Online trapezoid calculator

Online calculator and formulas for trapezoid computations

Trapezoid Calculator

Trapezoid calculation

To compute the trapezoid provide either the parallel sides a and c, height h and excess x; alternatively supply a angle and three side lengths.

Select calculation method
Choose between excess-based or angle-based calculation
Excess in length units or angle in degrees
Enter trapezoid parameters
Distance between the parallel sides
First parallel side of the trapezoid
Second parallel side of the trapezoid
Calculation results
Side a:
Side b:
Side c:
Side d:
Diagonal e:
Diagonal f:
Height h:
Middle width m:
Area A:
Perimeter P:
Angle α:
Angle β:
Angle γ:
Angle δ:
Excess x:
Excess y:

Trapezoid diagram

The diagram shows a general trapezoid with all parameters.
Computations are performed using different combinations of sides, angles and height.

Trapezoid

Calculation methods for the trapezoid

The trapezoid calculator offers several calculation methods depending on available parameters:

  • Excess method: sides a, c, height h and excess x
  • Angle α/δ method: three sides and angle α or δ
  • Angle β/γ method: three sides and angle β or γ
  • Automatic computation: All missing parameters are calculated
  • Complete results: sides, angles, area, perimeter, diagonals
  • Accurate formulas: trigonometric and geometric calculations

Formulas for the trapezoid

Side lengths
Side a: \[a = \frac{2A}{h} - c = 2m - c\] Side b: \[b = \frac{h}{\sin(\beta)} = \frac{h}{\sin(\gamma)}\] Side c: \[c = \frac{2A}{h} - a = 2m - a\] Side d: \[d = \frac{h}{\sin(\alpha)} = \frac{h}{\sin(\delta)}\]

Basic side calculations

Area and perimeter
Area: \[A = \frac{(a + c) \cdot h}{2} = m \cdot h\] Perimeter: \[P = a + b + c + d\] Middle width: \[m = \frac{a + c}{2} = \frac{A}{h}\]

Area and perimeter calculations

Angles
Angle α: \[\alpha = \arcsin\left(\frac{h}{d}\right) = 180° - \delta\] Angle β: \[\beta = \arcsin\left(\frac{h}{b}\right) = 180° - \gamma\] Angle γ: \[\gamma = 180° - \beta\] Angle δ: \[\delta = 180° - \alpha\]

Angle relationships in the trapezoid

Diagonals and excesses
Diagonal e: \[e = \sqrt{a^2 + b^2 - 2ab\cos(\beta)}\] Diagonal f: \[f = \sqrt{a^2 + d^2 - 2ad\cos(\alpha)}\] Excess x: \[x = \sqrt{d^2 - h^2}\] Excess y: \[y = \sqrt{b^2 - h^2}\]

Diagonals and horizontal excesses

Calculation example

Given (excess method)
Side a = 7 Side c = 4 Height h = 3 Excess x = 1

Find: All parameters of the trapezoid

1. Compute legs
\[d = \sqrt{h^2 + x^2} = \sqrt{3^2 + 1^2} = \sqrt{10} ≈ 3.16\] \[y = \frac{|a - c|}{2} - x = \frac{|7 - 4|}{2} - 1 = 0.5\] \[b = \sqrt{h^2 + y^2} = \sqrt{9 + 0.25} ≈ 3.04\]

Calculation of the slanted sides

2. Area and perimeter
\[A = \frac{(a + c) \cdot h}{2} = \frac{(7 + 4) \cdot 3}{2} = 16.5\] \[P = a + b + c + d = 7 + 3.04 + 4 + 3.16 = 17.2\] \[m = \frac{a + c}{2} = \frac{11}{2} = 5.5\]

Area and perimeter calculation

3. Compute angles
\[\alpha = \arcsin\left(\frac{h}{d}\right) = \arcsin\left(\frac{3}{3.16}\right) ≈ 71.6°\] \[\beta = \arcsin\left(\frac{h}{b}\right) = \arcsin\left(\frac{3}{3.04}\right) ≈ 80.5°\] \[\gamma = 180° - 80.5° = 99.5°\] \[\delta = 180° - 71.6° = 108.4°\]

All four angles of the trapezoid

4. Diagonals
\[e = \sqrt{a^2 + b^2 - 2ab\cos(\beta)} ≈ 7.67\] \[f = \sqrt{a^2 + d^2 - 2ad\cos(\alpha)} ≈ 7.28\]
Trapezoid fully computed

All geometric parameters determined

Practical applications of trapezoid calculations

General trapezoid calculations are applied across many technical and scientific fields:

Construction & Architecture
  • Roof structures with variable slopes
  • Foundation cross-sections and slopes
  • Bridge piers and retaining walls
  • Stair runs and ramps
Engineering & Production
  • Flow channels with trapezoidal cross-sections
  • Tool profiles and cutting edges
  • Gear wheels and V-belt profiles
  • Containers and hopper designs

The trapezoid in geometry

The general trapezoid is a quadrilateral with one pair of parallel sides. This universal calculator enables computing all geometric parameters based on different input combinations. The flexible calculation methods make it a valuable tool for technical and scientific applications.

Computations can be performed either via the excess method (when height and horizontal offset are known) or via angle methods (when angles and three side lengths are known). All results are computed automatically and include side lengths, angles, area, perimeter, diagonals and excesses.

For specialized tasks there are additional trapezoid calculators available, optimized for specific trapezoid types (symmetric, right-angled) or dedicated calculations (area only, angles only).

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