About Converse of the Pythagorean Theorem Calculator
The converse of the Pythagorean theorem says that if a² + b² = c² the triangle is right-angled, and extends to acute and obtuse triangles by inequality. This calculator applies it to your three sides with the working. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
It opens on 6, 7, 9. Here 36 + 49 = 85 is greater than 81, so every angle is below 90 degrees and the triangle is acute.
How to use Converse of the Pythagorean Theorem Calculator
- Choose what to find: the hypotenuse c, leg a, leg b, or check three sides.
- Type the known sides. Only the boxes you need are shown.
- Pick a length unit if you want it printed in the answer.
- Read the answer, the area, the perimeter and the two acute angles.
- Open the step-by-step working to see the squares, the subtraction or addition and the square root.
- In check mode, read the verdict and the triple note, for example whether the sides are a primitive triple.
Features
- Find the hypotenuse, either leg, or test three sides.
- Step-by-step working with KaTeX formulas.
- Pythagorean triple detection, with the primitive triple and Euclid’s m and n.
- Right, acute or obtuse verdict from the converse of the theorem.
- A diagram with a labelled square on each side.
- Area, perimeter and both acute angles of the triangle.
- Clear errors, for example when the hypotenuse is not the longest side.
The converse
Compare the sum of the two smaller squares with the largest.
a² + b² > c² acute
a² + b² = c² right
a² + b² < c² obtuseWorked examples
6, 7, 9 gives acute
36 + 49 = 85 > 81.
Privacy: how it works
- All the arithmetic runs in your browser tab. The sides you enter are not sent to Ulkaa or to anyone else, and there is nothing to sign in to.
Tips
- The hypotenuse is always the longest side. If you enter a leg longer than c, the calculator refuses and says so.
- To test a right angle on site, measure 3 units along one wall and 4 along the other. The diagonal should be 5.
- Keep all sides in the same unit. The calculator does not convert between units for you.
- A triple needs whole numbers. 1.5, 2, 2.5 satisfy the theorem but are not counted as an integer triple.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your values are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your values are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What does the converse say?
If the square of the longest side equals the sum of the other two squares, the triangle has a right angle.
Does the converse cover acute and obtuse triangles?
The inequality form does: a larger sum means an acute triangle and a smaller sum means an obtuse one.
More Pythagorean Theorem Calculator pages
- Pythagorean Theorem CalculatorSolve for any side of a right triangle, check whether three sides are a Pythagorean triple, and see the proof in a picture.
- Hypotenuse CalculatorEnter the two legs and get the hypotenuse.
- Missing Leg CalculatorEnter one leg and the hypotenuse to find the other leg.
- Find Leg b CalculatorEnter leg a and the hypotenuse to solve for leg b.
- 3-4-5 Triangle CalculatorSee why 3, 4 and 5 make a right angle and how to scale it.
- Pythagorean Triples CalculatorEnter three whole numbers to test them and see the primitive triple and Euclid’s m and n.
- Right Triangle CheckerEnter three sides in any order and see whether the triangle is right, acute or obtuse.