Trapezoid Calculator
Calculate the area, perimeter, height, or base of a trapezoid from any known combination of values.
Select what you want to find, enter the known values, and get an instant result with the formula used.
Trapezoid Calculator
Calculate the area, perimeter, height, or base of a trapezoid from any known combination of values.
Calculate the area from both bases and the height. Formula: A = (a + b) × h / 2.
About the Trapezoid Calculator
A trapezoid (also called a trapezium in British English) is a quadrilateral with exactly one pair of parallel sides. Those parallel sides are called the bases, conventionally labeled a and b, while the two non-parallel connecting sides are called legs, labeled c and d. The perpendicular distance between the two bases is the height h.
The trapezoid is one of the most practically important shapes in geometry. Road cross-sections, structural beams, land surveying parcels, retaining walls, and countless architectural elements are trapezoidal in profile. Understanding how to compute the area, perimeter, and height of a trapezoid is therefore a fundamental skill in engineering, construction, and design.
The area formula A = (a + b) × h / 2 can be understood as the average of the two base lengths multiplied by the perpendicular height. This is the same as computing the area of a rectangle whose width equals the average base and whose height equals the trapezoid's height. The formula holds for all trapezoids regardless of whether the legs are equal (isosceles trapezoid) or different (scalene trapezoid), as long as the height h is measured perpendicularly between the two parallel bases.
The perimeter formula P = a + b + c + d is simply the sum of all four sides. In cases where the legs are not given directly but angles are known, you can compute leg lengths from the bases and height using trigonometry: c = h / sin(θ_c) and d = h / sin(θ_d). However this calculator takes the leg lengths directly, which is the most common situation in practical measurement.
The height can be recovered from the area and bases: h = 2A / (a + b). This is useful in surveying when you have measured all four sides and computed the area by another method (such as the shoelace formula), and you need the perpendicular distance for height-clearance or drainage gradient calculations.
Finding a missing base given the area, height, and other base uses a = (2A / h) − b. This is common in land layout: you know how large a plot must be, you know one boundary and the depth of the lot, and you need to calculate the length of the opposite boundary to achieve the target area.
All four modes of this calculator apply standard Euclidean geometry and are valid for any trapezoid with positive real values for its dimensions. The results carry the same units as the inputs: if you enter lengths in meters, area is in square meters; if in feet, area is in square feet.
Trapezoid calculator examples
Four scenarios showing each calculation mode with realistic dimensions.
| Known Values | Result | Explanation |
|---|---|---|
| Find Area: a = 10, b = 15, h = 8 | Area = 100 sq units | A = (10 + 15) × 8 / 2 = 25 × 4 = 100. A standard trapezoid with parallel bases of 10 and 15 and height of 8. |
| Find Perimeter: a = 10, b = 15, c = 9, d = 9 | Perimeter = 43 units | P = 10 + 15 + 9 + 9 = 43. An isosceles trapezoid with equal legs of length 9. |
| Find Height: A = 100, a = 10, b = 15 | Height = 8 units | h = 2 × 100 / (10 + 15) = 200 / 25 = 8. Recovering the height from the area and bases. |
| Find Base a: A = 120, h = 10, b = 14 | Base a = 10 units | a = (2 × 120 / 10) − 14 = 24 − 14 = 10. Finding the unknown parallel side from area, height, and other base. |
How to use the Trapezoid Calculator
- Select the quantity you want to find: Area, Perimeter, Height, or a Base.
- Enter the values that are known for your trapezoid in the displayed input fields.
- Click Calculate. The result appears instantly along with the formula used.
- Click Reset to clear the fields and start a new calculation with different values.
- Switch to a different mode if you need to solve for another property of the same trapezoid.
Trapezoid Calculator FAQ
What is the formula for the area of a trapezoid?
The area formula is A = (a + b) × h / 2, where a and b are the lengths of the two parallel sides (bases) and h is the perpendicular height between them. This can be read as the average base length multiplied by the height, and it applies to all trapezoids regardless of whether the legs are equal.
What is the difference between a trapezoid and a parallelogram?
A parallelogram has two pairs of parallel sides, while a trapezoid has exactly one pair. This means a rectangle, rhombus, and square are all parallelograms but not trapezoids. In North American convention a trapezoid has exactly one pair of parallel sides; in some other conventions any quadrilateral with at least one pair of parallel sides is called a trapezoid (making parallelograms a special case).
How do I find the height of a trapezoid if I only know the area?
Use the Find Height mode. Enter the area and both base lengths. The calculator applies h = 2A / (a + b) to recover the perpendicular height. Note that you need both bases as well as the area — you cannot determine height from area alone without additional information.
Can I find a leg length using this calculator?
The Find Perimeter mode requires you to enter all four sides including the legs, so it works in the other direction — you provide legs to find perimeter, not the other way around. To find leg length from height and base offset, you would use the Pythagorean theorem: c = √(h² + offset²), where offset is the horizontal distance by which one base extends beyond the other. This calculator focuses on the four standard modes.
What is an isosceles trapezoid?
An isosceles trapezoid is a special case where the two legs (non-parallel sides) are equal in length. This also means the two base angles on each base are equal. Isosceles trapezoids are symmetric about the perpendicular bisector of both bases, and they are common in architecture and graphic design. All four modes of this calculator work for isosceles trapezoids.
Why does the area formula use a half?
The factor of one-half comes from averaging the two bases. Because the trapezoid has one short parallel side and one long parallel side, the average width at any horizontal slice is not simply one of the bases but their arithmetic mean (a + b) / 2. Multiplying this average width by the height gives the area. The formula is also easy to derive by cutting the trapezoid into a rectangle and two triangles.