Triangle Similarity Calculator
Check if two triangles are similar by comparing their side ratios (SSS similarity test). Enter three sides of each triangle to determine if corresponding sides are proportional and find the scale factor, essential for geometry proofs and real-world scaling problems.
This free online triangle similarity calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
First side of triangle 1
Second side of triangle 1
Third side of triangle 1
First side of triangle 2
Second side of triangle 2
Third side of triangle 2
Results
Scale Factor (T2/T1)
2
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Triangle Similarity Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Triangle Similarity Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
Formula Reference
Triangle Similarity Calculator Formula
See calculator inputs for the governing equation
Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.
When to Use This Calculator
- •Use the Triangle Similarity Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
- •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
- •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
- •Use it to explore the behavior of mathematical functions across a range of inputs.
About This Calculator
The Triangle Similarity Calculator is a free mathematical calculation tool for students, educators, and professionals who need quick, reliable results. Check if two triangles are similar by comparing their side ratios (SSS similarity test). Enter three sides of each triangle to determine if corresponding sides are proportional and find the scale factor, essential for geometry proofs and real-world scaling problems. The underlying algorithms implement well-established mathematical formulas and numerical methods. Results are computed instantly in the browser. This tool is useful for learning, verification of hand calculations, and rapid exploration of mathematical relationships. All computation happens locally — no data is sent to a server.
About Triangle Similarity Calculator
The Triangle Similarity Calculator checks whether two triangles are similar using the SSS (Side-Side-Side) similarity criterion and computes the scale factor. Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. The SSS similarity test checks that the ratios of sorted sides are all equal. Similar triangles are fundamental in geometry: they underlie proportional reasoning, the definition of trigonometric functions, indirect measurement techniques, and scaling in engineering and architecture. Map-making, shadow measurements, and photographic enlargement all rely on triangle similarity.
The Math Behind It
Formula Reference
SSS Similarity Test
a1/a2 = b1/b2 = c1/c2 (after sorting corresponding sides)
Variables: Sides of triangle 1 and triangle 2 sorted in ascending order
Worked Examples
Example 1: Similar Triangles: 3-4-5 and 6-8-10
Check if triangles (3,4,5) and (6,8,10) are similar.
Similar with scale factor 2.
Example 2: Non-Similar Triangles: 3-4-5 and 3-5-7
Check if triangles (3,4,5) and (3,5,7) are similar.
Not similar (ratios differ: 1, 1.25, 1.4).
Common Mistakes & Tips
- !Comparing sides in the wrong order. Always sort both triangles' sides (smallest to largest) before comparing ratios.
- !Confusing similarity with congruence. Similar triangles have the same shape but can be different sizes. Congruent triangles are both the same shape and size (scale factor = 1).
- !Expecting exact floating-point equality. Due to rounding, ratios may differ by tiny amounts. Use a small tolerance (like 0.001) when comparing.
Related Concepts
Used in These Calculators
Calculators that build on or apply the concepts from this page:
Frequently Asked Questions
How does the area of similar triangles relate?
If two triangles are similar with scale factor k, the ratio of their areas is k^2. For example, if one triangle has sides twice as long as another (k=2), its area is 4 times larger.
Can I determine similarity from just two sides?
Not with sides alone. You need either all three side ratios (SSS), two sides and the included angle (SAS), or two angles (AA). Two sides without the angle between them are insufficient.
How did ancient Greeks use triangle similarity?
Thales measured the height of the Great Pyramid by comparing his shadow length to the pyramid's shadow. Since the sun's rays create similar triangles, the ratio of shadow to height is the same for both. Eratosthenes used similar geometry to estimate Earth's circumference by comparing shadow angles at two cities.