Geometry Calculator
Calculate areas, volumes, perimeters, and angles for various geometric shapes. Get instant results for 2D and 3D geometry problems.
Geometry Concepts
Geometry is the branch of mathematics that studies the properties, measurement, and relationships of points, lines, angles, surfaces, and solids. It provides tools for understanding shapes and spatial relationships in both 2D and 3D space.
Key Geometric Concepts
- Area: The amount of space inside a 2D shape, measured in square units.
- Perimeter: The distance around a 2D shape, measured in linear units.
- Volume: The amount of space inside a 3D shape, measured in cubic units.
- Surface Area: The total area of all surfaces of a 3D shape.
- Angles: Formed by two rays sharing a common endpoint, measured in degrees or radians.
- Congruence: When shapes have the same size and shape.
- Similarity: When shapes have the same shape but different sizes.
Common Geometric Formulas
Circle
Area = πr²
Circumference = 2πr
Rectangle
Area = length × width
Perimeter = 2(length + width)
Triangle
Area = ½ × base × height
Perimeter = a + b + c
Sphere
Volume = (4/3)πr³
Surface Area = 4πr²
Geometric Theorems
| Theorem | Description |
|---|---|
| Pythagorean Theorem | In a right triangle, a² + b² = c² |
| Triangle Angle Sum | The sum of angles in a triangle is 180° |
| Polygon Angle Sum | Sum of interior angles = (n-2) × 180° |
| Thales' Theorem | Any angle inscribed in a semicircle is a right angle |
| Cavalieri's Principle | Objects with same cross-sectional area at every height have same volume |
Geometry Tip:
When solving geometry problems, draw a clear diagram and label all known values. Look for special relationships like similar triangles, parallel lines, or right angles to simplify calculations.
Geometry Calculator Answers
What does the geometry calculator do?
The geometry calculator helps you quickly calculate measurements such as area, perimeter, volume, surface area, and angles for various geometric shapes like circles, triangles, rectangles, and 3D solids.
What shapes are supported?
Common shapes like squares, rectangles, circles, triangles, trapezoids, spheres, cylinders, cubes, and cones are supported. Some calculators also include polygons and complex 3D shapes.
Is it useful for students and teachers?
Yes. It’s a helpful tool for solving geometry problems, checking homework, and visualizing shape properties. It saves time and reinforces understanding of geometric formulas and relationships.
Does it explain the formulas used?
Many geometry calculators show the formula used for each calculation, making it easier to learn how results are derived and apply those formulas manually when needed.