Similar Triangles Calculator
Scale a known side of one triangle to a corresponding side of a similar triangle.
How the result changes
Only first known side changes; all other inputs stay at your current values. The line illustrates the formula across the shown range. This is not a forecast of real-world outcomes.
About this calculation
Similar Triangles Calculator: Scale a known side of one triangle to a corresponding side of a similar triangle. Enter first known side, corresponding side, other side in first triangle; the reported quantities are matching side in second triangle (cm), linear scale factor. The equations and examples below show how those inputs lead to the result and where the model's assumptions matter.
Formula
unknown side = target side × reference side B / reference side A
Worked example
With First known side: 3 cm, Corresponding side: 9 cm, Other side in first triangle: 4 cm, matching side in second triangle is 12 cm.
Method and inputs
Identify a pair of corresponding sides, one from each similar triangle. Divide the second triangle’s side by the first to obtain the linear scale factor, and multiply the other known side of the first triangle by that factor.
Worked example
If a 3-centimeter side corresponds to a 9-centimeter side, the scale factor is 3. A different 4-centimeter side in the first triangle therefore matches a 12-centimeter side in the second.
A threefold linear enlargement turns a 4-centimeter matching side into 12 centimeters, but its area becomes nine times larger. This square-law distinction matters in models, maps and photographs where a length scale is mistakenly applied to material area.
How to read the result
Similarity preserves angles and side ratios, not necessarily orientation. The result is a linear length; the ratio of areas would be the square of the scale factor, so do not apply this length result directly to area.
If a second measured side disagrees with the predicted scale, the triangles may not be similar or the sides may be paired incorrectly. Use multiple corresponding measurements when available. A single side pair defines a ratio but cannot independently prove shape similarity.
Assumptions and checks
The triangles must actually be similar, with correct corresponding sides. Equal angle evidence or proportional sides can establish similarity, but this calculator does not test that condition from a diagram.
Swapping nonmatching sides in the ratio gives an incorrect scale. A drawing may be mirrored or rotated, so correspondence should be based on angle labels rather than position on the page. Use one consistent length unit for all inputs.
Common questions
What does the similar triangles calculator calculate?
It returns a missing corresponding side and the linear scale factor between two similar triangles. It assumes the stated sides match the same angles.
When should I recalculate or check another method?
Recalculate if a different pair of sides is confirmed to correspond. If the two triangles are merely close in shape, a precise missing length needs more measurements rather than a similarity assumption.
Inputs
- First known side (cm)
- Corresponding side (cm)
- Other side in first triangle (cm)