The Draw a Shape Area Calculator calculates the area and perimeter of a shape you draw by clicking its corners on a grid.
Each click adds a corner; the calculator joins them in order and applies the shoelace formula to the corner coordinates. Choose what one grid square represents (for example 1 m or 1 ft) to get real-world units, or edit the coordinate list directly for exact positions.
Draw a Shape Area Calculator
Draw any shape on the grid by clicking its corners — or type coordinates — and get its area and perimeter instantly.
Formula
Area (shoelace formula):
A = ½ |Σ (xᵢ × yᵢ₊₁ − xᵢ₊₁ × yᵢ)|
Perimeter:
P = Σ √((xᵢ₊₁ − xᵢ)² + (yᵢ₊₁ − yᵢ)²)
Where (xᵢ, yᵢ) are the corners in the order you clicked them, and the last corner connects back to the first.
How the Calculation Works
Step 1: Click the grid to place corners in order around the shape. Points snap to the nearest half square.
Step 2: The calculator reads each corner as an (x, y) coordinate in grid units and multiplies by the size you set for one square.
Step 3: It applies the shoelace formula for area and adds the side lengths for perimeter. Use Undo to remove the last corner or Clear to start again.
Variables Explained
| Item | Meaning |
|---|---|
| Corner | A point where two sides meet |
| Grid square | The real length one square represents (cm, m, in, ft…) |
| Area | Space inside the drawn shape |
| Perimeter | Total length of the outline |
Example Calculation
Given: corners at (2, 2), (12, 2), (14, 8), (7, 12), (3, 9), with one grid square = 1 m
Shoelace sum: the cross products add up to 175
Result: A = 175 ÷ 2 = 87.5 m²; perimeter ≈ 36.46 m
Scaling a sketch
If the same drawing represents a plan where one square = 2 ft, every length doubles and the area becomes 4 times larger: 87.5 × 4 = 350 ft².
Common Area Conversion Table
| Unit | Equivalent |
|---|---|
| 1 m² | 10.7639 ft² |
| 1 yd² | 9 ft² |
| 1 acre | 43,560 ft² |
Shape Properties
Any shape made of straight sides can be drawn this way — triangles, L-shapes, lots, rooms or garden beds. Curved edges can be approximated by adding more corners along the curve; the more corners, the closer the result.
Dimensions Explained
Tips for accurate drawings
- Choose a grid size that lets the whole shape fit on the grid.
- Click the corners in order, either clockwise or counterclockwise.
- Don’t let sides cross; a figure-eight shape has no single area.
- For exact measurements, type coordinates into the list instead of clicking.
Frequently Asked Questions
How do I calculate the area of a shape I draw?
Place the corners on the grid; the calculator uses their coordinates in the shoelace formula to find the area.
Can I draw curved shapes?
Approximate the curve with many short straight sides.
How do I change the units?
Set what one grid square represents; the area and perimeter update automatically.
What if my sides cross?
The calculator warns you, because a self-crossing outline doesn’t enclose a single area.
Can I enter exact coordinates?
Yes. Type one corner per line as x, y in the list under the grid.
