2D Geometry Calculators & Solvers
Explore 13 free online 2D geometry calculators to solve area, perimeter, diagonals, and missing dimensions. Features instant step-by-step arithmetic, verified formulas, and dynamic visual diagrams.
Available 2D Geometry Solvers
Select a calculator to view formula and step-by-step solution
Quadrilaterals
6 calculators
Rectangle Area & Perimeter Calculator
Calculate rectangle area (l × w), perimeter (2(l + w)), and diagonal length with interactive SVG diagram.
Square Calculator (Area, Perimeter & Diagonal)
Calculate square area (s²), perimeter (4s), and diagonal (s√2) from side length with step-by-step working.
Parallelogram Calculator
Calculate parallelogram area (b × h) and perimeter (2(a + b)) using base, height, or side angles.
Trapezoid (Trapezium) Calculator
Calculate trapezoid area ((a + b)/2 × h), midsegment, and perimeter with step-by-step solutions.
Rhombus Calculator
Calculate rhombus area from diagonals (d₁ × d₂ / 2) or side length and interior angles.
Kite Area & Perimeter Calculator
Calculate area from intersecting diagonals (d₁ × d₂ / 2) and perimeter from unequal side pairs.
Regular Polygons
4 calculators
Regular Polygon Calculator (n-gon)
Calculate area (1/2 × P × apothem), perimeter, and interior angles for any regular n-sided polygon.
Hexagon Calculator (6-Sided Regular Hexagon)
Calculate regular hexagon area (3√3/2 × s²), perimeter (6s), and diagonal distance with live SVG geometry.
Octagon Calculator (8-Sided Regular Octagon)
Calculate octagon area (2(1 + √2)s²), perimeter, and corner spans for woodworking and stop-sign geometry.
Pentagon Calculator (5-Sided Regular Pentagon)
Calculate area, perimeter, and diagonal width of regular 5-sided pentagons step-by-step.
Planar Shapes & Properties
3 calculators
Ellipse Calculator (Oval Shape Area & Perimeter)
Calculate 2D ellipse area (πab) and Ramanujan perimeter approximation from semi-major and semi-minor axes.
Polygon Angles Calculator (Interior & Exterior)
Calculate sum of interior angles ((n - 2) × 180°), each interior angle, and exterior angles (360°/n).
Scale Factor & Similarity Calculator (2D)
Calculate 2D scale factor ratio (k), enlarged/reduced dimensions, and area scaling ratios (k²).
Understanding 2D Geometry: Planar Shapes, Boundaries, and Areas
Two-Dimensional (2D) Geometry is the study of flat geometric figures lying on a single infinite Euclidean plane. Every 2D shape possesses two primary spatial dimensions: length and width. Because they exist on a flat plane without depth, all 2D shapes are measured by their outer boundary distance, known as the perimeter ($P$), and the two-dimensional surface space they enclose, known as the area ($A$).
Explore 2D Geometry by Mathematical Categories
Fundamental Quadrilaterals
Calculate area, perimeter, and corner diagonals for rectangles, squares, parallelograms, trapezoids, rhombuses, and geometric kites.
Regular Polygons (n-gons)
Solve any regular $n$-sided shape (pentagons, hexagons, octagons) using apothem height ($a$) and equilateral triangle decompositions.
Planar Shapes & Scale Ratios
Calculate ellipse oval areas ($\pi ab$), Ramanujan perimeter approximations, polygon interior/exterior angles, and 2D scale factor ratios ($k, k^2$).
Master 2D Geometry Formulas Quick Reference
Below is a summary of the standard formulas utilized throughout our 2D geometry calculator suite:
| 2D Geometric Shape | Area Formula (A) | Perimeter Formula (P) | Diagonal / Specialty Formula |
|---|---|---|---|
| Rectangle | A = l × w | P = 2(l + w) | d = √(l² + w²) |
| Square | A = s² | P = 4s | d = s√2 |
| Parallelogram | A = b × h | P = 2(a + b) | h = Altitude (90°) |
| Trapezoid | A = ((a + b) / 2) × h | P = a + b + c + d | Midsegment = (a + b) / 2 |
| Rhombus | A = (d₁ × d₂) / 2 | P = 4s | s = √((d₁/2)² + (d₂/2)²) |
| Regular Hexagon | A = (3√3 / 2)s² | P = 6s | Long d = 2s, Short d = s√3 |
| Regular Octagon | A = 2(1 + √2)s² | P = 8s | Span Width = s(1 + √2) |
| Ellipse (Oval) | A = π × a × b | P ≈ π[3(a+b) - √((3a+b)(a+3b))] | Foci c = √(a² - b²) |
| Regular Polygon | A = (1/2) × P × a | P = n × s | Apothem a = s / (2 tan(180°/n)) |
Real-World Applications of 2D Geometry
While two-dimensional geometry is a core subject taught throughout middle school and high school mathematics, its practical formulas are utilized continuously across modern trades and industries:
- Architecture & Construction: Calculating square footage for flooring tiles, hardwood installations, drywall drywall sheets, and property boundary fencing.
- Carpentry & Cabinetmaking: Building octagonal gazebos, hexagonal shelving units, and picture frame miter angles using polygon angle theorems.
- Graphic Design & UI/UX: Scaling vectors and screen layouts proportionally using linear ($k$) and area ($k^2$) similarity scale factors.
- Civil Engineering: Designing road cross-sections and drainage canals shaped as trapezoids to maximize fluid transport efficiency while stabilizing soil embankments.