Enlargement Calculator

Enter enlargement details

Use the three-column grid on large screens, two columns on smaller screens, and one column on mobile screens.

Shape name

Measurement unit

Decimal places

Scale factor

Centre x

Centre y

Point A x

Point A y

Point B x

Point B y

Point C x

Point C y

Point D x (optional)

Point D y (optional)

Example data table

Item	Value
Shape	Triangle ABC
Centre of enlargement	(1, 1)
Scale factor	1.5
A	(2, 3)
B	(5, 3)
C	(4, 6)
A′	(2.5, 4)
B′	(7, 4)
C′	(5.5, 8.5)

Formula used

Coordinate enlargement
x′ = c_x + k(x − c_x)
y′ = c_y + k(y − c_y)

Length and perimeter scaling
Enlarged length = |k| × original length
Enlarged perimeter = |k| × original perimeter

Area scaling
Enlarged area = k² × original area

The calculator transforms every point from the chosen centre, then recomputes side lengths, perimeter, centroid position, and polygon area using the shoelace method for accurate coordinate geometry results.

How to use this calculator

Enter a shape name and choose a unit label.
Type the scale factor. Values above one enlarge. Values between zero and one reduce.
Enter the centre of enlargement coordinates.
Provide coordinates for points A, B, and C. Add D if your shape is a quadrilateral.
Choose the number of decimal places for the output.
Press Calculate Enlargement to place the result block below the header and above the form.
Review transformed coordinates, side lengths, area, perimeter, centroid values, and the visual comparison chart.
Use the CSV and PDF buttons to save the calculated report.

Frequently asked questions

1. What does a scale factor larger than one mean?

It means the image is bigger than the original shape. Every distance from the centre is multiplied by that factor, so side lengths grow proportionally.

2. What happens when the scale factor is between zero and one?

The transformation becomes a reduction. The image stays similar to the original shape, but every length becomes smaller in the same ratio from the chosen centre.

3. Can I use a negative scale factor?

Yes. A negative factor places the image on the opposite side of the centre while scaling it. This creates a half-turn effect combined with enlargement or reduction.

4. Why does the area change faster than the perimeter?

Perimeter scales by the absolute scale factor, but area scales by the square of that factor. Doubling lengths makes the area four times larger.

5. Why do I need the centre of enlargement?

The centre controls where the image is positioned. Every original point and image point must lie on a straight line passing through that centre.

6. Does the calculator work for quadrilaterals?

Yes. Enter point D as well as A, B, and C. The page will treat the shape as a four-sided polygon and calculate the new coordinates and measures.

7. How is the area calculated from coordinates?

The tool uses the shoelace formula. It multiplies paired x and y values around the polygon, subtracts the reverse products, and halves the absolute difference.

8. What can I export from this page?

You can export a CSV summary of coordinates and key measures, or save a formatted PDF report containing the main results and comparison tables.