How do I know which side is the hypotenuse?

The hypotenuse is always the side opposite the right angle (90 degree corner). It is always the longest side in a right triangle.

Can I use this to verify that a triangle is a right triangle?

Yes. If a^2 + b^2 = c^2 holds for the three given side lengths (with c as the longest), the triangle is a right triangle by the converse of the Pythagorean theorem.

What if I know both legs and need the hypotenuse?

Use the standard Pythagorean theorem: c = sqrt(a^2 + b^2). This calculator is specifically for finding a missing leg when the hypotenuse and one leg are known.

Pythagorean Leg Calculator

Find the missing leg of a right triangle when the hypotenuse and one leg are known. Uses the rearranged Pythagorean theorem to solve for leg b = sqrt(c^2 - a^2). Instant result.

By AbraCalc Editorial Team · Reviewed by AbraCalc Methodology Review · Last reviewed: 2026-06-25

Embed this tool on your site

<iframe src="https://abracalc.com/calculator/pythagorean-leg-calculator/embed.html" width="340" height="320" style="border:1px solid #e4e7ec;border-radius:12px" loading="lazy"></iframe>

How to use this tool

Enter hypotenuse c and known leg a in the fields above.
Results update instantly as you type — or click Calculate.
Read your missing leg b and the full breakdown beneath it.

Formula

b = sqrt(c^2 - a^2)

How it works

Rearrange the Pythagorean theorem: b = √(c² − a²). The hypotenuse must be longer than leg a.

Worked example

3-4-5 triangle (find 4)

c
=
5
,
a
=
3
.
b
=
s
q
r
t
(
2
5
-
9
)
=
s
q
r
t
(
1
6
)
=
4
.

Common mistakes to avoid

Entering the two legs instead of the hypotenuse and one leg — this calculator solves for a missing leg given the hypotenuse c and known leg a; entering two legs instead gives a meaningless result.
Getting the formula backwards and computing sqrt(a^2 + c^2) instead of sqrt(c^2 - a^2), giving a number larger than c which violates triangle geometry.
Entering a value for the known leg that is larger than the hypotenuse — since b = sqrt(c^2 - a^2), if a > c the argument is negative and there is no real solution.

Key terms

Frequently asked questions

How do I know which side is the hypotenuse?: The hypotenuse is always the side opposite the right angle (90 degree corner). It is always the longest side in a right triangle.
Can I use this to verify that a triangle is a right triangle?: Yes. If a^2 + b^2 = c^2 holds for the three given side lengths (with c as the longest), the triangle is a right triangle by the converse of the Pythagorean theorem.
What if I know both legs and need the hypotenuse?: Use the standard Pythagorean theorem: c = sqrt(a^2 + b^2). This calculator is specifically for finding a missing leg when the hypotenuse and one leg are known.