Similar Triangles Calculator — Scale Factor, Sides and Areas

How to use the similar triangles calculator

1. Choose whether the scale factor comes from a pair of corresponding sides, the two triangle areas, or a factor you already know.
2. Keep the direction consistent: this page defines k = Triangle 2 ÷ Triangle 1.
3. Optionally enter one additional side or area to calculate its corresponding value.
4. Select Calculate to see the scale factor, reverse factor, area ratio, conversions, and substituted formulas.

Privacy: calculations run entirely in your browser. This tool does not upload or track the measurements you enter.

Similar triangle formulas

Similar triangles have equal corresponding angles and proportional corresponding lengths. If s₁ is a side in Triangle 1 and s₂ is its match in Triangle 2, the linear scale factor is:

k = s₂ / s₁

Every other corresponding length—including sides, altitudes, medians, inradius, circumradius, and perimeter—uses that same factor:

length₂ = k × length₁    and    length₁ = length₂ / k

Area is two-dimensional, so it uses the square of the linear factor:

A₂ / A₁ = k²    and    k = √(A₂ / A₁)

For example, corresponding sides 3 and 5 give k = 5/3. A 12-unit side becomes 20 units, while an area of 36 square units becomes 36 × (5/3)² = 100 square units.

What the calculator assumes

The calculator uses Euclidean geometry and assumes that Triangle 1 and Triangle 2 are similar. It does not establish similarity from raw angles or three side pairs. Before using a scale factor, establish similarity with one of the standard tests:

• AA: two angles in one triangle equal two corresponding angles in the other.
• SAS similarity: two pairs of sides are proportional and the included angles are equal.
• SSS similarity: all three pairs of corresponding sides are proportional.

All corresponding lengths must use the same unit before division. Likewise, compare areas expressed in the same square unit. The display is rounded to your chosen significant figures, but calculations retain JavaScript floating-point precision.

Scale factor examples

Enlargement from corresponding sides

If a 4 cm side corresponds to a 10 cm side, k = 10/4 = 2.5. Every Triangle 2 length is 2.5 times the corresponding Triangle 1 length, and its area is 2.5² = 6.25 times as large.

Reduction

If k = 0.5, a 14 m side becomes 7 m. The area factor is 0.5² = 0.25, so Triangle 2 has one quarter of Triangle 1’s area.

Scale factor from area

If Triangle 1 has area 81 square units and Triangle 2 has area 144 square units, then k = √(144/81) = 4/3. The reverse factor is 3/4.

Similar Triangles Calculator: FAQs

How do you find the scale factor of similar triangles?

Divide a side length in Triangle 2 by its corresponding side length in Triangle 1. Keep the direction consistent: k = side 2 ÷ side 1.

How do areas change when a triangle is scaled?

Areas change by the square of the linear scale factor. If every side is multiplied by k, the area is multiplied by k².

Can the scale factor be found from two areas?

Yes. Divide Area 2 by Area 1 and take the positive square root: k = √(A₂/A₁).

Does the perimeter use the same scale factor as the sides?

Yes. Every length, including each side, altitude, median, radius, and the perimeter, changes by the linear scale factor k.

What does a scale factor less than 1 mean?

It means Triangle 2 is a reduction of Triangle 1. For example, k = 0.5 halves every corresponding length and makes the area one quarter as large.

Do corresponding sides need to use the same unit?

Yes. Convert corresponding lengths to the same unit before calculating. Areas must likewise use the same square unit.

Can this calculator prove that two triangles are similar?

No. The calculator assumes the triangles are already known to be similar. Similarity can be established using AA, SAS similarity, or SSS similarity.

Are my measurements uploaded?

No. The calculation runs locally in your browser and the tool does not transmit the values you enter.