Calculator Inputs
Example Data Table
| Shape | Input Values | Formula | Area Result |
|---|---|---|---|
| Rectangle | Length = 12 cm, Width = 5 cm | A = l × w | 60 cm² |
| Circle | Radius = 7 cm | A = πr² | 153.938 cm² |
| Trapezoid | b₁ = 8 m, b₂ = 11 m, h = 4 m | A = ½(b₁+b₂)h | 38 m² |
| Regular Polygon | n = 6, side = 10 ft | A = ns² / [4 tan(π/n)] | 259.808 ft² |
| Annulus | Outer = 9 in, Inner = 4 in | A = π(R²-r²) | 204.204 in² |
Formula Used
| Shape | Area Formula | Notes |
|---|---|---|
| Rectangle | A = l × w | Multiply length by width. |
| Square | A = s² | Square the side length. |
| Triangle | A = ½bh | Use perpendicular height with the base. |
| Triangle (Heron) | A = √[s(s-a)(s-b)(s-c)] | Use when all three sides are known. |
| Circle | A = πr² | Radius is measured from center to edge. |
| Semicircle | A = ½πr² | Half of a full circle’s area. |
| Ellipse | A = πab | a and b are semi-axis lengths. |
| Trapezoid | A = ½(b₁+b₂)h | Average both bases, then multiply by height. |
| Parallelogram | A = bh | Use perpendicular height, not side length. |
| Rhombus / Kite | A = ½d₁d₂ | Multiply diagonals and divide by two. |
| Sector | A = (θ/360)πr² | θ is the central angle in degrees. |
| Annulus | A = π(R²-r²) | Subtract inner circle area from outer circle area. |
| Regular Polygon | A = ns² / [4 tan(π/n)] | n is number of sides and s is side length. |
This calculator uses standard geometric area relationships. Keep all length inputs in the same unit so the final area is consistent and meaningful.
How to Use This Calculator
- Select the geometric shape from the dropdown list.
- Choose a length unit such as centimeters, meters, inches, or feet.
- Enter only the dimensions required for the chosen shape.
- Set the number of decimal places for the output.
- Press Calculate Area to show the result above the form.
- Use the CSV button for spreadsheet export.
- Use the PDF button to save the displayed result summary.
- Check the formulas and example table to verify your method.
FAQs
1. What does this calculator solve?
It computes area for many common shapes, including circles, triangles, trapezoids, annuli, ellipses, and regular polygons. It also shows the formula used.
2. Do I need matching units for all inputs?
Yes. Keep every length in the same unit before calculating. Mixed units create incorrect results because area depends on squared length values.
3. Why does the triangle by sides option reject some values?
Heron’s formula only works for valid triangles. The entered sides must satisfy the triangle inequality, or a real enclosed area does not exist.
4. What is the difference between a circle and a sector?
A circle uses the full 360 degrees. A sector uses only part of the circle, so its area is a fraction based on the central angle.
5. When should I use the regular polygon formula?
Use it when all sides are equal and all angles are equal, such as in equilateral triangles, squares, pentagons, hexagons, and similar shapes.
6. What is an annulus?
An annulus is the ring-shaped region between two circles sharing the same center. Its area equals the outer circle area minus the inner circle area.
7. Can I export the result?
Yes. After calculation, you can download a CSV for spreadsheet use and a PDF summary for printing, sharing, or project records.
8. Why is area shown in squared units?
Area measures surface coverage, not single-direction length. That is why centimeters become square centimeters, meters become square meters, and so on.