Calculate area, perimeter, diagonals, angles, and oblique leg length of a right trapezoid with one pair of right angles.
A right trapezoid (also called a right trapezium in British English) is a quadrilateral with one pair of parallel sides and two consecutive right angles. The perpendicular side connecting the two parallel sides serves as both a leg and the height, making area calculations especially straightforward.
Right trapezoids appear frequently in real-world applications: cross-sections of road embankments and retaining walls, ramp profiles, roof sections, staircase stringers, and architectural trim pieces. Civil engineers use right-trapezoid geometry to calculate cut-and-fill volumes; carpenters encounter the shape when framing angled roof sections with one vertical wall.
This calculator takes three inputs — the two parallel sides (a and b) and the height (which equals the right-angle leg) — and computes eight results: area, perimeter, the oblique (non-right) leg length, both diagonals, the two non-right angles, and a confirmation of the two 90° angles. You can switch between unit systems and adjust decimal precision.
Eight preset buttons cover textbook examples, roof cross-sections, road embankments, and ramps. A side-length comparison bar chart shows how the four sides relate visually, and a reference table lists common right trapezoids with their areas and perimeters for quick comparison. Whether you are solving homework, designing a retaining wall, or cutting sheet metal, this tool delivers every measurement you need at a glance.
Right trapezoids come up whenever one side is vertical and the opposite side is sloped, which makes them common in ramps, embankments, retaining walls, duct transitions, and trim pieces. This calculator saves time because those jobs rarely stop at area alone: perimeter affects cut length, diagonals help with layout checks, and the oblique leg plus non-right angles matter for fabrication and fit. It is a useful bridge between textbook geometry and practical measurement work where several dependent values have to be right at the same time.
Area = (a + b) × h / 2 Oblique Leg = √((a − b)² + h²) Perimeter = a + b + h + oblique leg Diagonal 1 = √(a² + h²) Diagonal 2 = √(b² + h²) Bottom-Right Angle = arctan(h / |a − b|) Top-Right Angle = 180° − Bottom-Right Angle
Result: Area = 25 cm², Perimeter ≈ 20.385 cm, Oblique Leg ≈ 5.385 cm
Using base 6 cm, top 4 cm, and height 5 cm, the area is ((6 + 4) / 2) × 5 = 25 cm². The horizontal offset is |6 − 4| = 2 cm, so the oblique leg is √(2² + 5²) = √29 ≈ 5.385 cm. Perimeter is then 6 + 4 + 5 + 5.385 ≈ 20.385 cm, and the bottom-right angle is arctan(5 / 2) ≈ 68.2°.
A right trapezoid is easier than a general trapezoid because one leg is perpendicular to both bases. That means the height is already built into the side lengths, so area becomes straightforward. At the same time, the second leg remains oblique, which introduces an offset triangle that controls the slant length and the two non-right angles. Seeing that rectangle-plus-triangle structure makes the formulas much easier to remember and verify.
This shape appears in stair framing details, road shoulder sections, concrete forms, sheet-metal transitions, and wall profiles where one side stays plumb while another tapers. In those cases, area helps with material quantities, perimeter helps with edging or trim, and diagonals give a quick field check when confirming a drawing. The angle outputs are especially useful when you need a saw setting, bend angle, or slope reference instead of just a dimension list.
Label the longer base, shorter base, and perpendicular height before you compute anything. Then compare the base difference to the height so you can estimate whether the sloped side should be shallow or steep. This calculator is a fast way to test that intuition, confirm whether a near-rectangle is effectively square-edged, and catch mistakes where the slant side has been entered as the vertical height.
A trapezoid (one pair of parallel sides) with two consecutive right angles. The perpendicular side connecting the parallel sides acts as the height.
Yes — a right trapezoid has exactly two 90° angles, both on the same perpendicular leg. The other two angles are supplementary (they add up to 180°).
A "regular" (isosceles) trapezoid has equal non-parallel sides and equal base angles. A right trapezoid has one leg perpendicular to the bases, giving it two right angles — it is generally not isosceles.
If a = b, the shape becomes a rectangle (the oblique leg equals the height, and all angles are 90°). Use this as a practical reminder before finalizing the result.
Multiply the trapezoid area by the prism's depth: V = [(a + b) × h / 2] × d. Understanding this concept helps you apply the calculator correctly and interpret the results with confidence.
The median connects the midpoints of the two non-parallel sides and equals the average of the parallel sides: m = (a + b) / 2. It is also parallel to both bases.