Area Calculator
Pick a shape, enter the dimensions, and get the area in square metres and square feet — for rooms, plots, craft projects, and geometry homework.
Calculate
Calculate
Measurements convert when you switch units
Result
The formula
Rectangle area is length × width. Square is side². Circle is πr². Ellipse is πab. Triangle is ½ × base × height, or Heron’s formula from three sides. Parallelogram is base × height. Trapezoid is ½(a + b) × height. Results convert with 1 m² ≈ 10.7639 ft².
Worked example
- Rectangle 5 m × 4 m → 20 m²
- Circle r = 2 m → π×4 ≈ 12.57 m²
- Trapezoid a = 4 m, b = 6 m, h = 3 m → ½(4+6)×3 = 15 m²
Result: Shape formulas with automatic m²/ft² display
How multi-shape area is calculated
Each mode applies the standard Euclidean area formula for that shape, then converts between square metres and square feet.
Rectangles, squares, and circles
A rectangle is length times width in the same unit. A square is side squared. A circle uses πr² with the radius measured to the rim — diameter ÷ 2 if you only know the diameter. An ellipse uses π × a × b with the two semi-axes.
Triangles, parallelograms, and trapezoids
When you know a base and the perpendicular height to that base, use ½bh for a triangle or base × height for a parallelogram. A trapezoid uses the average of the two parallel sides times height. When you know all three triangle side lengths, Heron’s formula applies — but only if the sides satisfy the triangle inequality.
Units
Metric mode expects metres and reports m² first. Imperial mode expects feet and reports ft² first. Mixed units (e.g. metres × feet) are not converted automatically — convert sides first.
What we do not model
No flooring waste factor, wall paint area, or GIS survey feet. For legal property area, use a surveyor’s plan.
Interesting facts
π is irrational
Circle and ellipse area use Math.PI (≈ 3.141592653589793). Display rounds; engineering tolerances may need more digits.
Height must be perpendicular
Triangle, parallelogram, and trapezoid “height” is the altitude between the bases — not a slanted side length.
Heron needs a valid triangle
Sides 2, 3, 9 cannot form a triangle; the calculator hides the result instead of inventing an area.
m² ↔ ft²
1 m² ≈ 10.7639 ft² using the international foot (0.3048 m exactly).
Composite shapes
Split L-shapes into rectangles (or mix shapes), compute each area, then add or subtract cut-outs.
Frequently asked questions
Choose Circle, enter the radius, and calculate. Area = πr². If you know the diameter, divide by 2 first.
For sides a, b, c: let s = (a+b+c)/2. Area = √[s(s−a)(s−b)(s−c)]. Use the three-sides mode when you lack height.
No — pick metric or imperial so all inputs share a unit. Convert lengths first with the unit converter if needed.
Split it into rectangles (or mix shapes), calculate each area, then add. Subtract any rectangular cut-outs the same way.
Choose Ellipse and enter the two semi-axes (half the long and short diameters). Area = π × a × b. If you only have full diameters, divide each by 2 first.
Not directly — this calculator needs base and perpendicular height. If you only know two sides and an angle, area = side₁ × side₂ × sin(angle); convert that to a height first or use a different tool.
Heron’s formula only works for valid triangles, where each side is shorter than the sum of the other two. If the sides fail that triangle inequality, no real area exists and the calculator hides the result.
References
- SI units — metre SI length basis for area units.
- International foot International foot = 0.3048 m exactly.
- Heron’s formula Classical formula for triangle area from three sides.