Daft Logic Acreage Calculator

Shoelace Formula:

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

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 called "shoelace" because of the cross-multiplication pattern resembles lacing shoes.

2. How Does the Calculator Work?

The calculator uses the shoelace formula:

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

Where:

\( A \) — Area in acres
\( x_i, y_i \) — Coordinates of the vertices in feet
43560 — Square feet in one acre

Explanation: The formula sums the cross products of each vertex coordinate pair, takes half the absolute value, and converts from square feet to acres.

3. Importance of Area Calculation

Details: Accurate area calculation is essential for land surveying, property assessment, agricultural planning, and construction projects.

4. Using the Calculator

Tips: Enter coordinates as x,y pairs (one per line) in feet. The polygon must be closed (first and last point should be the same for accurate results).

5. Frequently Asked Questions (FAQ)

Q1: How many points do I need to enter?
A: You need at least 3 points to form a polygon. More points increase accuracy for irregular shapes.

Q2: Does the order of points matter?
A: Yes, points must be entered in consecutive order (clockwise or counter-clockwise) around the perimeter.

Q3: What units should I use?
A: This calculator expects coordinates in feet. For other units, convert to feet first.

Q4: Can I use decimal coordinates?
A: Yes, decimal coordinates are accepted for precise measurements.

Q5: Why is 43560 used in the formula?
A: There are 43,560 square feet in one acre, which converts the result from square feet to acres.