Kite Area Calculator
Find the area of a kite from its two diagonals using A = (d1 x d2) / 2, or from two adjacent sides and the angle between them using A = a x b x sin(angle). Switch modes to match the measurements you actually have. You also get the perimeter, the incircle radius, and all interior angles in one calculation.
Formula
Worked example
Diagonal method: d1 = 10 cm, d2 = 6 cm. Area = (10 x 6) / 2 = 30 cm2. Side-and-angle method: a = 5 cm, b = 7 cm, alpha = 90 deg. Area = 5 x 7 x sin(90 deg) = 35 cm2; perimeter = 2(5 + 7) = 24 cm; incircle radius = 2 x 35 / 24 = 2.917 cm. Reverse: area = 30 cm2, d1 = 10 cm, then d2 = 2 x 30 / 10 = 6 cm.
Two ways to find the area of a kite
A kite is a quadrilateral with two pairs of adjacent, equal-length sides and an axis of symmetry. Its area can be reached from two different starting points depending on what you have measured. If you know both diagonals, use A = (d1 x d2) / 2. The diagonals of every kite cross at right angles, so the kite occupies exactly half the rectangle bounded by the two diagonals, and no trigonometry is needed. If instead you know the two adjacent unequal sides and the angle between them, use A = a x b x sin(alpha). This is the formula for the area of a parallelogram halved, and it reduces to the first formula when the angle is 90 degrees. Both formulas give the same answer for the same shape, so choose whichever matches the measurements you already have.
Perimeter and the incircle radius
Every kite has a perimeter of P = 2(a + b), since the two pairs of equal sides each appear twice. A notable property of kites is that every kite has an inscribed circle, called the incircle, that touches all four sides. Its radius is r = 2A / P, where A is the area and P is the perimeter. To compute the perimeter and incircle radius in diagonal mode, toggle the "Also compute perimeter" option and enter the two side lengths. In sides-and-angle mode the calculator derives them automatically from a, b and alpha.
Reverse-solve: finding a diagonal from the area
Sometimes you know the area and one diagonal but need the other, for example when working from a survey plan or a pattern template. Rearranging A = (d1 x d2) / 2 gives d2 = 2A / d1. Switch to "Reverse" mode, enter the known area and one diagonal, and the calculator returns the missing diagonal. This is useful for fabric-cutting templates, kite-making, and land measurement where the area is recorded in a deed and you need a physical dimension to lay out on the ground.
Special cases and related shapes
A rhombus is a kite whose two pairs of equal sides happen to be equal to each other (a = b), so A = (d1 x d2) / 2 gives the rhombus area too. A square is a special rhombus with equal diagonals, so its area equals half the diagonal squared. A dart (arrowhead) is a concave kite where the axis-of-symmetry diagonal lies outside the shape; the area formula still holds. If your quadrilateral is not a kite, that is, its diagonals are not perpendicular, this formula overstates the area and you should split the shape into triangles instead.
Kite area quick reference
| d1 | d2 | Area | Ratio (long:short) |
|---|---|---|---|
| 6 | 4 | 12.00 | 1.50 |
| 10 | 6 | 30.00 | 1.67 |
| 12 | 8 | 48.00 | 1.50 |
| 15 | 9 | 67.50 | 1.67 |
| 20 | 12 | 120.00 | 1.67 |
| 20 | 14 | 140.00 | 1.43 |
| 25 | 10 | 125.00 | 2.50 |
| 30 | 20 | 300.00 | 1.50 |
All areas via A = (d1 x d2) / 2. Perimeter assumes equal sides a = d1/2 and b = d2/2 for illustration only.
Frequently asked questions
What is the formula for the area of a kite?
There are two equivalent formulas. If you know the diagonals: A = (d1 x d2) / 2. If you know two adjacent sides and the angle between them: A = a x b x sin(alpha). Both give the same area for the same kite because the diagonals of every kite are perpendicular.
How do I calculate the perimeter of a kite?
The perimeter is P = 2 x (a + b), where a and b are the two unequal side lengths. Each side length appears twice because a kite has two pairs of equal adjacent sides. The perimeter cannot be determined from the diagonals alone without extra information about where they cross.
What is the incircle of a kite and how is its radius found?
Every kite has an inscribed circle (incircle) that touches all four sides. Its radius is r = 2A / P, where A is the area and P is the perimeter. This property is shared with rhombuses and squares, which are special kites.
Can I find a missing diagonal if I know the area?
Yes. Rearrange A = (d1 x d2) / 2 to get d2 = 2A / d1. Switch the calculator to "Reverse" mode, enter the known area and one diagonal, and it returns the missing diagonal. This is useful for making kite patterns, tile layouts, or reading survey plans where the area is given.
Does the kite area formula work for a rhombus or a square?
Yes. A rhombus is a kite where both pairs of equal sides are the same length, so A = (d1 x d2) / 2 still applies. A square is a special rhombus with equal diagonals, giving A = d2 / 2. For a dart (concave kite) the formula also holds, even though the shape bends inward.
Do I measure the full diagonal or the half-diagonal?
Always measure the full diagonal from one corner to the opposite corner. The formula A = (d1 x d2) / 2 already accounts for the fact that the diagonals cross at the midpoint of one of them. If you have only the two halves of a diagonal, add them together before entering the value.