Trapezoid Calculator
Calculate area, perimeter, median, leg lengths, and interior angles from a consistent trapezoid geometry.
Dimensions
Use one unit for all lengths. The lower base must be at least as long as the upper base.
Controls how the horizontal base difference is divided between the two legs.
Changing units converts the current dimensions and all displayed results.
Required lower parallel base; enter a positive decimal using a period.
Required upper parallel base; it cannot exceed Base (a) in this model.
Required perpendicular distance between the two parallel bases.
Required only for Custom; use 0 to align the left leg vertically.
Live results
Values update as you type and use the selected length unit.
Area (A)
38.0000 m²
The surface enclosed by the trapezoid.
A = ((a + b) × h) ÷ 2
Area 38.0000 square meters; perimeter 28.4721 meters.
Geometry breakdown
| Quantity | Symbol | Value | Interpretation |
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How to use this trapezoid calculator
What this calculator does
This calculator turns a consistent set of trapezoid dimensions into area, perimeter, median length, both leg lengths, and all four interior angles. It models a convex trapezoid whose lower base is at least as long as its upper base. It is useful for geometry exercises, estimating a trapezoidal panel or plot, checking a technical drawing, and comparing isosceles, right, and offset trapezoids. It does not determine whether a real object is level, square, or built to tolerance; those questions require physical measurements and an appropriate surveying or fabrication method.
When to use it
Use the calculator when you know the two parallel bases and the perpendicular height, and you also know or can choose how the upper base is positioned horizontally. Typical applications include checking a homework solution, estimating the face area of a retaining-wall section, finding the edge length needed for a trapezoidal sign, or deriving angles for a layout sketch. OpenStax explains the same base-and-height area relationship in its trapezoid properties and area lesson.
How to calculate
- The calculator opens with a complete demonstration: Custom shape, meters, Base (a) = 12, Base (b) = 7, Height (h) = 4, and Left horizontal offset (x) = 2. The results and a validated example XLSX workbook are available immediately.
- Choose Shape type. Isosceles splits the base difference equally, Right aligns the left leg vertically, and Custom lets you enter the left offset directly.
- Choose the Length unit, then replace the sample values in Base (a), Base (b), and Height (h). The unit selector converts existing dimensions rather than merely relabeling them.
- For Custom, enter Left horizontal offset (x) between zero and the difference a – b. Read the live area and the secondary results, then review the geometry breakdown for the angles.
- Select Download Excel to create a fresh workbook from the current validated state. Select Reset to clear the demonstration and all calculated content. Reset may disable Download Excel until you enter another complete valid set.
Input guide
Shape type is required and accepts Isosceles, Right, or Custom. Isosceles produces equal legs and matching base angles; Right sets the left offset to zero; Custom accepts any feasible left offset. Length unit is required and applies to every length. Available choices are millimeters, centimeters, meters, inches, feet, and yards. Lengths use a period as the decimal separator; grouped values such as 1,250.5 are accepted, while ambiguous decimal-comma values such as 1,5 are rejected.
Base (a) is the required lower parallel side. Enter a positive value, such as 12 m. Base (b) is the required upper parallel side, such as 7 m, and must be no greater than Base (a) for this acute/right-oriented model. Increasing either base increases the area and usually increases the perimeter. Height (h) is the required perpendicular distance between the bases, such as 4 m. Increasing height increases area directly and also lengthens the legs. Do not substitute a slanted leg for the height.
Left horizontal offset (x) is required only in Custom mode. It is the horizontal run from the lower-left vertex to the upper-left vertex. For the sample, x = 2 m and the remaining right offset is 3 m because a – b = 5 m. Enter zero for a vertical left leg. The value cannot be negative or greater than a – b. In Isosceles and Right modes the field is derived and locked, preventing an inconsistent combination.
Output guide
Area (A) is an exact geometric identity from the supplied dimensions, shown in square units. Perimeter (P) is the sum a + b + c + d in linear units. Median is the segment joining the leg midpoints and equals (a + b) ÷ 2. Leg (c) and Leg (d) are calculated with the Pythagorean theorem from the height and each horizontal offset. A zero horizontal offset makes the corresponding leg equal to the height.
The geometry table also reports α, β, γ, and δ in degrees. α and δ are the lower interior angles; β and γ are their supplementary upper angles. An angle of 90° marks a perpendicular leg. Smaller lower angles indicate a more strongly sloped leg. The table values are derived results, not independent recommendations, and all four angles sum to 360°.
Worked example
With a = 12 m, b = 7 m, h = 4 m, and x = 2 m, the base difference is 5 m, so the right horizontal offset is 3 m. The area is ((12 + 7) × 4) ÷ 2 = 38.0000 m². The median is (12 + 7) ÷ 2 = 9.5000 m. The legs are √(4² + 2²) = 4.4721 m and √(4² + 3²) = 5.0000 m, giving a perimeter of 28.4721 m. The lower angles are approximately 63.43° and 53.13°, with supplementary upper angles of 116.57° and 126.87°.
Formula notes and common mistakes
The trapezoid area formula averages the parallel bases and multiplies that average by the perpendicular height. This is the same as multiplying the median by the height. Perimeter, by contrast, needs all four side lengths; it cannot be found from area alone. A common mistake is to use a slanted leg as h, which overstates the area unless that leg is perpendicular to both bases.
The angle calculations come from right-triangle trigonometry. The Pythagorean theorem links each leg to the height and its horizontal run; Wolfram MathWorld's Pythagorean theorem reference gives the underlying relationship. For broader terminology and geometric properties, see the MathWorld trapezoid reference.
Keep all inputs in one length unit. Switching the unit control converts the current values and recalculates linear and square-unit results. Very large values are accepted only while the derived calculations remain finite and within the calculator's supported numeric range.