Similar Triangles Calculator

Work out similar triangles instantly with clear inputs, formula shown and shareable results.

About Similar Triangles Calculator

Similar triangles have equal angles and proportional sides. One pair of corresponding sides fixes the scale factor k; every other length multiplies by k, areas by k² and volumes by k³.

Formula

Scale factor

k = side₂ ÷ side₁, area ratio = k², volume ratio = k³

Worked example

With the default values below, Similar Triangles Calculator returns Matching side on triangle 2 of 12.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Side on triangle 1minimum 0: 6
Corresponding side on triangle 2minimum 0: 9
Another side on triangle 1minimum 0: 8

Results

Matching side on triangle 2: 12.0000
Scale factor (linear): 1.5000
Area ratio: 2.2500
Volume ratio: 3.3750

Step by step

1Values used
2Scale factor
3Matching side on triangle 2= 12.0000
4Scale factor (linear)= 1.5000
5Area ratio= 2.2500
6Volume ratio= 3.3750

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How do I prove two triangles are similar?

Any of AA (two equal angles), SSS (all three side ratios equal) or SAS (two side ratios equal with the included angles equal) is sufficient.

Why do areas scale by k²?

Area depends on two length dimensions, so each of them is multiplied by k, giving k × k.