Online Calculator for Geometry
Comprehensive collection of calculators for geometric calculations in 1D, 2D and 3D
1D Geometry - Lines and Curves
Lines and Curves 1D
Calculations with points, lines, straight segments and curves
2D Geometry - Plane Figures
Angles Deg/Rad
Angle calculations, conversion between degrees and radians
Triangles A = ½bh
All triangle types - right-angled, isosceles, scalene
Quadrilaterals 4 Sides
Square, rectangle, rhombus, parallelogram
Trapezoids Parallel
Trapezoid, isosceles trapezoid, parallelogram variants
Polygons Regular
Pentagon, hexagon, octagon - equal sides and angles
Circular Figures A = πr²
Circles, ellipses, circular sectors and segments
3D Geometry - Polyhedra and Angular Solids
Angular Solids
Cuboids, cubes, prisms and general polyhedra
Pyramids V = ⅓Ah
Tetrahedron, square pyramids, truncated pyramids
Platonic Solids 5 Types
Tetrahedron, cube, octahedron, dodecahedron, icosahedron
Archimedean Solids 13 Types
Semi-regular polyhedra with different face types
Catalan Solids 13 Types
Dual polyhedra to the Archimedean solids
Johnson Solids 92 Types
Convex polyhedra with regular polygon faces
3D Round Bodies - Solids of Revolution
Spherical Solids V = ⁴⁄₃πr³
Spheres, ellipsoids, torus and other round forms
Cones V = ⅓πr²h
Circular cones, elliptical cones, truncated cones
Cylinders V = πr²h
Circular cylinders, elliptical cylinders, hollow cylinders
About Geometry and Geometric Calculations
Geometry is one of the oldest mathematical disciplines with diverse applications:
- Architecture - Buildings, bridges, structures
- Engineering - Mechanical engineering, construction
- Design - Product design, art, graphics
- Science - Physics, astronomy, chemistry
- Technology - CAD, 3D modeling, VR
- Navigation - GPS, cartography
Fundamental geometric formulas
2D Areas
Circle: A = πr²
Triangle: A = ½bh
Rectangle: A = ab
Triangle: A = ½bh
Rectangle: A = ab
3D Volumes
Sphere: V = ⁴⁄₃πr³
Cylinder: V = πr²h
Cone: V = ⅓πr²h
Cylinder: V = πr²h
Cone: V = ⅓πr²h
Surface Areas
Sphere: S = 4πr²
Cylinder: S = 2πr(r+h)
Cube: S = 6a²
Cylinder: S = 2πr(r+h)
Cube: S = 6a²
Special Forms
Torus: V = 2π²Rr²
Ellipsoid: V = ⁴⁄₃πabc
Tetrahedron: V = ⅙abc
Ellipsoid: V = ⁴⁄₃πabc
Tetrahedron: V = ⅙abc
Euclid (around 300 BC): "The Elements" - Foundation of Euclidean geometry
with axioms, postulates and logical proofs that are still valid today.
History and Development of Geometry
Ancient Foundations
- Egypt & Babylon: Practical geometry for land surveying
- Thales (624-546 BC): First geometric proofs
- Pythagoras (570-495 BC): Pythagorean theorem
- Euclid (around 300 BC): "The Elements" - systematic geometry
Modern Developments
- René Descartes (1596-1650): Analytical geometry
- Gauss, Bolyai, Lobachevsky: Non-Euclidean geometry
- Riemann (1826-1866): Riemannian geometry
- Klein (1849-1925): Erlangen program, group theory
Dimensions and Spaces
- 1D: Lines, curves, one-dimensional objects
- 2D: Surfaces, polygons, plane geometry
- 3D: Solids, volumes, spatial geometry
- nD: Higher-dimensional spaces, topology
Modern Applications
- Computer Graphics: 3D modeling, rendering
- Robotics: Path planning, collision detection
- Geodesy: Earth surveying, GPS navigation
- Crystallography: Molecular structures, materials science
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Quick Reference
πr²
Circle area
⁴⁄₃πr³
Sphere volume
½bh
Triangle area
a²+b²=c²
Pythagoras
V = Base Area × Height
Prism/Cylinder
Geometric Principles
Euclidean Axioms: The foundations of classical geometry with parallel lines and constant space.
Cavalieri's Principle: Solids with equal cross-sections have equal volume.
Duality: Every Platonic solid has a dual partner (cube ↔ octahedron).
Units of Measurement
📏
Length: mm, cm, m, km, in, ft
📐
Area: mm², cm², m², km², in², ft²
📦
Volume: mm³, cm³, m³, liters, gal
📊
Angles: Degrees (°), Radians (rad)
🌍
Coordinates: Cartesian, Polar, Spherical
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