How do I find the hypotenuse?

Square the two shorter sides, add them, and take the square root. So with sides 3 and 4, the hypotenuse is the square root of 9 plus 16, which is 5. Enter the two sides and the calculator finds it.

Can I find a shorter side instead?

Yes. If you know the hypotenuse and one short side, subtract the square of the short side from the square of the hypotenuse and take the square root. The calculator solves for whichever side you leave blank.

Pythagorean Theorem Calculator

This calculator finds the missing side of a right angled triangle using the Pythagorean theorem, the rule that the square of the hypotenuse equals the sum of the squares of the other two sides, written as a² + b² = c². Enter any two of the three sides, side a, side b or the hypotenuse c, and leave the one you do not know blank. The calculator instantly returns the missing length, labelled as the hypotenuse, side a or side b depending on which field you left empty. Because the hypotenuse is always the longest side of a right triangle, sitting opposite the right angle, the tool flags an error if you try to solve a short side using a hypotenuse smaller than the side already entered, since that triangle cannot exist. You must fill in exactly two fields; leaving all three blank, or all three filled, will not produce a result. Results are shown to several decimal places, so the figure stays precise whether you are working in millimetres for joinery or metres for a building layout. It is useful for checking a corner is truly square, sizing a diagonal brace or ladder, working out a rafter or roof length, or any schoolwork or DIY job where you know two measurements and need the third.

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Side a

Side b

Hypotenuse c

c = 5

missing side

Fill in two sides and leave the third blank. The hypotenuse must be the largest value.

How it works

The theorem says a² + b² = c² for a right triangle. To find the hypotenuse, add the squares of the two short sides and take the square root. To find a short side, subtract the known short side squared from the hypotenuse squared and take the square root.

Worked example

With sides a equals 3 and b equals 4, the hypotenuse is the square root of 9 plus 16, which is the square root of 25, so c equals 5. This is the well known 3, 4, 5 triangle.

Related calculators

Right Angle Triangle Calculator: sides and angles.
Trigonometry Calculator: sine, cosine, tangent.
Roof Pitch Calculator: rafter length.
Square Root Calculator: roots of a number.

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