How this instrument works
Two triangles are similar when they share an identical shape but not necessarily an identical size — every angle matches, and every pair of corresponding sides shares one single ratio, called the scale factor. Knowing just one matched pair of sides is enough to pin that ratio down completely, since every other pair of corresponding sides between both shapes is guaranteed to carry the exact same value.
This site also carries a calculator built specifically for right triangles, which tests similarity by comparing leg ratios within each right triangle and checking whether those two ratios match — a yes-or-no test that never actually reports a scale factor. This page instead assumes the two triangles are already known to be similar, of any shape at all rather than just right triangles, and simply reports how much bigger or smaller one is than the other, straight from a single matched pair of sides.
A scale factor above 1 means the second triangle is larger; below 1 means it's smaller; and exactly 1 means the two shapes aren't merely similar but fully congruent, identical in both shape and size. One detail catches almost everyone off guard the first time: while every length scales by the factor itself, area scales by that factor squared. Triple every side and the enclosed surface doesn't triple — it grows ninefold.
- Enter a side length from the first triangle into the Triangle 1: a side field.
- Enter the matching, corresponding side from the second triangle into the Triangle 2: the corresponding side field.
- Read Scale factor: how many times larger, or smaller, the second triangle is than the first, along every corresponding side.
- A result of exactly 1 signals the two triangles are congruent rather than merely similar.
Worked example — sides of 3 and 9
The golden case: triangle one has a side of 3, and the corresponding side on triangle two measures 9. The scale factor is 9 divided by 3, which is 3 exactly — triangle two is three times the size of triangle one along every matching side, not just the one measured. Their areas, though, differ by 3 squared, meaning triangle two encloses nine times the surface of triangle one, despite each side only being three times as long.
Change the corresponding side to 5 while triangle one's side stays 5 too, and the scale factor drops to 5 divided by 5, or exactly 1 — the two triangles are congruent, not just similar. Change it again to a side of 1 against triangle one's side of 4, and the scale factor becomes 1 divided by 4, or 0.25: triangle two is a quarter the size of triangle one, with an area just one-sixteenth as large.
Questions
What is the scale factor between two similar triangles?
It's the ratio between any pair of corresponding sides — divide a side on the second triangle by the matching side on the first, and that single number applies to every other corresponding pair between the two shapes, since similar triangles are stretched uniformly in every direction.
Does the scale factor also apply to area?
No — area scales by the square of that number, not by the number itself. A scale factor of 3 multiplies every side length by 3 but multiplies the enclosed area by 9; a value of 0.25 shrinks area down to a sixteenth, not a quarter.
What does a scale factor of exactly 1 mean?
Both triangles are congruent — identical in both shape and size, not merely similar. A pair of matching sides measuring 5 and 5, for instance, gives a scale factor of 1 and describes matching shapes that are exact copies of each other.
How is this different from testing similarity in right triangles specifically?
A separate calculator on this site tests whether two right triangles are similar at all, by comparing their own internal leg ratios and checking for a match — a yes-or-no result with no scale factor reported. This page instead assumes similarity is already established, for shapes of any kind, and reports the actual scale factor straight from one matched pair of sides.
Does it matter which triangle is labeled 'triangle 1'?
Only in which direction it points. Swapping the two shapes inverts the result — a scale factor of 3 becomes roughly 0.333 if the labels are reversed — so keep the assignment consistent with whichever triangle you consider the original one.
Can the scale factor be less than 1?
Yes — a scale factor below 1 simply means the second triangle is smaller than the first, such as the 0.25 result when a side of 1 corresponds to a side of 4. Nothing about the math requires the second shape to be the larger one.