When to use this calculator
Heron’s formula avoids finding the perpendicular height when the three side lengths are easier to measure.
Explore the triangle calculators for other questions in this topic. For a related calculation, use the Pythagorean Theorem Calculator: Find the hypotenuse of a right triangle from its two shorter sides.
PUTTING IT INTO PRACTICE
Herons Formula: 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 |
| Third side | 5 |
| Result | 6 square units |
- Check the input labels and enter the example values above.
- Apply the relationship: s = (a+b+c)/2; area = √(s(s−a)(s−b)(s−c)).
- The result is 6 square units, rounded for display.
How to interpret your result
Every pair of sides must sum to more than the third side.
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 herons formula calculator useful?
Heron’s formula avoids finding the perpendicular height when the three side lengths are easier to measure.
How do I use the herons formula calculator?
Enter first side, second side, third side. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
s = (a+b+c)/2; area = √(s(s−a)(s−b)(s−c)).
What should I check before using the result?
Every pair of sides must sum to more than the third side.
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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