Shape Diagram
The letters identify sides, corners, opposite angles, and both possible diagonals.
Formula Used
Coordinate method: the shoelace formula calculates exact polygon area from ordered corner coordinates.
Diagonal methods: split the quadrilateral into triangles. Calculate each triangle with Heron’s formula, then add the areas.
Four sides and angles: Bretschneider’s formula uses all sides and two opposite angles.
Cyclic assumption: Brahmagupta’s formula applies when the four vertices lie on one circle.
How to Use This Calculator
- Select the measurement method matching your available field data.
- Choose one input length unit for all dimensional entries.
- Enter corners in boundary order, or enable automatic ordering.
- For diagonal methods, identify whether AC or BD was measured.
- Add deductions, repeated shapes, waste, package coverage, and pricing when needed.
- Select the desired area unit and decimal precision.
- Press Calculate Area and review validation messages.
- Copy the result, download CSV, or print the page as PDF.
Example Data
Use these examples to check each supported method.
| Method | Sample inputs | Best use |
|---|---|---|
| Coordinates | (0,0), (8,1), (7,6), (1,5) | Surveying, mapping, floor plans |
| Sides and AC diagonal | 8, 6, 7, 5; diagonal 9 | Manual tape measurements |
| Opposite angles | 8, 6, 7, 5; A 80°, C 100° | Measured side-angle layouts |
| Offsets | 0,2; 5,3.5; 10,4; 15,2.5 | Land strips and irregular boundaries |
| Average dimensions | Length 8; width 5.5 | Quick material estimates |
Calculation History
No saved calculations yet.
Understanding Uneven Four-Sided Areas
An uneven square is usually an irregular quadrilateral. Its sides may differ, and its corners may not form right angles. Accurate area calculation therefore needs more information than four side lengths.
Coordinates provide the most dependable general method. They describe each corner directly and support convex or concave shapes. The calculator also checks for crossing edges, which would make the entered boundary invalid.
A measured diagonal is another practical choice. It divides the shape into two triangles. Heron’s formula then finds both triangle areas using only their side lengths.
Bretschneider’s formula is useful when four sides and two opposite angles are known. Brahmagupta’s formula is simpler, but it assumes all corners lie on a common circle. That assumption often represents the maximum possible area for the entered sides.
Survey offsets suit plots measured from a straight baseline. The calculator applies the trapezoidal rule between stations. More closely spaced offsets usually improve the estimate along curved or changing boundaries.
For flooring, roofing, landscaping, and paving, measured area is only the starting point. Deductions remove openings or excluded zones. Waste allowance covers cutting, breakage, overlap, and future repairs.
Frequently Asked Questions
Is an uneven square really a square?
Usually not. The phrase commonly describes an irregular four-sided shape or quadrilateral.
Can four side lengths determine the area?
Not for a general quadrilateral. You also need a diagonal, angles, coordinates, height data, or a special assumption.
Which method is most accurate?
Ordered corner coordinates are usually the most reliable when each corner has been measured carefully.
What order should coordinates follow?
Enter corners continuously around the boundary, either clockwise or counterclockwise.
Does the calculator support concave shapes?
Yes. The coordinate method identifies concavity and calculates the area with the shoelace formula.
What is a self-intersecting shape?
It occurs when non-adjacent edges cross. Such corner ordering does not describe one simple boundary.
When should Brahmagupta’s formula be used?
Use it for cyclic quadrilaterals or as a clearly labelled maximum-area estimate.
How are survey offsets calculated?
Adjacent offsets form trapezoidal strips. Their areas are added across the measured baseline.
What does measurement tolerance mean?
It estimates how dimensional uncertainty may affect the reported area. It is not a formal survey confidence interval.
How is material quantity calculated?
The calculator applies deductions, multiplies repeated shapes, adds waste, then divides by package coverage.
How can I save a PDF?
Use Print / Save PDF and select your browser’s PDF destination.