When to use this calculator
Find a triangle’s area from two sides and their included angle. The angle must lie between the two supplied sides.
Explore the triangle calculators for other questions in this topic. For a related calculation, use the Triangle Circumradius Calculator: Find the radius of the circle through all three triangle vertices.
PUTTING IT INTO PRACTICE
Triangle Area From Two Sides: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| First side | 3 |
| Second side | 4 |
| Included angle (degrees) | 90 |
| Result | 6 square units |
- Check the input labels and enter the example values above.
- Apply the relationship: Area = ab sin(included angle)/2.
- The result is 6 square units, rounded for display.
How to interpret your result
The angle must lie between the two supplied sides.
Use base and perpendicular height for the simplest area calculation. With three known sides, Heron’s formula avoids measuring height. Triangle side lengths must satisfy the triangle inequality before any area result is meaningful.
Frequently asked questions
Can I use the sloping side as triangle height?
Only if it is perpendicular to the chosen base. A general sloping side is not the perpendicular height.
When is the triangle area from two sides calculator useful?
Find a triangle’s area from two sides and their included angle. The angle must lie between the two supplied sides.
How do I use the triangle area from two sides calculator?
Enter first side, second side, included angle (degrees). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Area = ab sin(included angle)/2.
What should I check before using the result?
The angle must lie between the two supplied sides.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see OpenStax: non-right triangles ↗. This is a topic reference, not an external review or endorsement of this tool.
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