# Similar Triangles Calculator

URL: https://speedycalculator.com/calculators/math/similar-triangles/
Last updated: 2026-10-30

> The similar triangles calculator checks whether triangles ABC and DEF are similar by SSS, SAS or AA, or finds the missing sides of a similar triangle from the scale factor.

## Inputs

- Mode
- Criterion
- AB
- BC
- AC
- DE
- EF
- DF
- ∠A (°)
- ∠D (°)
- ∠B (°)
- ∠E (°)
- AB
- BC
- AC
- DE

## Results

- Result
- Details
- Scale factor and area ratio

## Formula

```
SSS: DE/AB = EF/BC = DF/AC · SAS: DE/AB = EF/BC and ∠B = ∠E · AA: ∠A = ∠D and ∠B = ∠E
Area ratio = k²
```

## Explanation

Similar triangles have the same shape but not necessarily the same size. They let you measure tree heights from shadows, scale maps and models, and they underlie all of trigonometry.

### How to use the Similar Triangles Calculator

- **Mode**
- **Criterion**
- **AB**
- **BC**
- **AC**
- **DE**
- **EF**
- **DF**
- **∠A (°)**
- **∠D (°)**
- **∠B (°)**
- **∠E (°)**
- **AB**
- **BC**
- **AC**
- **DE**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

In check mode choose the criterion and enter the matching sides or angles. In find mode enter the three sides of ABC and the side DE of the similar triangle; the scale factor gives the rest.

## Worked example

Inputs — Mode: Check similarity; Criterion: SSS (three sides); AB: 3; BC: 4; AC: 5; DE: 6; EF: 8; DF: 10.

Results — **Result = The triangles are similar (SSS)**; Details = DE/AB = 2, EF/BC = 2, DF/AC = 2; Scale factor and area ratio = Scale factor k = 2, area ratio k² = 4.

## Key terms

- **Scale factor**: The ratio of corresponding sides.

## FAQ

**What are similar triangles?**
Triangles with equal angles and proportional sides.

**Are congruent triangles similar?**
Yes, with scale factor 1.

**How does area scale?**
By the square of the scale factor.

**How do shadows measure heights?**
The object and a stick form similar triangles with their shadows.


## Sources

- [OpenStax – Algebra and Trigonometry 2e](https://openstax.org/details/books/algebra-and-trigonometry-2e)
- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Similar triangles](https://mathworld.wolfram.com/SimilarTriangles.html)