Area Calculator
Pick a shape and the input fields adapt: rectangle, triangle (three sides), trapezoid, circle, circular sector, ellipse, or parallelogram. Results show in your chosen unit — square feet or square meters — with the formula and substitution below.
Substitution
Seven formulas, one habit
Every plane-area formula is some flavor of base × height. A rectangle is literally that; a parallelogram is the same because slanting doesn’t change area; a triangle is half of one; a trapezoid averages its two parallel sides before multiplying by height. Circles swap in πr², a sector takes the fraction of the circle its angle covers, and an ellipse is π times both semi-axes. The habit that prevents most errors: check that every input is in the same unit before multiplying — and remember the answer comes out in that unit squared.
How it’s calculated
Rectangle: l × w. Triangle from three sides (Heron): √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2. Trapezoid: (b₁+b₂)/2 × h. Circle: πr². Sector: (θ/360) × πr² with θ in degrees. Ellipse: πab (semi-axes). Parallelogram: b × h (perpendicular height). Conversion: 1 m² = 10.7639 ft².
Results update as you type and are for education, not professional advice — double-check any number that matters.
Worked example
A 12 × 8 ft rectangle is 96 ft² (8.92 m²). A triangle with sides 3, 4, 5: s = 6, area = √(6×3×2×1) = 6. A trapezoid with parallel sides 8 and 5 and height 4: (8+5)/2 × 4 = 26. A 60° sector of a radius-6 circle: (60/360) × π × 36 = 18.85. An ellipse with semi-axes 5 and 3: π × 15 = 47.12.
Common mistakes
- Using a slanted side as the height — parallelograms and trapezoids need the perpendicular height.
- Entering the full axes of an ellipse — the formula πab takes the semi-axes (half of each).
- Adding sides for a triangle’s area — three sides need Heron’s formula, which this shape mode applies for you.
Where it is used
- Flooring, paint, lawn, and mulch estimates before buying materials.
- Geometry homework across all seven classic shapes.
- Land and garden plots — including circular beds and sector-shaped corners.
Frequently asked questions
Why does the triangle mode ask for three sides instead of base and height?
Because three sides are usually what you can measure. Heron’s formula converts them straight to area with no height needed: for 3-4-5, s = 6 and area = √(6×3×2×1) = 6. If you do know base and height, base × height ÷ 2 gives the same answer.
How do I convert between square feet and square meters?
Multiply square meters by 10.7639 to get square feet, or divide going the other way. The calculator’s second row does this automatically — 96 ft² is 8.92 m².
What angle does the sector formula expect?
Degrees, out of 360. A 90° sector is a quarter circle. If your angle is in radians, area is simply ½r²θ — or multiply your radian angle by 180/π ≈ 57.2958 to use the degree field.
Does a parallelogram have the same area as the matching rectangle?
Yes — base × perpendicular height, regardless of slant. What the slant changes is the perimeter, not the area.
What if my triangle sides can’t form a triangle?
If one side is as long as the other two combined (like 1, 2, 5), no triangle exists and Heron’s formula would take the square root of a negative number. The calculator reports the impossibility instead.