Trapezoid Calculator

Professional online calculators for all types of trapezoid calculations

Special Trapezoid Types

Unsymmetrical Trapezoid
General trapezoid - calculation of all parameters from various inputs
Isosceles Trapezoid (b = d)
Symmetrical trapezoid with equal legs
Right-Angled Trapezoid (90°)
Trapezoid with one right angle - simplified calculations
Tri-Equilateral Trapezoid
Trapezoid with three equal sides - rare special form

Area and Basic Calculations

Trapezoid Area (A = ½(a+c)h)
Classic area calculation from parallel sides and height
Height from Sides and Area
Height calculation when area and parallel sides are known
Height from Side and Angle
Height calculation via trigonometric functions
Angle from Side and Height (α = arcsin(h/d))
Angle calculation via arcsine function

Diagonal Calculations

Diagonal e from Sides and Height
Calculation of the first diagonal from side lengths and height
Diagonal e from Sides and Angle
Diagonal calculation via law of cosines
Diagonal f from Sides and Height
Calculation of the second diagonal from side lengths and height
Diagonal f from Sides and Angle
Diagonal calculation via law of cosines from sides and angles

About Trapezoid Geometry

Trapezoid geometry forms an important part of mathematics and finds practical application in:

  • Architecture - Roof construction, building design
  • Engineering - Channel design, structural elements
  • Hydraulics - Water channel profiles
  • Surveying - Land measurement
  • Manufacturing - Machine part design
  • Education - Geometry learning
Fundamental Trapezoid Formulas
Area Calculations
Area: A = ½(a+c)×h
Height: h = 2A/(a+c)
Angle Relations
Height: h = d×sin(α)
Angle: α = arcsin(h/d)
Diagonal Calculations
Law of cosines
Pythagorean theorem
Special Types
Isosceles: b = d
Right-angled: α = 90°
Tip: A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases, the non-parallel sides are called legs.

Practical Application Examples

Civil Engineering
  • Bridge Construction: Trapezoidal cross-sections
  • Road Design: Embankment slopes
  • Dam Construction: Cross-sectional calculations
Hydraulic Engineering
  • Canal Design: Water flow optimization
  • Drainage Systems: Channel profiles
  • Irrigation: Trapezoidal channels
Architecture
  • Roof Structures: Trapezoidal roof shapes
  • Window Design: Trapezoidal openings
  • Foundations: Footing calculations
Manufacturing
  • Sheet Metal: Bent profiles
  • Machine Parts: Trapezoidal components
  • Packaging: Container design
Quick Reference
½(a+c)h
Area
a+b+c+d
Perimeter
h×sin(α)
Height
arcsin(h/d)
Angle
1 pair parallel sides
Definition
Trapezoid Types
General: No special properties Basic
Isosceles: Equal legs (b = d) Symmetric
Right-angled: One 90° angle Special
Tri-equilateral: Three equal sides Rare
Calculation Methods

Direct Formulas: For area and perimeter calculations

Trigonometry: For angles and heights

Law of Cosines: For diagonal calculations