Area Tool
Calculate the area of fourteen geometric shapes using relevant dimensions, including circles, triangles, polygons and ellipses. See perimeter where determinable, totals for repeated shapes, an interactive diagram, a results breakdown and comparison bars, with downloadable results.
| Measurement | Value |
|---|
Table of Contents
Highlights
- Area formulas for 14 common geometric shapes
- Interactive diagrams that adapt to selected dimensions
- Area, total area and available boundary lengths
- Detailed results table and visual comparison bars
- Export results as CSV or JSON and diagrams as SVG or PNG
How Area Tool Works?
Area describes the space enclosed by a two-dimensional boundary. Select one of 14 shapes and enter its relevant measurements. The chosen formula determines the area of one shape; multiplying this by the quantity gives the combined area. Where sufficient information is available, the boundary length is also shown.
Each shape uses its own dimensions and mathematical relationship:
| Shape | Required measurements | Area formula |
|---|---|---|
| Rectangle / square | Width and height / side | A = wh / s² |
| Circle / annulus | Radius / outer and inner radii | A = πr² / π(R² − r²) |
| Triangle / right triangle | Base and perpendicular height / perpendicular sides | A = bh/2 |
| Triangle (three sides) | Side lengths a, b, c | A = √[p(p−a)(p−b)(p−c)], p = (a+b+c)/2 |
| Equilateral triangle | Side | A = √3s²/4 |
| Parallelogram | Base, perpendicular height, slanted side | A = bh |
| Trapezium | Two parallel sides and perpendicular height; horizontal offset for boundary | A = (a+b)h/2 |
| Rhombus | Two diagonals | A = d₁d₂/2 |
| Ellipse | Two semi-axes | A = πab |
| Circular sector | Radius and central angle in degrees | A = (θ/360)πr² |
| Regular polygon | Number of sides and side length | A = ns²/[4tan(π/n)] |
The diagram adapts to the chosen shape, while the result table lists entered measurements, area per shape, quantity, total area and perimeter where available. The comparison graphic shows selected area measures.
Practical Use Cases
Homeowners and decorators: Estimate rectangular floor or wall areas, or use combined areas to plan coverage across several identical rooms or panels.
Landscapers: Calculate circular beds, annular paths, trapezium plots and regular polygon planting areas to estimate materials.
Builders and fabricators: Work with triangles, parallelograms, ellipses and rhombuses when estimating sheet material or cut-out surface areas.
Students and teachers: Explore how radius, height, angle and side count influence area, using the changing diagram and formulas for comparison.
Architects and designers: Check simple geometric components and export a calculation table or shape illustration for preliminary planning.
Accuracy and Limitations
Areas use standard geometric formulas with JavaScript floating-point arithmetic; displayed values are rounded to the selected decimal precision. The ellipse boundary is approximate (Ramanujan’s second approximation), while areas remain formula-based. An arbitrary triangle entered using base and height has no determinable perimeter. The parallelogram requires a slanted side at least as long as its perpendicular height; the three-side triangle must satisfy the triangle inequality; sectors are restricted to angles greater than 0° and up to 360°; and regular polygons require 3–100 whole-number sides. Trapezium perimeter depends on the supplied horizontal offset, and combined area assumes identical, non-overlapping shapes.
