How this instrument works
When two triangles are similar — identical in shape, differing only in size — every one of their corresponding measurements relates by the same single ratio. Given just one matching pair of sides, one from each triangle, that number is found with plain division: scale factor = a₂ ⁄ a₁. This one value then applies uniformly to every other side and to the perimeter, which also scales in direct proportion.
Area behaves differently, and this is the detail worth remembering: area scales with the SQUARE of this ratio, not the plain value itself, since area is built from a length multiplied by another length. A doubling scale doubles every side and the perimeter, but it quadruples the area — the same 2D-versus-1D distinction that shows up in scaling any shape, not just triangles.
This page returns only the ratio itself, the single defining number of the relationship between two similar triangles. For recovering the actual missing side lengths of the second triangle once that number is known, this site's companion Solve Similar Triangles page carries the calculation the rest of the way.
- Enter the known side from the first (reference) triangle into the Triangle 1: known side field.
- Enter the corresponding side from the second, similar triangle into the Triangle 2: corresponding side field.
- Read Scale factor: the sheet divides the second side by the first directly.
Worked example — sides 3 and 6
A side of 3 in triangle 1 corresponds to a side of 6 in a similar triangle 2, giving a scale factor of exactly 2. Every other side of triangle 2, and its full perimeter, is exactly double triangle 1's — but its area would be exactly FOUR times triangle 1's, since area scales with the square of this factor rather than the factor alone.
Matching sides of 5 and 5 give a scale factor of exactly 1 — the two triangles are congruent, identical in both shape and size, the boundary case where similarity collapses into outright equality. A side of 4 against a corresponding side of 10 gives a scale factor of 2.5, a triangle two and a half times larger in every linear dimension.
Questions
How do you find the scale factor between two similar triangles?
Divide a side of the second triangle by the corresponding side of the first: scale factor = a₂ ⁄ a₁. Because the two triangles are similar, this single number then applies uniformly to every other pair of corresponding sides.
Does this ratio apply to area the same way it applies to sides?
No — area scales with the SQUARE of the value, not the plain number itself. A scale of 3 multiplies every side and the perimeter by 3, but multiplies the area by 9.
What does a result of 1 mean?
The two triangles are actually congruent — identical in both shape and size, not merely similar. A value of exactly 1 means no scaling has actually occurred between the two.
Can the result be less than 1?
Yes — if the second triangle is smaller than the first, the ratio comes out between 0 and 1, correctly reflecting a shrinking rather than an enlarging relationship.
How do I find the actual missing sides, not just the scale factor?
This site's companion Solve Similar Triangles page takes the same known pair plus the first triangle's other two sides, and carries the calculation the rest of the way to the second triangle's full missing sides.