What is a trapezoid calculator?
A trapezoid calculator computes the area of a trapezoid from the lengths of its two parallel sides (bases) and the height. A trapezoid (or trapezium in some regions) is a four-sided shape with at least one pair of parallel sides. You enter base 1, base 2, and the perpendicular height; the calculator gives you area = ½ × (base₁ + base₂) × height. No sign-up or download is required; the tool runs in your browser and is useful for geometry homework, land area, and any task involving trapezoidal shapes.
Trapezoids appear in road embankments, table tops, and many real-world surfaces. Knowing the area helps with material coverage, paving, or land measurement. This free trapezoid calculator gives you the area in square units—meters, feet, inches—as long as you use the same unit for both bases and height. The height must be the perpendicular distance between the two parallel bases, not the length of a slanted leg.
How to use this trapezoid calculator
Enter the length of the first base (base 1), the length of the second base (base 2), and the height. The two bases are the parallel sides; they can be in any order. The height is the perpendicular distance between the lines containing the two bases—measure straight across, not along a slanted side. All three values must be positive numbers. As soon as they are valid, the area appears in square units. The formula is shown under the inputs: area = ½ × (base₁ + base₂) × height. If you leave a field empty or enter zero or a negative value, the calculator will ask you to enter positive dimensions. Use the same unit for all three; the area will be in square units of that measure.
Trapezoid area formula
The area of a trapezoid is A = ½ × (base₁ + base₂) × height. You can think of it as the average of the two bases times the height. For example, if base 1 is 10 units, base 2 is 6 units, and the height is 4 units, the area is ½ × (10 + 6) × 4 = ½ × 16 × 4 = 32 square units. The formula works for any trapezoid: the two bases must be the parallel sides, and the height must be perpendicular to them. Do not use the length of a non-parallel side as the height unless it is perpendicular to both bases. The trapezoid calculator applies this formula so you get an accurate area without doing the arithmetic by hand.
Why “average of bases times height”?
If you cut a trapezoid and rearrange it, you can form a rectangle with one side equal to the height and the other equal to the average of the two bases. So the trapezoid area equals the area of that rectangle: (base₁ + base₂)/2 × height = ½(base₁ + base₂) × height. Alternatively, you can split the trapezoid into two triangles that share the height and have bases that add up to (base₁ + base₂); their combined area is ½(base₁ + base₂) × height. Either way, the same formula holds. This trapezoid calculator uses that formula for every valid input.
Bases and height
The two bases of a trapezoid are the pair of parallel sides. They can have different lengths (giving an isosceles or scalene trapezoid) or the same length (giving a parallelogram). The order does not matter: base 1 and base 2 can be swapped and the area is the same. The height is the perpendicular distance between the two parallel sides. You can measure it by drawing a line from one base to the other that is perpendicular to both; that line’s length is the height. In a right trapezoid, one leg is perpendicular to the bases, so that leg’s length is the height. In other trapezoids, you may need to use the Pythagorean theorem or trigonometry if you only know the leg lengths; this calculator assumes you have the height, which is the most direct way to get area.
Trapezoid vs parallelogram and rectangle
A parallelogram has two pairs of parallel sides; if you use it as a trapezoid, both “bases” are the same length, so base₁ = base₂ and area = ½ × (2 × base) × height = base × height, which is the parallelogram formula. A rectangle is a parallelogram with right angles; again, the two bases are equal (length and width), and area = base × height. So the trapezoid formula includes rectangles and parallelograms as special cases. This calculator is aimed at trapezoids where the two bases can differ; if they are equal, you still get the correct area (rectangle or parallelogram).
Applications of trapezoid area
Trapezoid area is used in geometry, construction, and land surveying. In education, the trapezoid is a standard shape when studying quadrilaterals and area. In construction, some cross-sections (e.g. channels, embankments) are trapezoidal. In surveying, irregular plots are sometimes approximated by trapezoids. This trapezoid calculator gives you quick, accurate area from the two bases and height. Always measure height perpendicular to the bases, and keep units consistent: same unit for both bases and height; area in square units.
Summary
This trapezoid calculator finds the area of a trapezoid from the lengths of the two parallel bases and the perpendicular height. Enter base 1, base 2, and height (all positive) and get area = ½ × (base₁ + base₂) × height instantly. The tool is free, runs in the browser, and requires no account. Use it for homework, land area, or any trapezoidal shape. Remember: the two bases are the parallel sides, and the height is perpendicular to them. Keep units consistent for accurate results.