Calculate the similarity ratio of two similar figures or triangles from corresponding sides, with the scale factor, area ratio and a missing side.

For image dimensions, select px for both sides before entering values.

Find a missing side (optional)
Gives the matching side of figure B, using the same scale factor.

Related Calculators

Similarity Ratio Formula

The formula below compares corresponding lengths of figures already known to be similar. One pair of lengths alone does not establish similarity. Convert physical lengths to a common unit before dividing; this calculator supports mm, cm, m, km, in, ft, yd and mi. Pixel lengths can be compared with each other, but cannot be converted to a physical length without a specified resolution. See AMSI: scale drawings and similarity and NIST length conversion factors.

SR = S1 / S2
  • SR is the decimal ratio A/B; the corresponding length ratio is A:B.
  • S1 is the positive length in Figure A.
  • S2 is the positive corresponding length in Figure B, expressed in the same unit as S1.

Divide A by B for SR. The scale factor that maps A to B has the opposite direction: k = B/A. For similar plane figures, the perimeter ratio is A:B and the area ratio is A²:B². For similar solids, the surface-area ratio is A²:B² and the volume ratio is A³:B³; triangles do not have volume. Thus A→B area and volume factors are k² and k³. These relationships require similarity, not just a matching pair of lengths. See properties of similar polygons and Big Ideas Geometry: similar solids.

How to Calculate Similarity Ratio?

The following example problems outline how to calculate Similarity Ratio.

Example Problem #1:

  1. First, determine the side length in the first triangle.
    • The side length in the first triangle is given as 6.
  2. Next, determine the side length in the second triangle.
    • The side length in the second triangle is provided as 10.
  3. Finally, calculate the Similarity Ratio using the equation above: 

SR = S1 / S2

The values given above are inserted into the equation below and the solution is calculated:

SR = 6 / 10 = 0.60, so A:B = 3:5 and the scale factor A→B is 10/6 = 5/3. The area ratio is 9:25 for similar plane figures; the volume ratio is 27:125 only for similar solids. The reduced ratios are exact for the entered values; decimal displays may be rounded.

Example Problem #2: 

For this problem, the variables required are provided below:

side length in the first triangle = 7

side length in the second triangle = 12

Test your knowledge using the equation and check your answer with the calculator above.

SR = S1 / S2 = ?