square_foot Area Calculator star

How Area Is Calculated

Each of the six shapes needs a different formula and, just as important, different inputs — mixing them up is the most common source of wrong answers. Square: side², rectangle: length × width, circle: π × r², parallelogram: base × height, and trapezoid: ((a+b)/2) × height, where a and b are the two parallel sides. The triangle is the trickiest: this tool asks for a base and its perpendicular height, so it computes ½ × base × height directly — but if all you have is three side lengths and no height, you can still get the area by hand first with Heron's formula: √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (a+b+c)/2.

Take a triangle with sides 5, 6 and 7 units and no height measured. Semi-perimeter s = (5+6+7)/2 = 9. Area = √(9×(9-5)×(9-6)×(9-7)) = √(9×4×3×2) = √216 ≈ 14.7 square units — found entirely from the three side lengths, without ever measuring a height directly. Had the same triangle instead given a base of 6 and a perpendicular height of 4.9, entering those into the tool gives ½×6×4.9 ≈ 14.7 — the same answer reached through the other route, which is a good way to sanity-check a hand measurement.

What's Worth Knowing

• Match the inputs to the shape: a rectangle needs two different sides, a square needs only one, a parallelogram needs a base and a height — entering the wrong pair for the wrong shape is the single most common mistake.
• Height means perpendicular distance: for a triangle, parallelogram or trapezoid, height is always measured at a right angle to the base, never along a slanted side — using the slanted side length instead of the true height will always overstate the area.
• Units square automatically: entering centimetres returns cm², entering metres returns m²; multiply by 10,000 to convert m² to cm² (not by 100, since both dimensions are squared).
• Irregular shapes: split any polygon into rectangles and triangles, calculate each piece separately with this tool, then add the results together for the total.