Area Calculator

Select Shape:

Side (a):

Length (a):

Width (b):

Base (b):

Height (h):

Radius (r):

Angle (θ):

Semi-Major Axis (a):

Semi-Minor Axis (b):

Base 1 (a):

Base 2 (b):

Height (h):

Base (b):

Height (h):

Side (s):

Angle (θ):

Diagonal 1 (e):

Diagonal 2 (f):

Side (a):

Outer Radius (R):

Inner Radius (r):

Diagonal 1 (e):

Diagonal 2 (f):

Angle Between Diagonals (α):

Note: You can enter either angle between the diagonals, as they are supplementary (i.e., their sum is 180°).

Number of Sides (n):

Side Length (a):

1. What is the Area Calculator?

Definition: This calculator computes the area of various geometric shapes based on user inputs.

Purpose: It assists students, engineers, and designers in calculating areas for educational, architectural, and engineering applications.

2. How Does the Calculator Work?

The calculator uses specific formulas for each shape:

Square: \( A = a^2 \)
Rectangle: \( A = a \times b \)
Triangle: \( A = \frac{b \times h}{2} \)
Circle: \( A = \pi r^2 \)
Semicircle: \( A = \frac{\pi r^2}{2} \)
Sector: \( A = \frac{r^2 \theta}{2} \)
Ellipse: \( A = \pi \times a \times b \)
Trapezoid: \( A = \frac{(a + b) \times h}{2} \)
Parallelogram: \( A = b \times h \)
Rhombus: \( A = s^2 \times \sin(\theta) \)
Kite: \( A = \frac{e \times f}{2} \)
Regular Pentagon: \( A = \frac{a^2 \sqrt{25 + 10\sqrt{5}}}{4} \)
Regular Hexagon: \( A = \frac{3\sqrt{3} \times a^2}{2} \)
Regular Octagon: \( A = 2 \times (1 + \sqrt{2}) \times a^2 \)
Annulus (Ring): \( A = \pi (R^2 - r^2) \)
Regular Polygon: \( A = \frac{n \times a^2 \times \cot(\pi/n)}{4} \)

Steps:

Select the shape from the dropdown menu.
Enter the required dimensions and their units (mm, cm, m, in, or ft).
Convert all inputs to SI units (m).
Calculate the area using the appropriate formula.
Convert the area to the selected output unit (mm², cm², m², in², or ft²).
Display the result, formatted in scientific notation if the absolute value is less than 0.001, otherwise with 4 decimal places.

3. Importance of Area Calculation

Calculating areas is essential for:

Geometry:

Design:

Engineering:

Education:

4. Using the Calculator

Example 1 (Square, Metric Units): Calculate the area of a square:

Side: \( a = 5 \, \text{m} \);
Output Unit: Square Meters;
Area: \( A = 5 \times 5 = 25 \, \text{m}^2 \);
Result: \( A = 25.0000 \, \text{m}^2 \).

Example 2 (Irregular Quadrilateral, Metric Units): Calculate the area of an irregular quadrilateral:

Diagonal 1: \( e = 4 \, \text{m} \);
Diagonal 2: \( f = 6 \, \text{m} \);
Angle between diagonals: \( \alpha = 60^\circ \);
Output Unit: Square Meters;
Area: \( A = \frac{1}{2} \times 4 \times 6 \times \sin(60^\circ) = \frac{1}{2} \times 24 \times \frac{\sqrt{3}}{2} \approx 10.3923 \, \text{m}^2 \);
Result: \( A = 10.3923 \, \text{m}^2 \).

5. Frequently Asked Questions (FAQ)

Q: Can I use different units for different inputs?
A: Yes, the calculator converts all inputs to meters internally and then converts the result to your selected output unit.

Q: What if my shape is not listed?
A: This calculator covers common shapes. For unlisted shapes, you may need to break them down into simpler shapes and sum their areas.

Q: Why is the area zero when inputs are zero?
A: If any dimension is zero, the area will be zero, as area requires positive dimensions.