How to use the area calculator
- Select the shape you want to measure from the dropdown menu.
- Enter the required dimensions in the fields labeled Dimension A, B and C. The hint text below each field explains what measurement is expected for your chosen shape.
- The figure area calculator updates automatically as you type, showing the formula used and the computed area.
- Change the shape or adjust the numbers at any time to compare different configurations.
Formulas Used for Each Shape
Every shape uses a standard geometric formula. Here is how the math works for each option in this figure area calculator.
- Rectangle:
A = length × width. A square is simply a rectangle where both values are equal. - Circle:
A = π × r². Enter the radius in Dimension A. - Triangle:
A = ½ × base × height. Dimension A is the base and Dimension B is the perpendicular height. - Trapezoid:
A = ½ × (a + b) × h. Dimensions A and B are the two parallel sides, and Dimension C is the perpendicular distance between them. - Ellipse:
A = π × a × b. Dimensions A and B are the semi-major and semi-minor axes.
For example, a circle with a radius of 7 units gives π × 7² = π × 49 ≈ 153.938 square units.
Quick Reference Table
The table below shows precomputed areas for common dimension values so you can verify your own calculations quickly.
| Shape | Dimensions | Area |
|---|---|---|
| Square | side = 4 | 16 |
| Rectangle | 5 × 3 | 15 |
| Circle | radius = 1 | 3.14159 |
| Circle | radius = 10 | 314.159 |
| Triangle | base = 6, height = 4 | 12 |
| Trapezoid | sides 3 and 7, height 4 | 20 |
| Ellipse | axes 5 and 3 | 47.1239 |
Practical Uses for Area Calculations
Knowing how to find the area of a shape comes up constantly in everyday projects. When buying paint, one gallon typically covers about 400 square feet, so calculating wall areas as rectangles tells you exactly how many cans to purchase. Gardeners use the same approach to determine how much mulch or topsoil a rectangular bed requires.
Circular areas matter when sizing a round rug, planning a patio or ordering material for a cylindrical tank base. Triangles appear in roof gables and land surveying. Trapezoids show up in architecture for sloped lots and tapered panels. For larger construction projects, you may also need a dedicated flooring calculator that factors in waste and board dimensions.
Common Mistakes to Avoid
The most frequent error when using any figure area calculator is mixing units. If one dimension is in feet and another in inches, the result will be meaningless. Always convert everything to the same unit before entering values. You can use a unit conversion table if you need to switch between metric and imperial.
Another mistake is confusing diameter with radius for circles. The formula requires the radius, which is half the diameter. Entering a 10-inch diameter as the radius produces an area four times too large. For triangles, ensure the height you enter is the perpendicular distance from the base to the opposite vertex, not the length of a slanted side.
Understanding Square Units
Area is always expressed in square units. If your inputs are in meters, the output is in square meters. This applies regardless of the shape. A rectangle that is 3 meters long and 2 meters wide has an area of 6 square meters, written as 6 m².
When converting between square units, remember that the conversion factor itself must be squared. One foot equals 12 inches, but one square foot equals 144 square inches (12 × 12). Similarly, one meter equals 100 centimeters, so one square meter equals 10,000 square centimeters. Keeping this in mind prevents errors when working across measurement systems.
Worked examples
Each result below was produced by the same code the tool runs, so you can check your own numbers against them.
| Example | Input | Result |
|---|---|---|
| Rectangle 5 by 3 | Shape: rectangle; Dimension A: 5; Dimension B: 3 | Shape: Rectangle; Formula: A = length × width; Area: 15 |
| Circle radius 7 | Shape: circle; Dimension A: 7 | Shape: Circle; Formula: A = π × r²; Area: 153.938040026 |
| Triangle base 10 height 4 | Shape: triangle; Dimension A: 10; Dimension B: 4 | Shape: Triangle; Formula: A = ½ × base × height; Area: 20 |
| Trapezoid sides 8 and 12 height 5 | Shape: trapezoid; Dimension A: 8; Dimension B: 12; Dimension C: 5 | Shape: Trapezoid; Formula: A = ½ × (a + b) × h; Area: 50 |
FAQ
How do I calculate the area of a rectangle?
Multiply the length by the width. For a rectangle that is 8 units long and 5 units wide, the area is 8 multiplied by 5, which equals 40 square units.
What is the formula for the area of a circle?
The area of a circle is pi multiplied by the radius squared. If the radius is 3, the area is approximately 28.27 square units.
Can I use this tool for irregular shapes?
This figure area calculator handles five standard shapes. For irregular shapes, break the figure into smaller rectangles, triangles or circles, compute each area separately and add them together.
Do I need to use the same units for every dimension?
Yes. All input dimensions must be in the same unit of measurement. If one side is in feet and another in inches, convert them so they match before calculating.
Is my data sent to a server?
No. All calculations happen locally in your browser. Nothing you type is transmitted anywhere.
How do I find the area of a trapezoid?
Add the lengths of the two parallel sides, multiply by the perpendicular height and divide by two. For parallel sides of 6 and 10 with a height of 4, the area is (6 + 10) multiplied by 4 divided by 2, which equals 32.