Calculate area, perimeter, diagonals, angles, and median of a trapezoid. Supports general, isosceles, and right trapezoid types with unit selection, presets, side proportion visualization, and a re...
A trapezoid (also called a trapezium in British English) is a four-sided polygon with exactly one pair of parallel sides. The parallel sides are called the bases, while the non-parallel sides are the legs. Trapezoids are everywhere in the built environment — from bridge cross-sections and retaining walls to table tops and architectural facades.
Calculating the area of a trapezoid is straightforward: take the average of the two parallel sides and multiply by the height. The formula A = ½(a + b) × h captures this elegantly. But real-world problems often require more than just the area. You might need the perimeter to estimate edging material, the diagonal lengths for bracing calculations, or the base angles for cutting materials at the right angle.
This calculator handles three types of trapezoids: general (arbitrary legs), isosceles (equal legs), and right (one leg perpendicular to the bases). For each type, it computes area, perimeter, diagonals, base angles, and the median — the segment connecting the midpoints of the two legs, which is always equal to the average of the bases. Built-in presets and a reference table help you get started quickly and verify your results.
While the basic trapezoid area formula is simple, computing diagonals, leg lengths, and angles requires trigonometry and the Pythagorean theorem. Mistakes in these intermediate steps are common. This calculator does all the geometry for you and shows every property at once, making it ideal for construction planning, fabric cutting, land surveying, and homework verification.
Area = ½ × (a + b) × h Perimeter = a + b + leg₁ + leg₂ Median (midsegment) = (a + b) / 2 Isosceles leg = √(h² + ((a − b) / 2)²) Right trapezoid: left leg = h, right leg = √(h² + (a − b)²) Diagonals (coordinates): Place A at origin, B at (a, 0), D at (x₁, h), C at (a − x₂, h) d₁ = √((a − x₂)² + h²) d₂ = √((a − x₁)² + h²)
Result: Area = 50 cm², Perimeter ≈ 30.7703 cm, Median = 10 cm
With an isosceles trapezoid where a = 12 cm, b = 8 cm, and h = 5 cm, the area is ½ × (12 + 8) × 5 = 50 cm². The median is (12 + 8) / 2 = 10 cm. Because the bases differ by 4 cm, each side offsets by 2 cm, so each equal leg is √(5² + 2²) = √29 ≈ 5.3852 cm, giving a perimeter of about 30.7703 cm.
Trapezoids appear whenever two opposite edges are parallel but not equal in length. That makes them common in roof profiles, retaining walls, bridge sections, window awnings, planters, and cut panels. In these situations, finding the area is only the first step. You may also need the perimeter for trim material, the legs for side pieces, the diagonals for bracing, or the base angles for cutting parts accurately. This calculator groups those measurements in one place instead of forcing you to switch between several formulas.
The solve mode matters because different trapezoids imply different geometry. A right trapezoid has one perpendicular leg, so one side is exactly the height. An isosceles trapezoid has matching legs and equal base-angle geometry, which lets the calculator derive leg lengths and diagonals symmetrically. A general trapezoid is more flexible, and this tool lets you enter optional left and right legs when you know them. Matching the UI selection to the actual shape is the key to getting perimeter, angle, and diagonal outputs that reflect the object you are modeling.
A good quick check is to compare the trapezoid's area with a rectangle using the same height and the average base length. Because the trapezoid area formula is one-half times the sum of the bases times the height, the result should always equal height multiplied by the median. The side proportion chart in this calculator helps you spot distorted entries at a glance, and the reference table gives examples across small and large scales so you can compare your dimensions against familiar shapes.
A = ½ × (a + b) × h, where a and b are the parallel sides and h is the perpendicular height between them. Use this as a practical reminder before finalizing the result.
In American English, a trapezoid has one pair of parallel sides. In British English, this same shape is called a trapezium. The terminology is essentially reversed between the two conventions.
For an isosceles trapezoid: h = √(leg² − ((a − b) / 2)²). For a general trapezoid, you need additional information such as an angle or diagonal.
The median (or midsegment) connects the midpoints of the two legs. Its length is always (a + b) / 2 — the average of the two bases.
Yes — a right trapezoid has two right angles. One leg is perpendicular to both bases.
Place the trapezoid on a coordinate grid with one base along the x-axis. Then use the distance formula between opposite corners. This calculator does it automatically.
By the inclusive definition (used in most modern textbooks), yes — a parallelogram is a special trapezoid with both pairs of sides parallel. Under the exclusive definition, a trapezoid has exactly one pair of parallel sides.
Handbags, lamp shades, some table tops, bridge cross-sections, dam profiles, roof outlines, and many architectural elements are trapezoidal. Keep this note short and outcome-focused for reuse.