Centered bases
For B = 10, b = 6, and h = 3, centered mode gives offset 2. Area is 24 square units, each leg is √13, and perimeter is approximately 23.21110255.
Trapezoid Calculator inputs
Changing the unit relabels the numbers. Convert measurements to one common unit before entering them.
Height h is the perpendicular gap between the parallel bases. In general mode, offset x locates the top-left corner relative to the bottom-left corner. Negative offsets and overhangs are allowed.
Calculated measurements
Area
24 units²
| Measurement | Value |
|---|---|
| Area | 24 units² |
| Perimeter | 23.21110255 units |
| Left leg | 3.605551275 units |
| Right leg | 3.605551275 units |
| Midline length | 8 units |
| Top-left horizontal offset | 2 units |
Formula: A = (B + b)h/2; left = √(h² + x²); right = √[h² + (B − b − x)²]
Offset x is measured from the bottom-left vertex to the top-left vertex, positive to the right. Equal bases are accepted as a parallelogram.
Results use full floating-point precision internally and display up to 10 significant digits. Angles are in degrees.
Calculations run locally in your browser. Measurement values are not sent to a calculation service. The downloadable text contains your selected inputs and computed results.
How to use the Trapezoid Calculator
- 01
Choose general mode for a measured offset or centered isosceles mode for equal legs.
- 02
Enter bottom base B, top base b, and perpendicular height h in one unit.
- 03
In general mode, enter the signed horizontal displacement from the bottom-left to top-left vertex.
- 04
Inspect the fitted shape, area, both legs, perimeter, and midline; copy or download the results.
Examples
One vertical leg
For B = 10, b = 6, h = 3, and offset 0, the left leg is 3 and right leg is 5. Area stays 24, while the perimeter is 24.
An overhanging top
For B = 10, b = 6, h = 3, and offset −2, the upper left vertex lies left of the bottom-left origin. Area is still 24; the two leg lengths change.
Area needs three lengths; perimeter needs more
The area formula is (B + b)h/2, so the two bases and perpendicular height suffice for area. They do not generally fix the legs: sliding the top base sideways preserves area but changes the boundary. The extra offset in general mode supplies that missing geometric information.
Define the horizontal offset consistently
Place the bottom-left corner at (0, 0) and bottom-right at (B, 0). The top-left corner is (x, h) and top-right is (x + b, h). A positive x moves the upper base right; a negative x moves it left. Large offsets can put the upper base beyond the lower one without invalidating the quadrilateral.
Recover the two nonparallel edges
The left leg is √(h² + x²). The right leg is √[h² + (B − b − x)²]. Perimeter adds these legs to both bases. Centered mode uses x = (B − b)/2, making the legs equal even when the top base is longer than the bottom base.
Height and midline are different segments
Height is the perpendicular separation between the parallel lines containing the bases. It is not generally either slanted leg. The midline joins the midpoints of those legs, runs parallel to the bases, and has length (B + b)/2. Multiplying the midline by height gives the same area formula.
What to know
- Straight-edged shapes with parallel bases and positive perpendicular height only.
- Input bases and height use the 10⁻⁹–10⁹ range; offset is bounded to ±10⁹.
Common questions
Why does the tool ask for an offset?
Bases and height determine area, but not a general trapezoid’s perimeter. The offset locates the upper base so both leg lengths can be calculated.
Must the bottom base be longer?
No. B and b identify location in the diagram. Either can be longer, and the height must remain positive.
Are equal bases allowed?
Yes. This tool uses the inclusive convention of at least one pair of parallel sides. Equal bases describe a parallelogram; centered equal bases give a rectangle.
Can offset be negative or greater than a base?
Yes. It is a signed coordinate difference rather than a side length. Supported offsets range from −10⁹ to 10⁹ units.