Pythagorean theorem calculator

Solve for

Leg a

Leg b

Quick triples

Tap a side to solve for it - the dashed side is the one being calculated.

Hypotenuse c: 5
Perimeter: 12
Area: 6
Angle opposite leg a: 36.87°
Angle opposite leg b: 53.13°

c = √(3² + 4²) = √25 = 5

Guide

Enter any two sides of a right triangle above and the calculator solves the third, redrawing the triangle to scale as you type. Tap a side of the diagram to solve for it, hit a quick-triple button to load a classic example, or toggle the squares view to see $a^2+b^2=c^2$ as areas with your own numbers.

Formula

$a^2 + b^2 = c^2$

You know	Formula for the missing side
Both legs	$c=\sqrt{a^2+b^2}$
Leg $b$ and hypotenuse	$a=\sqrt{c^2-b^2}$
Leg $a$ and hypotenuse	$b=\sqrt{c^2-a^2}$

The hypotenuse $c$ is always the longest side; enter a leg that matches or beats it and the calculator flags the error instead of returning an imaginary number.

Two worked examples, using the same steps the substitution line shows:

$c=\sqrt{3^2+4^2}=\sqrt{25}=5 \qquad a=\sqrt{13^2-5^2}=\sqrt{144}=12$

Video walkthrough

Video: Pythagorean theorem - finding the length of the hypotenuse (Math with Mr. J)

Scientific calculator - run the square and square-root steps by hand.
Stair calculator - the stringer is the hypotenuse of rise and run.
Tile calculator - diagonal layouts use the same room-diagonal math.

Sources and further reading

Wikipedia: Pythagorean theorem - statement, history, and proofs.
Wikipedia: Pythagorean triple - how triples like 3-4-5 are generated.
Cut the Knot: Pythagorean Theorem - over a hundred distinct proofs.

Pythagorean Theorem Calculator