Trapezoid Calculator
Find area, midsegment, and perimeter of a trapezoid
Results
Area
Midsegment
Height
Perimeter
Diagonal p
Diagonal q
Base Angle α (lower-left)
Base Angle β (lower-right)
Top-Left Angle
Top-Right Angle
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Trapezoid Calculator Formula
Area of a trapezoid:
A = (b₁ + b₂) / 2 × h
b₁, b₂ = the two parallel bases; h = the perpendicular height between them.
Midsegment (median) of a trapezoid:
m = (b₁ + b₂) / 2
b₁, b₂ = the two parallel bases.
Perimeter of a trapezoid (when both legs are known):
P = b₁ + b₂ + c + d
b₁, b₂ = the parallel bases; c, d = the two legs (non-parallel sides).
Diagonals of a trapezoid (when both legs are known), using leg offsets x = √(c² − h²) and y = √(d² − h²):
p = √((x + b₁)² + h²), q = √((y + b₁)² + h²)
x, y = horizontal offsets of the top base under each leg; b₁ = the shorter base; h = the height.
Interior angles of a trapezoid (when both legs are known):
α = arctan(h / x), β = arctan(h / y), top = 180° − base
α, β = the two base angles at the longer base; the two top angles are their supplements (180° − α and 180° − β). Angles are in degrees.
How to Use This Calculator
- Enter the two parallel sides as base 1 and base 2 (their order does not matter).
- Enter the perpendicular height between the two bases.
- Optionally, enter the two legs (the slanted, non-parallel sides) to also get the perimeter, diagonals, and interior angles.
- Click Calculate to see the area, midsegment, height, and — if you entered both legs — the perimeter, both diagonals, and all four interior angles.
- Copy the URL that updates automatically after calculating to share your result.
Frequently Asked Questions
How do you calculate the area of a trapezoid?
Use the trapezoidal area formula A = (b₁ + b₂) / 2 × h, where b₁ and b₂ are the two parallel bases and h is the perpendicular height between them. In other words, average the two bases and multiply by the height. For example, bases of 5 and 9 with a height of 4 give an area of (5 + 9) / 2 × 4 = 28 square units.
What is the midsegment of a trapezoid?
The midsegment (also called the median) is the segment connecting the midpoints of the two legs. Its length is the average of the two bases: m = (b₁ + b₂) / 2. It is always parallel to the bases and lies exactly halfway between them.
How do you find the perimeter of a trapezoid?
Add up all four sides: P = b₁ + b₂ + c + d, where c and d are the two legs (non-parallel sides). This calculator computes the perimeter automatically once you enter both legs. If you only enter the bases and height, it still gives you the area and midsegment.
How do you find the diagonals of a trapezoid?
Once you know both legs, the calculator resolves how far each leg slants inward — the horizontal offset x = √(c² − h²) under one leg and y = √(d² − h²) under the other — and then applies the Pythagorean theorem: diagonal p = √((x + b₁)² + h²) and diagonal q = √((y + b₁)² + h²). Enter the two bases, the height, and both legs to see both diagonals automatically. For an isosceles trapezoid the two diagonals are equal.
What are the interior angles of a trapezoid?
A trapezoid has four interior angles that always add up to 360°. With both legs entered, the calculator finds the two base angles from the leg offsets — α = arctan(h / x) and β = arctan(h / y) — and the two top angles are their supplements (180° − α and 180° − β), because each base and the leg meeting it form co-interior angles between the parallel sides. The angles are shown in degrees.
Why does the trapezoidal area formula use the average of the bases?
A trapezoid can be thought of as a rectangle whose width is the average of its two bases. Averaging the bases, (b₁ + b₂) / 2, gives that effective width — which is exactly the midsegment — and multiplying by the height h gives the area. This is why the area equals the midsegment times the height.
Do the two bases have to be entered in a specific order?
No. Because the formula adds the two bases together, b₁ and b₂ are interchangeable — entering 5 and 9 gives the same result as 9 and 5. The same is true for the two legs when calculating perimeter.
What units does the trapezoid calculator use?
The calculator is unit-agnostic: enter all measurements in the same unit. The area comes out in square units (square feet, square meters, etc.), while the midsegment, height, and perimeter are in the same linear unit as your inputs.
Can I calculate a trapezoid's area if I only know one base and the height?
No — the trapezoidal area formula needs both parallel bases plus the height. If your shape has four right angles and one pair of parallel sides equal, it may be a rectangle instead; in that case use the Rectangle Calculator. For a slanted four-sided shape with both pairs of sides parallel, use the Parallelogram Area Calculator.