Pythagorean Theorem Calculator

Written byOleh Soloninupdated 5 October 2026

Solve for

Leg a

Leg b or hypotenuse

Result

Missing side5
Workingc = √(3² + 4²) = √25 = 5
Acute angles36.87° and 53.13°
Triangle area6
Perimeter12

a² + b² = c², solved in either direction

Find the hypotenuse from two legs, or a missing leg from one leg and the hypotenuse, plus the triangle's area and perimeter.

The theorem only holds for right-angled triangles, and it works both ways: square the two legs and add for the hypotenuse, or subtract to recover a missing leg.

It shows up far outside geometry class. Checking that a room is square, working out a screen's dimensions from its diagonal, or measuring a diagonal brace all come down to the same equation.

How to use

Choose what to find: the hypotenuse from two legs, or a leg from the hypotenuse and the other leg.
Enter the two known sides.
Read the missing side, the angles, the area and the perimeter of the triangle.

The triples worth memorising

The theorem is a² + b² = c², and in most triangles the answer is irrational. A handful of integer triples break that rule, and they recur constantly in exercises and in construction: 3-4-5, 5-12-13 and 8-15-17.

Builders use the first of them as a squaring tool. Measuring three units along one wall, four along the other and checking that the diagonal is exactly five proves the corner is square without any instrument.

Integer triples, worked out with this calculator.
Legs	Hypotenuse	Perimeter	Area
3 and 4	5	12	6
5 and 12	13	30	30
8 and 15	17	40	60

What this calculator shows

The missing side, whether that is the hypotenuse or a leg
The triangle's area and perimeter alongside it
A clear error when the hypotenuse is shorter than a leg, which cannot happen

What to keep in mind

Applies only to right-angled triangles — for any other triangle you need the law of cosines.
The hypotenuse is always the longest side, so it must exceed either leg.

FAQs

How do I find a leg rather than the hypotenuse?

Subtract instead of adding: leg = √(c² − a²). Switch the mode above and enter the known leg and the hypotenuse.

What is a Pythagorean triple?

A set of three whole numbers that satisfy the theorem, like 3-4-5, 5-12-13 or 8-15-17. They are handy precisely because no decimals are involved.

Does this work for any triangle?

No, only right-angled ones. Without a 90° angle you need the law of cosines, which adds a term involving the angle between the sides.

How do I get a TV's width from its diagonal?

Use the aspect ratio as the leg proportions. For 16:9, a 55-inch diagonal works out to roughly 48 inches wide and 27 tall.

What is the hypotenuse of a 3-4 right triangle?

Five: 3² + 4² = 25, and the square root of 25 is 5. It is the best known of the triples whose three sides are all whole numbers.

Which other triples come out whole?

5-12-13 and 8-15-17 are the next two. They are handy as checks: sides that form such a triple make a corner exactly square rather than approximately so.

Worked example

Checking a corner is square

Input: Legs of 3 and 4

Output: Hypotenuse 5

Note: The 3-4-5 triangle is the builder's trick: measure 3 along one wall, 4 along the other, and if the diagonal is exactly 5 the corner is a true right angle.

Useful links

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Pythagorean Theorem Calculator

Result

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