Geometry Calculator
Calculate area, perimeter, volume, and surface area for various 2D and 3D shapes with our comprehensive geometry calculator.
Understanding Geometry
Geometry is the branch of mathematics that deals with the properties, measurement, and relationships of points, lines, angles, surfaces, and solids. Our geometry calculator helps you calculate various properties of 2D and 3D shapes.
2D Shapes
Two-dimensional shapes are flat shapes that have only length and width, but no thickness. Common 2D shapes include:
Rectangle
A rectangle is a quadrilateral with four right angles.
Area = Length × Width
Perimeter = 2 × (Length + Width)
Circle
A circle is a round shape where all points on the edge are the same distance from the center.
Area = π × Radius²
Circumference = 2 × π × Radius
Triangle
A triangle is a polygon with three edges and three vertices.
Area = ½ × Base × Height
Perimeter = Side A + Side B + Side C
Square
A square is a rectangle with all sides equal in length.
Area = Side²
Perimeter = 4 × Side
Trapezoid
A trapezoid is a quadrilateral with exactly one pair of parallel sides.
Area = ½ × (Base1 + Base2) × Height
Perimeter = Base1 + Base2 + Side A + Side B
3D Shapes
Three-dimensional shapes have length, width, and height. They occupy space and have volume. Common 3D shapes include:
Cube
A cube is a 3D shape with six square faces, all of equal size.
Volume = Side³
Surface Area = 6 × Side²
Sphere
A sphere is a perfectly round 3D shape where all points on the surface are the same distance from the center.
Volume = (4/3) × π × Radius³
Surface Area = 4 × π × Radius²
Cylinder
A cylinder is a 3D shape with two circular bases connected by a curved surface.
Volume = π × Radius² × Height
Surface Area = 2 × π × Radius × (Radius + Height)
Cone
A cone is a 3D shape with a circular base connected to a point (apex) by a curved surface.
Volume = (1/3) × π × Radius² × Height
Surface Area = π × Radius × (Radius + Slant Height)
where Slant Height = √(Radius² + Height²)
Rectangular Prism
A rectangular prism is a 3D shape with six rectangular faces.
Volume = Length × Width × Height
Surface Area = 2 × (Length × Width + Length × Height + Width × Height)
Applications of Geometry
Architecture and Construction
Architects and builders use geometry to design and construct buildings, bridges, and other structures. They calculate areas, volumes, and angles to ensure structural integrity and efficient use of materials.
Engineering
Engineers use geometry to design products, machines, and systems. They calculate dimensions, volumes, and spatial relationships to optimize performance and functionality.
Computer Graphics
Computer graphics and animation rely heavily on geometry to create and manipulate 2D and 3D objects. Geometric algorithms are used to render realistic images and animations.
Navigation and GPS
Navigation systems use geometric principles to calculate distances, angles, and positions on the Earth's surface. GPS technology relies on geometric calculations to determine locations accurately.
Art and Design
Artists and designers use geometric principles to create visually appealing and balanced compositions. Geometry influences proportion, symmetry, and perspective in art and design.