About the Trapezoid Calculator
A trapezoid, called a trapezium in British English, is a four-sided shape with one pair of parallel sides. Those parallel sides are the bases, and the distance between them is the height. This calculator finds the area from the two bases and the height, or works out the height from a known area. If you only know all four sides, it works out the height from the two legs and then gives both the area and the perimeter. It also reports the midline, which is the average of the two bases and runs halfway between them.
Updated October 2026
How to use the Trapezoid Calculator
- 1Choose what you know besides the bases: the height, the area or the legs.
- 2Enter the lengths of the two parallel sides.
- 3Enter the height, area or the two slanted legs as requested.
- 4Read the area, height or perimeter in the result.
- 5Use the same unit for every side, and read areas as square units.
A worked example
A garden bed has a long edge of 12 m, a short edge of 8 m and a width of 3 m between them. The area is (12 + 8) ÷ 2 × 3, which is 30 square metres. At 20 grams of seed per square metre you need 600 grams.
Trapezoids also hide inside other shapes. A right trapezoid has two right angles, so one leg is the height. An isosceles trapezoid has equal legs and equal base angles, and splitting it into a rectangle plus two identical triangles is another way to find its area. Cutting any trapezoid along a diagonal gives two triangles that share the height, and adding their areas always matches the trapezoid formula, so you can use that as a quick check.
Real-life trapezoids
- Roof sections and gable ends.
- Cross sections of ditches, dams and road embankments.
- Land plots that taper along one boundary.
- Bag, lamp shade and table shapes in design.
Working with the sides
If your plot has four known sides but no height, use the legs mode, which is the surveyor's approach. For triangles on the same plot use the Triangle Calculator, and the Area Calculator covers rectangles, circles and other shapes. The Pythagorean Theorem Calculator shows the right-triangle step by itself.
Features
- Area from bases and height
- Height from bases and area
- Area and perimeter from all four sides
- Midline of the trapezoid
- Warns when four sides can't form a trapezoid
- Works in any unit
Frequently asked questions
What is the formula for the area of a trapezoid?
Add the two parallel sides, halve the sum and multiply by the height. With bases of 10 and 6 and a height of 4, the area is (10 + 6) ÷ 2 × 4, which is 32 square units.
Which sides are the bases?
The bases are the two sides that run parallel to each other. The other two sides, the legs, slant between them. Height is measured at a right angle to the bases, not along a leg.
How do I find the height from the sides?
Slide one leg across to form a right triangle whose base is the difference between the parallel sides, then use the Pythagorean theorem. The calculator does this when you select the legs option, and tells you if the four lengths can't join up.
What is the midline of a trapezoid?
It is the line joining the midpoints of the two legs. It runs parallel to the bases, and its length is the average of the two bases. The area equals the midline times the height.
Is a parallelogram a trapezoid?
Under the inclusive definition used in many textbooks, yes, because a parallelogram has at least one pair of parallel sides. With equal bases the legs option cannot give a unique height, so the calculator suggests base times height.
Does the unit matter?
Only that it is the same for every side. If the bases are in metres, the height must be in metres too, and the area comes out in square metres. Convert first if your measurements are mixed.