Enter Triangle Data
Fractions, decimals, and scientific notation are accepted.
Calculation History
History stays inside this browser only.
| Select | Leg a | Leg b | Hypotenuse | Area | Unit |
|---|---|---|---|---|---|
| No saved calculations yet. | |||||
Formula Used
The Pythagorean theorem applies only to right triangles. It connects both legs with the longest side. The longest side always faces the right angle directly.
Solve for the hypotenuse using a square root. Solve a missing leg using square subtraction. Always select the positive geometric length answer only here.
How to Use
Select the mode matching your known measurements. Enter values and choose their measurement units. Then select precision and press the calculation button once.
Review the main result and detailed working. Check the diagram, angles, area, and perimeter. Copy or export results for later use very easily.
Example Data
| Leg a | Leg b | Hypotenuse | Area | Perimeter |
|---|---|---|---|---|
| 3 | 4 | 5 | 6 | 12 |
| 5 | 12 | 13 | 30 | 30 |
| 8 | 15 | 17 | 60 | 40 |
| 7 | 24 | 25 | 84 | 56 |
Frequently Asked Questions
What is a hypotenuse?
The hypotenuse is a right triangle's longest side. It always sits opposite the ninety-degree angle. No other triangle side can be called hypotenuse correctly.
Which formula finds the hypotenuse?
Use c equals square root of both squares. The two known values must be perpendicular legs. This theorem only works for right triangles correctly formed.
Can fractions be entered?
Yes, simple fractions like three over four work. Decimals and scientific notation also work correctly. Denominators cannot be zero in any valid input field.
Can different units be mixed?
Yes, each length has an independent unit selector. Values convert internally before calculations are performed. Select one preferred unit for every displayed result value.
How is a missing leg calculated?
Square the hypotenuse and known leg first. Subtract the known leg square from hypotenuse square. Then take the positive square root for final length.
Why must the hypotenuse be longest?
The hypotenuse lies opposite the triangle's largest angle. A right angle measures exactly ninety degrees. Therefore, its opposite side must always be the longest.
What does exact radical mean?
An exact radical keeps the square root unsimplified. Perfect-square factors are moved outside the radical. This avoids early rounding during detailed mathematical working steps.
How are the acute angles found?
The calculator uses inverse trigonometric functions on sides. Both acute angles always total ninety degrees. Their total with the right angle becomes exactly 180.
Can results be exported?
Results can be copied or downloaded as CSV. PDF export creates a printable calculation summary. Browser history can also compare saved triangle results later.