Triangle Calculator
Solve triangle area, perimeter, sides, and angles using SSS, SAS, AAS/ASA, right-triangle, or base-and-height inputs.
Angles are entered in degrees. For AAS/ASA, side a is treated as the side opposite angle A.
Results
Important Note: Triangle calculations are only valid when the entered sides and angles describe a possible triangle. For standard Euclidean geometry, the three interior angles must total 180°, and the sum of any two side lengths must be greater than the third side.
Use this Triangle Calculator to solve triangle area, perimeter, side lengths, and angles using multiple methods including SSS, SAS, AAS/ASA, right triangles, and base-height calculations.
Reviewed by: AjaxCalculators Editorial Team
Last updated: May 2026
Method source: Standard geometry and trigonometry formulas
Editorial standards: Built using transparent formulas, worked examples, interpretation guidance, and educational explanations.
What Is a Triangle Calculator?
A Triangle Calculator solves unknown triangle measurements using known side lengths, angles, and geometric formulas. Different solving methods apply depending on which dimensions are available.
Triangle calculators are commonly used in geometry, engineering, construction, surveying, and education.
Triangle Types Explained
| Type | Meaning |
|---|---|
| Equilateral | All sides equal |
| Isosceles | Two equal sides |
| Scalene | No equal sides |
| Acute | All angles below 90° |
| Right | One angle equals 90° |
| Obtuse | One angle greater than 90° |
Which Triangle Method Should You Use?
| Method | Use When |
|---|---|
| SSS | Three side lengths are known |
| SAS | Two sides and included angle are known |
| ASA/AAS | Two angles and one side are known |
| Base-height | Area calculation only |
| Right triangle | Right-angle relationships apply |
Common Triangle Formulas
Perimeter
P=a+b+c
Area (Base × Height)
Area=(base×height)÷2
Heron’s Formula
Area=√(s(s−a)(s−b)(s−c))
where:
s=(a+b+c)÷2
Pythagorean Theorem
a²+b²=c²
Triangle Validity Rule
A triangle can exist only if:
a+b>c
a+c>b
b+c>a
Example:
3+4>5 ✔
3+4<8 ✖
Triangle Angle Rule
The interior angles of a triangle always total:
180°
Example:
40°+60°+80°=180°
Worked Example
| Input | Value |
|---|---|
| Side a | 5 ft |
| Side b | 6 ft |
| Side c | 7 ft |
Using Heron’s Formula:
s=(5+6+7)÷2
=9
Area=√(9×4×3×2)
=14.70 ft²
Perimeter:
5+6+7=18 ft
How to Use This Calculator
- Select solving method.
- Enter dimensions.
- Select units.
- Click Calculate.
- Review sides, angles, perimeter, and area.
Common Mistakes
- Entering impossible side combinations
- Confusing included angle placement
- Mixing units
- Using incorrect solving methods
Assumptions and Limitations
- Calculator assumes entered values are accurate.
- Invalid dimensions produce impossible triangles.
- Rounding may slightly affect results.
Practical Uses
- Construction measurements
- Geometry education
- Surveying
- Engineering calculations
- Trigonometry problems
References
Related Calculators
Frequently Asked Questions
Can all triangles be solved with three sides?
Yes. SSS methods can determine all remaining measurements.
What is Heron’s Formula used for?
It calculates area from three side lengths.
What makes a triangle invalid?
If two sides together do not exceed the third side.
Do triangle angles always equal 180°?
Yes, for standard Euclidean geometry.
Can this calculator solve right triangles?
Yes. Right triangle methods are included.
Disclaimer: This Triangle Calculator uses standard Euclidean geometry and trigonometry formulas for educational and general measurement purposes. Results depend on accurate side lengths, angle values, selected units, and the correct solving method. Impossible side combinations, inconsistent angle entries, mixed units, or incorrect included-angle placement can produce invalid results. For construction, engineering, surveying, or safety-critical work, verify all measurements with appropriate professional tools or guidance.