When to use this calculator
Find the hypotenuse of a right triangle from its two shorter sides. This relationship applies only to right-angled triangles.
Explore the triangle calculators for other questions in this topic. For a related calculation, use the Right Triangle Leg Calculator: Recover a right triangle’s missing leg from the hypotenuse and another leg.
PUTTING IT INTO PRACTICE
Pythagorean Theorem: 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 leg | 3 |
| Second leg | 4 |
| Result | 5 units |
- Check the input labels and enter the example values above.
- Apply the relationship: Hypotenuse = √(a² + b²).
- The result is 5 units, rounded for display.
How to interpret your result
This relationship applies only to right-angled triangles.
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.
How do I use the pythagorean theorem calculator?
Enter first leg, second leg. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Hypotenuse = √(a² + b²).
What should I check before using the result?
This relationship applies only to right-angled triangles.
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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