use this calculator for real-world construction projects?
Yes, the calculator is accurate enough for planning and estimating purposes (flooring, garden beds, wall paint coverage, etc.). For official surveys, legal land measurements or structural engineering, always have the results verified by a licensed professional.
What units does the calculator use?
The calculator works with any consistent unit system. If you enter dimensions in metres, the area result is in m² and the perimeter in m. If you enter centimetres, results are in cm² and cm. Make sure all inputs use the same unit.
Results are for informational and educational purposes only. For construction, surveying and engineering applications we recommend having calculations verified by a professional.