Data Source and Methodology
Primary reference for planar area formulas: OpenStax, Geometry, 2015, CC BY 4.0. For unit conversion factors: NIST Special Publication 811 — Guide for the Use of the International System of Units (SI), 2008 Edition (updated 2023).
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formula Explained
Rectangle: A = l \times w
Circle: A = \pi r^{2} or A = \frac{\pi d^{2}}{4}
Triangle (base-height): A = \frac{b \times h}{2}
Trapezoid: A = \frac{(a + b)}{2} \times h
Parallelogram: A = b \times h
Regular polygon (n sides): A = \frac{n s^{2}}{4 \tan(\pi/n)}
Glossary of Variables
| Symbol/Field | Meaning |
|---|---|
| l | Length of rectangle |
| w | Width of rectangle |
| r | Radius of circle |
| d | Diameter of circle |
| b | Base of triangle or parallelogram |
| h | Height (perpendicular) of triangle, trapezoid, or parallelogram |
| a, b (trapezoid) | Lengths of the two parallel sides |
| n | Number of sides of a regular polygon (n ≥ 3) |
| s | Side length of a regular polygon |
| Area outputs | Displayed in selected unit squared, and converted to m², ft², acres, and hectares |
How It Works: A Step‑by‑Step Example
Suppose you need the area of a 12 ft by 9 ft room for flooring.
- Select “Rectangle”, choose unit “ft”.
- Enter Length = 12, Width = 9.
- Apply the formula:
A = l \times w. - Substitute:
A = 12 \times 9 = 108 \text{ ft}^{2}. - Convert to m²:
108 \text{ ft}^{2} \approx 10.033 \text{ m}^{2}.
Frequently Asked Questions (FAQ)
What if I only know the circle diameter?
You can input the diameter directly; the tool uses A = \frac{\pi d^{2}}{4}.
Can I change precision?
Yes. Use the “Display precision” selector to show 0–6 decimal places without affecting internal accuracy.
Do I need perpendicular height for triangles?
Yes. The height must be perpendicular to the base for the base–height formula to be valid.
How do regular polygon inputs work?
Provide the number of sides n (≥ 3) and side length s. The tool applies A = \frac{n s^{2}}{4 \tan(\pi/n)}.
Why do you also show m² and ft²?
These are the most commonly used area units globally. We also summarize acres and hectares for land-scale areas.
Are unit conversions exact?
They follow NIST-defined factors (e.g., 1 in = 0.0254 m exactly), ensuring precise conversions.
Is this calculator accessible?
Yes. It supports keyboard navigation, visible focus styles, descriptive labels, and ARIA live regions for results.