Calculate Square Feet with 4 Different Sides

This calculator works out the area of a four-sided shape (a quadrilateral) when all four side lengths are different. You enter the four side lengths in any unit, and it returns the area in square feet (or the same unit squared). The calculation uses Brahmagupta’s formula, which requires the shape to be cyclic (all four corners lie on a single circle) to be exact; for most real-world plots, it gives a very close approximation.

Formula

For a quadrilateral with side lengths a, b, c, and d, the area A is given by Brahmagupta’s formula:

A = √[(s − a)(s − b)(s − c)(s − d)]

where s = (a + b + c + d) / 2, called the semiperimeter.

All lengths must be in the same unit (e.g., feet). The result is in square feet (or square of whatever unit you used).

Worked Example

Using the default values: a = 10 ft, b = 15 ft, c = 12 ft, d = 8 ft.

1. Compute the semiperimeter: s = (10 + 15 + 12 + 8) / 2 = 45 / 2 = 22.5 ft
2. Subtract each side from s: (22.5 − 10) = 12.5, (22.5 − 15) = 7.5, (22.5 − 12) = 10.5, (22.5 − 8) = 14.5
3. Multiply those four: 12.5 × 7.5 = 93.75; 93.75 × 10.5 = 984.375; 984.375 × 14.5 = 14273.4375
4. Take the square root: √14273.4375 ≈ 119.47

The area is approximately 119.47 square feet, matching the calculator’s output.

When to Use This Calculator

This is ideal for irregularly shaped lots, rooms, gardens, or any four-sided area where the sides are not equal and you don’t have the angles. Common situations:

• Measuring a trapezoidal yard or field.
• Estimating floor area of an oddly shaped room.
• Calculating the size of a plot of land from a survey that lists only side lengths.

If you have the angles or the diagonals, more precise methods exist, but this formula is the standard when only the four sides are known.

How to Read the Result

The result is the area in square feet (if you entered feet). For example, 119.47 sq ft is about the size of a small bedroom. If you entered meters, the result is square meters; to convert to square feet, multiply by 10.764. For acres, divide square feet by 43,560.

Remember that the formula assumes the quadrilateral is cyclic. For most practical plots, the error is small (often under a few percent), but for very skewed shapes the actual area can differ noticeably. If you need exact area, measure one diagonal and use Heron’s formula for the two triangles instead.

Common Mistakes and Limitations

• Unit mix-ups: All sides must be in the same unit. Mixing feet and inches gives a wrong answer. Convert first (e.g., 6 ft 3 in = 6.25 ft).
• Rounding too early: Keep full precision in intermediate steps; round only the final answer.
• Assuming it’s exact: Brahmagupta’s formula is exact only for cyclic quadrilaterals. For non-cyclic ones, it slightly overestimates the area.
• Forgetting the semiperimeter: Using the perimeter directly (instead of half) is a common error.

Alternatives and More Accurate Methods

If you can measure one diagonal, you can split the quadrilateral into two triangles and use Heron’s formula for each triangle. This is exact for any shape. Alternatively, if you know two opposite angles, you can use the more general Bretschneider’s formula:

A = √[(s−a)(s−b)(s−c)(s−d) − abcd·cos²(θ/2)]

where θ is the sum of two opposite angles. For most practical purposes, the simple Brahmagupta formula is sufficient when you only have side lengths.

Frequently Asked Questions

Can I use this for a rectangular room?

Yes, but for a rectangle you can simply multiply length × width. The formula will give the same result, but the direct multiplication is simpler.

What if my sides are in feet and inches?

Convert all to feet first. For example, 10 ft 6 in becomes 10.5 ft. Then use the calculator.

Is the result exact for any four-sided shape?

No, it is exact only for cyclic quadrilaterals (where all four vertices lie on a circle). For other shapes, it is an approximation that is usually close but can be off by a few percent for very irregular shapes.

How do I convert square feet to square meters?

Multiply the square feet value by 0.092903 to get square meters. Conversely, multiply square meters by 10.7639 to get square feet.

Why does my land survey show a different area?

Surveyors use more precise methods, often measuring diagonals or angles. The side-only formula is a good estimate, but the actual area may differ slightly due to the shape not being perfectly cyclic.

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in a | Side A | ft | 10 | 0
in b | Side B | ft | 15 | 0
in c | Side C | ft | 12 | 0
in d | Side D | ft | 8 | 0
out area | Area | sq ft | sqrt((s-a)*(s-b)*(s-c)*(s-d)) where s=(a+b+c+d)/2 | 2
out semiperimeter | Semiperimeter (s) | ft | (a+b+c+d)/2 | 2