What is a kite in geometry?

In plane geometry, a kite is a quadrilateral with two distinct pairs of adjacent sides that are equal. That is, the two sides forming one vertex are equal, and the two sides forming the opposite vertex are equal. The diagonals of a kite are perpendicular, and one diagonal bisects the other.

What is the formula for the area of a kite using diagonals?

If d1 and d2 are the lengths of the diagonals of a kite, and they intersect at right angles, the area is given by A = d1 × d2 / 2. This formula is widely used in geometry because the diagonals split the kite into four right triangles.

How do I find the area of a kite from side lengths and angle?

If a and b are the lengths of two adjacent sides of a kite and θ is the angle between them, one way to express the area is A = a × b × sin(θ). This formula comes from splitting the kite into congruent triangles with base a and b and included angle θ.

Which units does the kite area calculator use?

You can work in any consistent length unit: meters, centimeters, feet, inches, or kite-surf sail sizes in square meters. The area will be in the squared unit of your input (for example m² if the diagonals are in meters).

Is this kite area calculator for geometry or kitesurfing equipment?

The calculator is primarily a geometry tool for computing the area of a planar kite. However, the same formulas apply whenever the planform of a wing or sail is kite-shaped, so it can be used as a support tool when estimating kite or kitesurf sail area from key geometric dimensions.

Kite Area Calculator – Area of a Kite from Diagonals or Sides

Compute the area of a geometric kite using either its diagonals or two adjacent sides and the included angle. Ideal for geometry practice, exam prep, and simple engineering or design estimates.

Definition of a kite (geometry)

In plane geometry, a kite is a quadrilateral with two pairs of adjacent sides equal in length. If we label the vertices in order as \(A, B, C, D\), then a typical kite has

\(AB = AD\)
\(BC = CD\)
but usually \(AB \ne BC\).

One important property is that the diagonals are perpendicular and one diagonal (the one connecting the vertices where the equal sides meet) bisects the other.

Area of a kite from diagonals

Let \(d_1\) and \(d_2\) be the lengths of the diagonals of a kite. If they are perpendicular, then the area is

\[ A = \frac{d_1 \cdot d_2}{2}. \]

Geometrically, the diagonals split the kite into four right triangles. The total area is the sum of the areas of these triangles.

Area of a kite from sides and angle

Suppose two adjacent sides have lengths \(a\) and \(b\), and the angle between them is \(\theta\). When the kite is symmetric about the diagonal through the equal sides, the area can be written as

\[ A = a \cdot b \cdot \sin(\theta). \]

This formula comes from viewing the kite as two congruent triangles with side lengths \(a\) and \(b\) and included angle \(\theta\).

Side–angle formula

For each triangle, \[ A_{\triangle} = \frac{1}{2} a b \sin(\theta), \] and there are two such triangles, so \[ A_{\text{kite}} = 2 \cdot A_{\triangle} = 2 \cdot \frac{1}{2} a b \sin(\theta) = a b \sin(\theta). \]

Worked examples

1. Kite area from diagonals

Example: a kite has diagonals \(d_1 = 8\ \text{cm}\) and \(d_2 = 6\ \text{cm}\).

Compute the product of the diagonals: \(d_1 \cdot d_2 = 8 \times 6 = 48\ \text{cm}^2\).
Divide by 2: \(A = 48 / 2 = 24\ \text{cm}^2\).

So the area is \(24\ \text{cm}^2\).

2. Kite area from sides and angle

Example: a kite has two adjacent sides with lengths \(a = 5\ \text{m}\) and \(b = 4\ \text{m}\), and the included angle is \(\theta = 60^\circ\).

Compute \(\sin(60^\circ) \approx 0.8660\).
Multiply: \(A = a b \sin(\theta) = 5 \cdot 4 \cdot 0.8660 \approx 17.32\ \text{m}^2\).

So the area is approximately \(17.3\ \text{m}^2\).

Units: from geometry to kitesurf sail area

The formulas above are unit-agnostic. If all lengths are in meters, the area will be in square meters; if lengths are in centimeters, the area will be in square centimeters, and so on.

This is also how kite or kitesurf sail sizes are given: a “9 m² kite” has an approximate planform area of 9 square meters. When the kite has a kite-like planform, you can approximate its area with the same diagonal or side–angle formulas, treating the key geometry dimensions as \(d_1\), \(d_2\), \(a\), and \(b\).

Common pitfalls and checks

Ensure the diagonals correspond to the actual kite, and that they intersect at right angles (or nearly so) if you use the diagonal formula.
For side–angle input, the angle must be the one between the equal sides \(a\) and \(b\), not some other angle in the quadrilateral.
Keep units consistent. Mixing centimeters and meters will give an incorrect area.
Quickly sanity check: the area should be smaller than the square built on the longest diagonal or the rectangle \(a \times b\), depending on which formula you use.

Kite Area Calculator

Calculate kite area from your preferred dimensions

Area from diagonals

Area from sides and angle