Acreage Calculator Four Sides

Area Formula:

\[ A = \frac{1}{2} \times \sum(x_i y_{i+1} - x_{i+1} y_i) / 43560 \]

X Coordinate 1:

Y Coordinate 1:

X Coordinate 2:

Y Coordinate 2:

X Coordinate 3:

Y Coordinate 3:

X Coordinate 4:

Y Coordinate 4:

Calculated Area:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Shoelace Formula?

The shoelace formula (also known as Gauss's area formula) is a mathematical algorithm to determine the area of a simple polygon whose vertices are defined in the plane. It's particularly useful for calculating land areas from survey coordinates.

2. How Does the Calculator Work?

The calculator uses the shoelace formula:

\[ A = \frac{1}{2} \times \sum(x_i y_{i+1} - x_{i+1} y_i) / 43560 \]

Where:

\( x_i, y_i \) — Coordinates of the vertices
The sum wraps around (x5 = x1, y5 = y1)
43560 — Square feet in one acre

Explanation: The formula calculates the area in square feet and converts it to acres by dividing by 43,560.

3. Importance of Area Calculation

Details: Accurate land area calculation is essential for property assessment, construction planning, agricultural purposes, and legal documentation.

4. Using the Calculator

Tips: Enter the coordinates of all four corners in order (clockwise or counter-clockwise). The coordinates can be in any consistent unit (feet, meters, etc.) as long as all use the same unit.

5. Frequently Asked Questions (FAQ)

Q1: Does the order of coordinates matter?
A: Yes, the points must be entered in order around the perimeter (either clockwise or counter-clockwise).

Q2: Can I use this for more than four sides?
A: This calculator is specifically for four-sided plots, but the shoelace formula works for any polygon.

Q3: What coordinate system should I use?
A: Any consistent coordinate system works - latitude/longitude, UTM, or local survey coordinates.

Q4: How accurate is this method?
A: The accuracy depends on the precision of your coordinates. More decimal places mean more precise results.

Q5: Why divide by 43,560?
A: There are 43,560 square feet in one acre, which is the standard unit for land measurement in the US.