Area Calculator
Area of rectangles, circles, triangles and more.
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Find the area of common shapes quickly. Pick a shape, enter the dimensions, and this calculator applies the right geometry formula — showing the working and converting the result to square feet for construction and DIY use.
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Area — The Quick Answer
Each shape has its own formula: a rectangle is length × width, a circle is πr², a triangle is ½ × base × height, and a trapezoid is ½ × (a + b) × height.
Shortcut
Rectangle: L × W | Circle: πr² | Triangle: ½bh | Trapezoid: ½(a+b)h
Area formulas by shape
| Shape | Formula | Inputs |
|---|---|---|
| Rectangle | A = L × W | length, width |
| Square | A = s² | side |
| Circle | A = πr² | radius |
| Triangle | A = ½ × b × h | base, height |
| Trapezoid | A = ½ × (a + b) × h | two parallel sides, height |
For a square, just use the rectangle mode with equal length and width. For an ellipse, use π × a × b, where a and b are the two semi-axes.
How It Works
The Formulas
Geometry by shape
Formula
Rectangle: A = L × W Circle: A = π r² Triangle: A = ½ × b × h Trapezoid: A = ½ × (a + b) × h
Variables
Radius
Distance from the centre of a circle to its edge — half the diameter.
Base and height
For a triangle, the base and the perpendicular height from that base to the opposite vertex.
Parallel sides
For a trapezoid, the two parallel sides; h is the perpendicular distance between them.
Note: All dimensions must be in the same unit before multiplying. This calculator keeps them consistent and converts the result for you.
Worked Example: A 12 × 10 ft Room
And how to handle an L-shape
Pick the shape
Rectangle
Apply its formula
A = length × width = 12 × 10
Compute
= 120 sq ft
For odd rooms, split and add
An L-shape = two rectangles calculated and summed
Reference Guide
| Shape | Formula | Inputs |
|---|---|---|
| Rectangle / square | A = L × W | length, width |
| Circle | A = π r² | radius |
| Triangle | A = ½ × b × h | base, height |
| Trapezoid | A = ½ × (a + b) × h | two parallel sides, height |
Handling Odd Shapes & Units
The practical side of area
A rectangle's length × width is just how many unit squares fit in the grid. A triangle is half a rectangle (hence the ½), and a circle's πr² comes from rearranging thin wedges into a near-rectangle. Seeing this makes the formulas intuitive rather than memorised.
Best for: Understanding where the formulas come from
Real rooms and plots are rarely a clean rectangle. Break them into rectangles, triangles, and parts of circles, calculate each, and add them — or calculate a full shape and subtract a missing piece.
Best for: Measuring real-world floors and plots
Multiplying a length in feet by a width in inches gives nonsense. Convert everything to one unit first, and remember the answer is always in square units because you've multiplied two lengths.
Best for: Avoiding the most common area error
How to Calculate Area
Area is the amount of flat surface a shape covers, measured in square units — and every area formula is really a shortcut for counting unit squares. A rectangle is length × width; a triangle is half of that (½ × base × height); a circle is πr². The practical trick for real spaces, which are rarely tidy rectangles, is to split them into simple shapes, work out each area, and add them together (or subtract a cut-out). The one rule that trips people up is units: keep every measurement in the same unit before multiplying, and the result comes out in square units. This calculator handles rectangles, circles, triangles, and trapezoids and converts to square feet.
Key Features
💡 Pro Tips
- →For an L-shaped or irregular room, slice it into rectangles, compute each, and add them up.
- →For a shape with a bite taken out, calculate the full area and subtract the missing piece.
- →Convert all measurements to one unit before multiplying — mixing feet and inches is the classic mistake.
- →A square is just the rectangle mode with equal sides.
Common Mistakes
Mixing units
Multiplying feet by inches gives a meaningless figure. Convert everything to the same unit first, then calculate.
Using a slanted side as a triangle's height
A triangle's height must be the perpendicular distance from the base to the opposite vertex, not the length of a sloping side. Using the wrong value overstates the area.
Treating an irregular room as one rectangle
Real rooms with alcoves or angles aren't single rectangles. Splitting them into simple shapes and summing gives the correct area.
Research & Citations
Sources and standards referenced for the factual claims on this page
- [1]
Euclid (-300). Elements — the foundations of plane geometry. Classical mathematics.
Classical source for area and plane geometry.
View source - [2]
National Council of Teachers of Mathematics (NCTM) (2023). Measurement and area standards. nctm.org.
Educational standards for area and measurement.
View source
This calculator is a reference tool, not a substitute for professional advice. Verify important health, financial, legal, or safety decisions with a suitably qualified professional.
Last updated: October 7, 2026
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Frequently Asked Questions
How do I calculate the area of a rectangle?
Multiply length by width: A = L × W. A 12 ft × 10 ft room has an area of 120 square feet, which is what you'd order flooring or paint for.
How do I find the area of a circle?
Use A = π × r², where r is the radius (half the diameter). A circle with a 5 ft radius has an area of π × 25 ≈ 78.54 square feet.
What's the formula for a triangle's area?
A = ½ × base × height. The height must be measured perpendicular to the base. A triangle with a 6 ft base and 4 ft height has an area of ½ × 6 × 4 = 12 square feet.
How do I measure an irregular area?
Break it into simple shapes — rectangles, triangles, circles — calculate each area separately, then add them together. This calculator handles each shape individually so you can total them.