Area Calculator
Pick a shape, enter the dimensions, and get the area with unit conversions. Optionally estimate material cost with a waste allowance.
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. Perimeter uses the matching edge formula when sides are known. Material cost = area × price × (1 + waste).
Worked example
- Rectangle 5 m × 4 m → 20 m² (perimeter 18 m)
- Circle r = 2 m → π×4 ≈ 12.57 m²
- 20 m² at $25/m² with 10% waste → buy 22 m² · cost $550
Result: 20 m² · 215.28 ft² · optional material cost
How multi-shape area is calculated
Each mode applies the standard Euclidean area formula for that shape, converts between common area units, and can scale area by a waste factor for purchasing.
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 and perimeter
Metric mode expects metres and reports m² first. Imperial mode expects feet and reports ft² first. Perimeter is shown when the inputs determine the outer path (for example 2(L+W) for a rectangle). Mixed length units are not converted automatically — convert sides first.
Material cost and waste
Optional price × area estimates a purchase total. Waste percentage increases the area you should buy (for cuts, overlaps, or mistakes). It is a planning estimate, not a supplier quote.
What we do not model
No wall openings, paint coats, 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).
Waste is buy-area, not markup on price alone
10% waste on 20 m² means planning for 22 m² of material, then multiplying by the unit price.
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.
Open Estimate material cost, enter the price per m² or ft² and a waste percentage (often 5–15% for flooring). The tool scales area by (1 + waste) then multiplies by price.
Perimeter needs the outer edge lengths. Base-and-height triangle or parallelogram modes do not define every side, so perimeter is omitted there. Use three-sides triangle when you want both area and perimeter.
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.