Area Calculator
Calculate the area of a rectangle, circle, triangle, trapezoid, parallelogram or ellipse — with the formula and substituted working shown for each shape.
About the Area Calculator
This area calculator covers the shapes you actually meet — rectangle, square, circle, triangle (from base and height, or from all three sides), parallelogram, trapezoid and ellipse. Pick the shape, enter its dimensions, and the area appears instantly along with the exact formula used and the calculation with your numbers substituted in, so it doubles as a worked example for homework.
The formulas: rectangle l × w; square s²; circle πr²; triangle ½ × base × height; three-sided triangle via Heron's formula A = √(s(s−a)(s−b)(s−c)) with s the semi-perimeter; parallelogram base × height; trapezoid ½(a + b) × h; ellipse πab. The calculator is unit-agnostic — enter metres and the answer is in square metres, enter feet and it is square feet — and it validates impossible inputs, like three sides that cannot form a triangle.
Students use it across geometry courses; practical users size floor tiles, paint coverage, plots of land, fabric and garden beds. A 30 × 40 ft plot is 1,200 sq ft; a round table of radius 0.75 m covers π × 0.75² = 1.77 m². Everything runs in your browser.
How to Use the Area Calculator
- 1Select the shape from the dropdown.
- 2Enter the dimensions the shape requires (any unit).
- 3Read the area in square units, with perimeter where applicable.
- 4Check the formula line to see your numbers substituted in.
Frequently Asked Questions
How do I find the area of a triangle from three sides?
Use Heron's formula. For sides 5, 6, 7: the semi-perimeter is s = (5+6+7) ÷ 2 = 9, and A = √(9 × 4 × 3 × 2) = √216 = 14.70 square units. If you know the base and height instead, ½ × base × height is quicker.
How do I calculate the area of a trapezoid?
Average the two parallel sides and multiply by the height: A = ½(a + b) × h. A trapezoid with parallel sides 8 and 12 and height 5 has area ½ × 20 × 5 = 50 square units. This shape covers ramps, roof cross-sections and irregular plot ends.
Why does the calculator say my three sides can't form a triangle?
The triangle inequality requires every side to be shorter than the other two combined. Sides 2, 3 and 8 fail because 2 + 3 = 5 < 8 — the two short sides cannot reach each other. Heron's formula would produce the square root of a negative number, so the tool flags the input instead.
How do I calculate the area of a plot of land?
For a rectangular plot, multiply length by width: a 30 × 60 ft plot is 1,800 sq ft (20 marla ≈ 5,445 sq ft in Pakistan's common convention, and 1 kanal = 20 marla). For irregular four-sided plots, split them into two triangles, use the three-sides mode for each, and add the areas.
What is the difference between area and perimeter?
Area measures the surface inside a shape (square units — needed for tiles, paint, fabric); perimeter measures the boundary length (linear units — needed for fencing, skirting, borders). A 4 × 9 rectangle and a 6 × 6 square both cover 36 square units, but their perimeters differ: 26 versus 24.