Quadrilateral Calculator

Find perimeter, semiperimeter, and cyclic area from four side lengths.

Four-side quadrilateral calculator
Enter four positive side lengths in order around a cyclic quadrilateral.

About quadrilateral measurements

A quadrilateral is a polygon with four sides, four vertices, and four interior angles. Its perimeter is always the sum of its side lengths, so that measurement can be found for any valid quadrilateral when all four sides are known. The semiperimeter is half of the perimeter and is useful in several area formulas. This calculator labels the sides a, b, c, and d in order around the shape, adds them for the perimeter, and then divides that total by two for the semiperimeter. Four side lengths alone do not usually determine one unique quadrilateral area. Flexible joints could change the angles while preserving every side, producing different areas. A definite area becomes available when an additional condition is known. This calculator uses Brahmagupta's formula, which applies when the quadrilateral is cyclic: all four vertices lie on one circle. If s is the semiperimeter, the area is the square root of the product (s - a)(s - b)(s - c)(s - d). A square and every rectangle are cyclic, as are many other useful configurations. For a general quadrilateral that is not known to be cyclic, the displayed cyclic area is the maximum area possible for those four side lengths. More information, such as one interior angle or the lengths of the diagonals and their included angle, is needed to determine its actual area. This distinction is important in land measurement, design, and construction. Treating arbitrary four-side data as a unique area can overstate the enclosed region when opposite angles do not add to 180 degrees. The side lengths must also satisfy the quadrilateral inequality. The longest side must be shorter than the sum of the other three; otherwise the segments cannot close to form a nondegenerate shape. All values must be positive and use the same unit. The perimeter and semiperimeter retain that unit, while area uses its square. Decimal measurements are accepted. The output is rounded for readability, so retain the original side data and appropriate precision when using the result in engineering, surveying, or material estimates.

Quadrilateral examples

Side lengthsMeasurementsShape assumption
5, 5, 5, 5Perimeter 20, area 25A cyclic equal-sided case includes the square
3, 4, 5, 6Perimeter 18, area about 18.9737Area is for the cyclic arrangement
4, 6, 4, 6Perimeter 20, area 24A 4 by 6 rectangle is cyclic

How to calculate a quadrilateral

  1. Measure the four sides in order around the quadrilateral using one unit.
  2. Enter each positive length in its labeled side field.
  3. Confirm the shape is cyclic if you need the displayed value as its exact area.
  4. Select Calculate quadrilateral and review the perimeter, semiperimeter, and area.

Frequently asked questions

Can four sides determine every quadrilateral area?

No, the angles can change while all four sides remain fixed. An exact area requires another condition, such as cyclic vertices, a known angle, or diagonal information.

What is a cyclic quadrilateral?

It is a quadrilateral whose four vertices all lie on a single circle. Its opposite interior angles add to 180 degrees.

What is Brahmagupta's formula?

It gives cyclic area as the square root of (s - a)(s - b)(s - c)(s - d), where s is the semiperimeter. It generalizes Heron's triangle formula to cyclic quadrilaterals.

How is perimeter calculated?

Add all four side lengths: a plus b plus c plus d. This result is valid for any quadrilateral, whether or not it is cyclic.

How do I know whether four sides form a quadrilateral?

Every side must be positive, and the longest must be shorter than the sum of the other three. Equality would create a flattened, zero-area figure rather than a proper quadrilateral.