Perimeter of Kite Calculator

What Is a Kite in Geometry?

A kite is a four-sided shape with two pairs of equal sides next to each other: two short sides a meet at one corner and two long sides b meet at the opposite corner. The diagonal joining those two corners is the axis of symmetry. The diagonals cross at a right angle, and the axis cuts the other diagonal in half. Because the sides come in two equal pairs, the perimeter only needs two lengths.

Perimeter of a Kite Formulas

Use the formula that matches what you know. The perimeter is always the total length of the four sides.

Perimeter From Two Sides

Add one short side and one long side, then double the total. For a kite with sides 5 cm and 8 cm: 5 + 8 = 13, and 2 × 13 = 26 cm. The angle between the sides changes the shape and the area, but not the perimeter.

The last row has a = b, so all four sides are equal and the kite is a rhombus.

Perimeter From the Diagonals

The two diagonals alone do not fix the sides: the cross diagonal d₂ can meet the axis d₁ anywhere along it. You also need x, the distance along d₁ from the corner between the two short sides to the crossing. The diagonals split the kite into four right triangles, so Pythagoras gives each side.

1. Halve d₂: 8 ÷ 2 = 4.
2. Short side: a = √(3² + 4²) = √25 = 5.
3. Long side: b = √((12 − 3)² + 4²) = √97 ≈ 9.8489.
4. Perimeter: 2 × (5 + 9.8489) ≈ 29.6977.

If x is not known, the calculator takes x = d₁ ÷ 2, which makes the kite a rhombus. Then all four sides are √((d₁ ÷ 2)² + (d₂ ÷ 2)²) and P = 2 × √(d₁² + d₂²), so diagonals 12 and 8 give about 28.8444.

Concave Kites (Darts)

A dart is a kite with one corner pointing inwards. Its perimeter is still 2 × (a + b). With diagonals, x is larger than d₁: the crossing lies outside the shape on the extended axis, and d₁ − x is negative, which does not matter once it is squared.

Here d₁ = 7, d₂ = 24 and x = 16, so a = √(16² + 12²) = 20 and b = √(9² + 12²) = 15. The perimeter is 2 × (20 + 15) = 70, the same as the convex kite with d₁ = 25 and x = 16, which has the same four sides.

Finding a Missing Side

Rearrange P = 2 × (a + b) to get b = P ÷ 2 − a. For a kite with a perimeter of 26 cm and a short side of 5 cm: 26 ÷ 2 = 13, and 13 − 5 = 8 cm. Swap a and b to find the short side instead.

Common Mistakes

• Adding only two sides: a + b is half the perimeter. Double it.
• Using a rhombus formula for any kite: 2 × √(d₁² + d₂²) is only right when x = d₁ ÷ 2.
• Forgetting to halve d₂: each right triangle uses d₂ ÷ 2, not d₂.
• Mixing units: convert both sides to the same unit before adding.
• Square units: a perimeter is a length, so write cm, not cm².

Key Terms

Perimeter

The total length around the kite.

Sides a, b

The short and the long pair of equal sides.

Axis d₁

The diagonal that is the line of symmetry.

Cross d₂

The other diagonal, cut in half by the axis.

Distance x

From the corner between the a sides to the crossing.

Dart

A concave kite, with one angle over 180°.

How to Use the Perimeter of Kite Calculator

1. Choose what you know. Pick Two sides if you know the short side a and the long side b, or Diagonals if you know the two diagonals.
2. Enter the lengths. Type the two sides, such as 5 and 8, or the axis d₁, the cross diagonal d₂ and, if you know it, the distance x from the corner between the short sides to where the diagonals cross. Pick a unit if you want one (mm, cm, m, km, in, ft, yd or mi).
3. Read and copy the result. The perimeter appears as you type, with a drawing, the working, each side, the type of kite and the perimeter in other units. Press Copy to copy it, or Clear or Esc to start again.

Example: a kite frame has short edges of 3 ft and long edges of 7 ft. Choose Two sides, enter 3 and 7 and pick ft. The perimeter is 20 ft, so you need 20 ft of edging tape.

Who Can Use This Calculator?

Frequently Asked Questions (FAQs)