Calculate all four angles of a trapezoid from sides and height or from two known angles. Shows angle bars, area, perimeter, diagonals, and midsegment with reference tables.
The angles of a trapezoid are closely linked to its sides, height, and special type. In any trapezoid the two angles on the same leg are supplementary — they add up to 180°. This property, known as the co-interior (or same-side interior) angle theorem, is a direct consequence of the parallel bases. Therefore, knowing just two base angles is enough to determine all four.
For an isosceles trapezoid the two base angles are equal, and the two top angles are equal, giving a beautifully symmetric shape. A right trapezoid has one leg perpendicular to the bases, producing two 90° angles, while the remaining two angles are supplementary.
When the two parallel bases (a, b) and the height (h) are known, trigonometry reveals the angles: if the left offset x₁ = √(leg₁² − h²), the bottom-left angle is arctan(h / x₁). In the isosceles case the offset simplifies to (b − a)/2 and only one arctan call is needed. Knowing the angles has practical value in construction (cutting roof trusses), metalwork (bending sheet metal), and land surveying (field plots).
This calculator supports three input modes: from sides and height, from two known base angles, or from parallel sides plus one leg and height. It outputs all four angles, area, perimeter, diagonals, and midsegment.
Angle questions often start with incomplete information: you may know the two bases and height, or just two base angles, but still need all four corner measures to finish a proof, sketch, or fabrication drawing. This calculator solves those mixed cases quickly and also shows area, diagonals, and midsegment so you can verify that the geometry is consistent. It is useful for classroom checks, roof and hopper layouts, and any trapezoid problem where supplementary angle relationships matter.
Co-interior angles: ∠bottom + ∠top = 180° (same leg) Isosceles: ∠BL = ∠BR = arctan(2h / (b − a)) General: ∠BL = arctan(h / x₁), where x₁ = √(leg₁² − h²) ∠TL = 180° − ∠BL; ∠TR = 180° − ∠BR Angle sum: ∠BL + ∠BR + ∠TL + ∠TR = 360°
Result: Bottom angles ≈ 63.43° each; top angles ≈ 116.57° each
With topBase = 6, bottomBase = 10, and height = 4, the trapezoid is treated as isosceles because both legs are left blank. The horizontal offset on each side is (10 - 6) / 2 = 2, so each bottom angle is arctan(4 / 2) ≈ 63.43°. Each top angle is 180° - 63.43° ≈ 116.57°.
A trapezoid has two bottom angles and two top angles, and the pair on each leg must sum to 180 degrees because the bases are parallel. That is the first pattern to check when you solve a problem manually. In an isosceles trapezoid the two bottom angles match and the two top angles match, while a right trapezoid forces one leg to create two 90 degree angles.
Use the sides-height mode when you know the two bases and the altitude, because the horizontal offsets determine the base angles through tangent. Use the two-angles mode when a diagram or proof already gives you two lower angles and you want the remaining pair immediately. The sides-plus-one-leg mode is helpful when one slanted side is measured directly and the other must be inferred from the base difference and height.
Angle values are often the last step before cutting material or confirming a drawing. A symmetric pair of 63.43 degree base angles, for example, tells you the shape behaves like an isosceles trapezoid and will produce equal diagonals. In geometry coursework, checking that all four interior angles total 360 degrees is also a quick way to catch a mistaken offset or an incorrect trigonometric setup.
Place the trapezoid on a coordinate plane with the bottom base along the x-axis. Compute the horizontal offsets from the legs and height, then use arctan(h / offset) for each base angle. The top angles are 180° minus the corresponding base angles.
Yes. Like any quadrilateral, the sum of the interior angles of a trapezoid is always 360°.
Co-interior (same-side interior) angles are the two angles on the same leg. Because the bases are parallel, they always add up to 180°.
Both base angles are equal and both top angles are equal. This means the shape is symmetric about the perpendicular bisector of the two bases.
Yes — a right trapezoid has one leg perpendicular to both bases, giving two 90° angles. It cannot have three or four right angles (that would be a rectangle).
If you know one pair of co-interior angles (on the same leg), you already know all four: the other pair is (180° − angle₁) and (180° − angle₂). Use the two-angles mode in this calculator.